CA2307532A1 - Wireless location system - Google Patents

Abstract

A wireless location system uses a statistical approach, in which a probability distribution is trained that relates reliable observations of a signal parameter to a known measure of location. The probability distribution is then used to locate a mobile transmitter when addition observations are available. Various precise wireless location techniques may be used to train the distribution or may be used alone to locate the mobile transmitter. In one wireless location technique, a wireless location algorithm uses weighted observations, where the observations are weighted with received signal strength.

Description

TITLE OF THE INVENTION
Wireless Location System NAMES OF INVENTORS
Michel Fattouche Kevin Oler Richard Klukas Mable M. C. Chow to FIELD OF THE INVENTION
This invention relates to methods and apparatus for locating transmitters and receivers, particularly mobile transmitters or receivers.
CROSS-REFERENCE TO OTHER APPLICATIONS
This application claims the priority of provisional application no. 60/132,814 filed May 6, 1999.
BACKGROUND OF THE INVENTION
Location of mobile transmitters has become of importance with government 2o requirements that wireless system operators be able to locate mobile transmitters operating within their service area. The invention described herein is directed towards improved location of wireless transmitters.
The concept of estimating the angle of arrival (AOA) of radio transmissions by comparing signal strengths at two or more receiving antennas is well established.
For example, U.S. patent 3,824,595 describes a system in which two receive antennas are aligned at different angles. When these antennas receive a signal transmitted from a single source, the AOA can be estimated from the strength difference of arrival (SDOA) using an AOA-SDOA relationship.
In many circumstances, it may be difficult or impractical to adequately 3o characterize the SDOA-AOA relationship. This relationship may change due to

2 modification of the antennas or their position, or of objects which reflect, refract, block, or otherwise affect the transmission path from a transmitter to the receiving antennas. As well, this SDOA-AOA relationship may not be single-valued, rather, a statistical relationship may exist between SDOA and AOA.
AOA estimation is usually implemented with the objective of determining the angle at which the transmitter is located, with respect to a receiver, or Angle of Transmission (AOT). It is generally presumed that the angle of arrival (AOA) of the signal at the receiver is identical to the AOT, and hence the perceived AOA is a suitable estimate of the AOT. In some circumstances, this presumption does not hold.
to One difficulty is that a signal transmitted by a mobile phone may arrive at a cellsite along a direct path, and may arrive by one or more reflected paths.
The direct path arrival should always occur before the reflected arrival.
With reference to Figs. 18, 19, the AOA is estimated by measuring the signal strength at receiver A and receiver G, both equipped with directional antennas. At receiver A, the direct path is detected with lower energy than the reflected path because the antenna has lower gain in the direction of the direct path than in the direction of the reflected path. In the following, three representative cases for the signal detection are discussed. Many alternate cases, not presented here, are possible, involving blockage of the direct path, additional reflections, and failure to detect 2o various signal arrivals.
Case 1: Suppose that AOA is estimated using the direct signal arrivals, which are the earliest signal arrivals, at receiver A and receiver G. In this case, the estimated AOA will probably be close to the AOT.
Case 2: Suppose that the AOA is estimated using the reflected signal arrivals at receiver A and receiver G. In this case, the AOA, in the strict sense, will be estimated correctly (for the reflected path). However, this angle of arrival along a reflected path is different from the AOT, and a subsequent estimate of the position of the transmitter would have significant error.
Case 3: Suppose that the AOA is estimated using the strongest signal arrivals 3o at each antenna. In this case, the strongest signal arrival at antenna G
will be the

3 direct path. However, the strongest signal arrival selected at antenna A is the multipath reflection. In this case, the estimated AOA or AOT would likely have significant error.
Receivers may not be capable of distinguishing between multiple arrivals and the strongest signal arrival would likely be selected by each receiver, resulting in the scenario described above in Case 3.
One obvious option is to select the earliest detected signal arrival at each individual antenna for use in AOA estimation. As the direct path will always arrive earlier than reflected paths, this approach will allow the AOT to be selected from 1o multiple perceived AOAs in some cases. This method will fail in cases in which detection of the direct path arrival fails at any of the involved antennas.
A problem also arises in detecting transmissions from a mobile transmitter.
Cohernet or non-coherent detection may be utilized. The sensitivity of coherent detection is degraded by frequency offset in the received signal. This degradation i 5 may be mitigated by executing coherent detection at multiple frequency offsets, but this solution may require prohibitive computational or hardware resources.
Noncoherent detection is computationally efficient and can also be used to mitigate the effects of frequency offset, but noncoherent detection suffers from reduced sensitivity, compared to coherent detection.
2o While the statistical nature of the problem, and problems in detection, are difficulties encountered in location of mobile transmitters, there also exist problems related to precise location of mobile transmitters. For example, least squares methods are commonly used in the location of mobile transmitters where redundant observations of a signal parameter exist. A function that expresses closeness of 25 location estimates, which are calculated from the observations, to an assumed location is minimized. The function is frequently the sum of squares of differences of the location estimates from a solution. The method of least squares is iterative, with modification of the solution in each iteration. If the method converges, the solution that minimized the function at the point of convergence is taken as the solution.
30 Various problems may arise in least squares and similar iterative methods, as for

4 example bifucation of solutions, blunders causing grossly inaccurate location estimates and overall inaccuracy of the estimates.
SUMMARY OF THE INVENTION
This invention is intended, in its various aspects, to address the previously mentioned problems.
According to one aspect of the invention, there is provided a system for estimating the AOT and/or location of a wireless receiver. The acronym MLR
(maximum likelihood region estimation) is used to refer to the method of the 1 o invention. In one aspect of the invention, multiple signals are transmitted from antennas which have differing directional gains and/or orientations and received by a receiver. The receiver unit measures a signal parameter such as the signal strength of the different transmitted signals, and these signal parametereir measurements are used to estimate the position of the receiver unit. In another aspect of the invention, multiple receivers with different antenna gain patterns receive signals transmitted from a single transmitter.
Thus, MLR can be implemented using either forward or reverse link signal measurements, or even a combination of both. The preferred embodiment of this invention is the reverse link embodiment (Reverse Link MLR), applied to an IS-2o CDMA cellular network.
Thus, according to an aspect of the invention, there is provided a method of locating a transmitter with respect to a receiver, where the transmitter is in communication with the receiver, the method comprising the steps of:
a) storing, in a database, a first set of likelihood functions, each likelihood function comprising a series of values representing the probability that a measure of location corresponds to a value of a first signal parameter, the first signal parameter being a function of a measured characteristic of signals received at the receiver;
b) receiving signals at the receiver from the transmitter;
c) estimating a value of the first signal parameter from the received signals;
3o and d) locating the transmitter with respect to the receiver by determining a measure of location which, by reference to the likelihood functions for the first signal parameter, corresponds to the estimated value of the first signal parameter.
In one aspect of the invention, there is provided a signal parameter estimate,

5 for example an AOA estimate. This signal parameter estimate may be combined with other location information in order to produce an estimate of the location of the receiver in latitude and longitude, or an equivalent co-ordinate system. The other location information might be a circle defined by a round trip delay measurement, a hyperbola defined by a time difference of arrival measurement, a line defined by a l0 separate AOA measurement, or some combination of these.
According to an implementation of the invention, the receiver relays the signal strength measurements to a device which estimates the AOT from the measurements.
The device may be integrated into the receiver, lie in close proximity to the receiver, or otherwise. Preferably, every pair of signal strength measurements is used to compute an SDOA, which in turn is used to select an AOA likelihood distribution which expresses the likelihood of various AOTs, given the observed SDOA.
Multiple AOA likelihood distributions may be selected, and these will be combined to yield a single AOA likelihood distribution from which the most likely AOT is selected.
In the case where one of a pair of receivers detects the signal and the other 2o does not achieve a detection of sufficient confidence, a fixed SDOA may be assigned to that receiver pair, indicative of a much stronger SOA at the receiver which detected than the receiver which did not.
If the gain within the receiver is varied in order to maintain a desired signal levels at various intermediate stages, the variation in gain can be compensated for by scaling the digital representation of the received signal by the multiplicative inverse of the current receiver gain. In this manner, the effect of gain changes at any point in time is compensated for.
In this statistical approach, mufti-valued relationships between SDOA and AOA are effectively used to estimate the AOA. For example, suppose that an observed SDOA between a particular pair of antennas of 10 dB indicates that the

6 AOT is equally likely to be 10 degrees or 90 degrees. Suppose that another observed SDOA indicates that the AOT is likely to be at an angle between 60 and 120 degrees.
The two selected likelihood distributions are combined, yielding an AOA
likelihood distribution which indicates that the AOT is about 90 degrees.
Using this statistical approach, the AOT may be correctly estimated when multipath reflections result in an AOA different from the AOT, even if the direct path is obscured. These multipath arrivals may result in mufti-valued relationships between SDOA and AOA such as the example in the preceding paragraph. Suppose that an SDOA of about 10 dB is typically observed when a direct path arrives at an AOA and AOT of 10 degrees, and an SDOA of about 10 dB is also typically observed when the AOT is 90 degrees, in which case a reflected path is received.
When an SDOA of 10 dB is observed, the AOA likelihood distribution corresponding to an observed SDOA of 10 dB will be selected, which will indicate that the AOT is likely 10 degrees or 90 degrees. The correct AOT can be selected by incorporating other information, such as another observed SDOA.
In addition, there are provided novel techniques for measuring and applying the relationship between SDOA and AOA, as for example by involving an empirical two-dimensional SDOA-AOA likelihood distribution.
Another advantage of the statistical approach is that the training of the SDOA-2o AOA likelihood distributions can be implemented using transmissions which are already available in a cellular network. For example, in an IS95 CDMA network, the mobiles will regularly report SOA measurements of pilot signals which are suitable for use in MLR training or estimation.
In a further aspect of the invention, several positioning systems are provided for making high-confidence position estimates of mobiles for use in MLR
training.
Alternatively, in a further aspect of the invention, conventional techniques may be used where available for providing position estimates in the training process.
To assist in avoiding multipath problems, the strongest ray for each of the received signals may be selected. The relationship between typical reflected rays and 3o the AOT can be accounted for by the SDOA-AOA distribution, and hence the AOT

7 can still be accurately estimated, even though strong multipath components are included in the estimation. Alternatively, the earliest arrival may be used to attempt to avoid multipath problems.
IS-95 CDMA provides a separate pilot signal from each sector of a cellsite. In a further aspect of the invention, the distinct pilot signals can be used as the multiple received signals for MLR. The strengths of these signals can be measured by an IS-95 CDMA mobile phone.
In one aspect of the invention, MLR collects multiple observations of signal strength of arrival at known angles of arrival in order to create empirical likelihood distributions (analogous to theoretical probability distribution functions) of SDOA
and AOA, which are in turn used to predict the AOA for subsequent SDOA
observations.
In another aspect of the invention, non-detection or failure to detect a signal is incorporated into the AOA information. For example, suppose that mobiles at azimuths of 10° to 30° relative to a cellsite are highly likely to detect the Sector A
pilot signal and to not detect the Sector B pilot signal, and furthermore suppose that this situation is unlikely to occur at other azimuths. As the distribution for Sectors A
and B is trained over time, the elements having bins valued high SDOA bin at azimuths from 10° to 30° will have values much larger than other bins from 10° to 30° azimuth. Whenever a mobile at unknown azimuth reports detection of the Sector A pilot and not the Sector B pilot, the distribution will indicate a high probability that the mobile is at an azimuth between 10° and 30°.
One object of the invention is to estimate the location of a transmitting device.
Alternatively, MLR may be used to resolve multiple location solutions or validate a location estimate from TDOA, AOA or other means. As well, MLR can be used in order to select between a number of probable locations for a transmitting device.
Additional uses of MLR include generating wireless coverage maps, and wireless capacity and coverage analysis and planning.
The preferred embodiment utilizes SDOA observations taken from pairs of 3o receiver SOA observations, rather than using SOA observations directly. In the

8 preferred and other embodiments, the transmit power of the transmitter can vary considerably and is difficult to predict. The use of SDOA obviates the need to determine the transmitted power.
In a further aspect of the invention, within the network area, there are a number of receivers which report SOA measurements of received transmissions to the MLR Host. The Host maintains an SDOA likelihood distribution, a means for training the likelihood distribution, and a means for using the likelihood distribution to estimate location.
In a further aspect of the invention, a secondary search method is used to 1 o enhance detection of a transmission by receivers. When a receiver reports detection of a transmission to the Host, the Host may order other receivers to conduct an enhanced search for said transmission. All receivers which detect the transmission report the observed SOA to the Host.
In an aspect of the invention, the Host then attempts to determine the location of the transmitter by means other than MLR. If this is successful then the Host trains the MLR distribution by incrementing the distribution elements corresponding to the all pairings of observed SOAs, and the known location.
In an aspect of the invention, if the Host is unable to determine the location of the transmitter by means other than MLR, then the Host proceeds to estimate the location by MLR. The Host extracts from its overall MLR distribution one or more (x,y) likelihood distributions which correspond to the observed SDOAs. These distributions are combined into a single (x,y) likelihood distribution from which the location is estimated.
In an aspect of the invention, if one of a pair of receivers reported successful detection and the other did not, then an observed SDOA can still be computed in which the SOA of the non-detecting receiver is assumed to be a number less than the smallest realizable SOA. In order to suppress the processing of SDOAs which offer negligible improvement to training or estimation, the assignment of the very low SOA to a non-detecting receiver is suppressed if there has been no previous occurrence of detection of a transmission by both receivers.

9 The various aspects of this invention afford a number of advantages over the prior art. These advantages include the ability of the invention to self train using transmissions which are already present, without requiring dedicated equipment or effort. A related advantage is the capability of the invention to add to the training information over time in order to adapt to changing propagation conditions.
Another advantage of an aspect of this invention is the ability to incorporate observations from an arbitrary number of receivers in order to make the best estimate possible of transmitter location. When a receiver is added or removed from the set of receivers, the adaptive training can incorporate this change and maintain near-optimal 1o usage of current and new training data.
Yet another advantage of an aspect of this invention is the ability to use non-detection information to assist in estimating the location of a transmitter.
For example, if a transmission is detected by only one receiver, and training data indicates that a transmission detected by said receiver alone and not by the neighboring receivers has a high likelihood of originating from a particular area, then MLR will yield a point in said area as a location estimate for the transmitter.
Yet another advantage of an aspect of this invention is the capability to learn and recognize non single-valued path losses within region. For example, if transmissions from a particular region exhibit an SDOA which has a multimodal (2 or 2o more peaks) likelihood distribution, the invention will not distort the observations by transforming them to a single average path loss (as would a signal strength contour map) nor to transforming them to a single average path loss with a large variance. By storing the observed likelihood distribution, the invention preserves all higher-order statistics of the observed SDOAs.
Yet another advantage of an aspect of this invention is applicability (as Forward Link MLR and/or Reverse Link MLR) to many types of wireless systems and transmission formats. All, some, or none of the receivers may be co-located with other wireless infrastructure such as cellular towers. Many wireless systems already incorporate signals and measurements which are usable as receiver SOA
observations. For example, in IS-136 TDMA cellular and GSM cellular, the mobile units monitor and report on the SOA of control channel signals from multiple base station sectors. In AMPS cellular, base stations in the vicinity of a mobile monitor and report on the SOA of mobile transmissions.
Yet another advantage of an aspect of this invention is the ability to 5 incorporate multiple types of measurements into the training of and estimation using likelihood distributions. Phase difference of arrival information is as readily represented in lieu of or along with SDOA information, as is TDOA, and any other signal characteristic which can have any relation, directly or indirectly, to the positions and orientations of transmitter and receivers.
to Yet another advantage of an aspect of this invention is the ability to incorporate myriad forms of location relevant information. Position information provided by a network-based TDOA system or from GPS system can readily be incorporated as training data. If such a TDOA or GPS system, or an AOA system, is able to resolve the transmitter location to a locus (such as a hyperbola), this may be superimposed with an MLR likelihood distribution in order to select the location which best satisfies all available observations.
In further aspects of this invention, there are provided non-statistical methods of locating a mobile transmitter, and in particular a CDMA transmitter, with precision, which may be used to train the MLR method of locating a mobile 2o transmitter or may be used alone. These non-statistical methods are outlined in the following aspects of the invention.
According to a further aspect of the invention, there is provided a network-based Wireless Location System (WLS) whereby existing CDMA CTs can be located passively without modification to the CT or to the cellular antenna infrastructure.
According to a further aspect of the invention, there is provided a method of estimating the static and kinematic positional information of a CDMA CT which transmits a signal, s(t) by monitoring the corresponding received signal r;,k(t) at the k'n antenna of the itn MS.
According to a further aspect of the invention, there is provided a method of 3o correcting for the sources of error that affect the different location technologies for an IS-95 CT in a unique and novel way, including frequency errors, clock offsets, overall group delays, multipath and interference, while minimizing the effect of noise and reducing HDOP (Horizontal Dilution of Precision).
According to a further aspect of the invention, there is provided a method of locating a powered-up IS-95 CT in a passive manner by using the signal transmitted by the CT over the Access channel or the Reverse Traffic channel. In order for the CT
to be truly passive, it is possible to turn its ringer off, and request the BS
to page it (e.g. by calling the CT from the HOST or by other means).
According to a further aspect of the invention, there is disclosed the use of an i o Access message for locating the CT by processing the signal representation of the message by the MS or associated equipment, without transferring the complete signal representation of the received Access message to the host.
According to a further aspect of the invention, there is provided a method of locating a powered-up IS-95 CT by using the signal transmitted by the CT over the 15 Reverse Traffic channel without incurring air time charges and while the CT
remains in the "waiting for answer" mode.
According to a further aspect of the invention, there is provided a method of locating an IS-95 CT by estimating the Phase of Arrival (POA) of existing or generated tones either over the Access channel or the Reverse Traffic channel.
The 2o phases can be extracted using SR algorithms in order to reduce the effect of multipath.
Preferably, the overall group delay variations through the receiver at each MS
caused by the effect of temperature, interference and aging in the receiver are reduced by replacing some analog RF components by digital components. Preferably, the 25 effect of Local Oscillator (LO) drift and clock offsets is reduced by using the Global Positioning System (GPS) as a source for a common reference.
According to a further aspect of the invention, there is provided a method of locating a 911 Cellular caller and to transfer its positional information to the appropriate PSAP during "unanswered conversation" mode.

According to a further aspect of the invention, there is provided a method of locating a mobile transmitter in which the observations of the received signal at a receiver are weighted in the wireless location algorithm, such as an iterative minimizing algorithm, according to the received signal strength of the received signals. It is desirable to minimize HDOP by allowing more MSs to tune to the same CT while at the same time reducing the effect of noise and multipath by solving for the position of the CT using Least Squares weighted by RSSI.
According to a further aspect of the invention, there is provided a method of locating a mobile transmitter using an iterative algorithm in which misclosures and to standardized residuals are used to flag the observations that might have a blunder.
According to a further aspect of the invention, there is provided Chaffee's method or Location On the Conic Axis (LOCA) is used to detect solution bifurcation in an iterative minimizing function. LOCA and/or Plane Intersection may be used to provide an initial position for the iterative minimizing function, such as by using Least Squares.
TDOA observations, hybrid TDOA observations and AOA observations may be used to locate the CT. TDOA information from two MSs or the AOA from several antennas at the same MS may be used to resolve the AOA ambiguity at such an MS.
Range information from two MSs or the AOA from several antennas at the same MS
2o may be used to resolve the AOA ambiguity at such an MS.
In hybrid TDOA, a transmitter is located by TDOA in which TDOA observations are calculated by subtracting the TOA of the received signal at a selected one the receiving sites from the TOA at all other receiving sites.
In a further aspect of the invention, grouped coherent detection of a mobile transmission is used to achieve near coherent detection accuracy, with less complexity. In a further aspect of the invention, an improved method of noncoherent detection is proposed in which the subcorrelations are low pass filtered (with a cutoff frequency of approximately the largest expected doppler frequency) before combining. Alternatively, the subcorrelations are passed through a set of filter banks, 3o whose passbands collectively cover the range of expected doppler frequencies.

Computer readable media containing instructions to a computer or signal processor for carrying out the methods (algorithms) described here are also claimed, as well as apparatus such as a computer or signal processor programmed or hardwired to carry out the methods described here.
These and other aspects of the invention are described in the detailed description of the invention and claimed in the claims that follow.
BRIEF DESCRIPTION OF THE DRAWINGS
There will now be described preferred embodiments of the invention, with 1 o reference to the drawings, by way of illustration only and not with the intention of limiting the scope of the invention, in which like numerals denote like elements and in which:
Fig. 1 illustrates transmission by a CT (101) of a signal s(t) (103)to a base station.
Fig. 2 illustrates the transmission of the signal s(t) by the CT at Time 'io' and its reception by the kth antenna at the ith Monitoring Site (MS) (201 ) at Time of Arrival:
Fig. 3 illustrates a three MS system which receives a signal transmitted from a Cellular Telephone (CT) located at (x,y).
2o Figure 4 illustrates the Direction of Travel (DOT) 'cp' (401) relative to Northing (in a clockwise manner from Northing) and the speed v (402) of the CT
(404) of coordinates (x,y) which together represent the velocity v of the CT.
Fig. 5 illustrates a possible Angle of Arrival (AOA) likelihood function, given a particular Phase of Arrival (POA) difference between two antennas. The graph has two peaks, at 30° and 150°. This indicates that when a certain difference in phase of arrival of a CT transmission is observed at the two antennas, it is likely that the angle of arrival of the CT transmission at the antennas is either 30° or 150°.
Figure 6 illustrates the two intersecting loci of Position for the two-dimensional (horizontal) coordinates (x,y) of the CT (603) based on TDOA2u>k,m (601) arid TDOA3,~,n,m (602). In other words, it is possible to solve for (x,y) as the intersection between the two trajectories obtained using three Times of Arrival (TOAs) (after choosing the correct side of each hyperbola). In order to solve for (x,y,z) we require four TOAs.
Figure 7 illustrates a Second Stage of a wireless location system where the itn MS down-loads its positional information to a central processor which we refer to as the Host (701). The Host uses all the positional information to estimate the coordinates (x,y) of the CT and its speed v and DOT cp. In the discussion of Fig. 7, it is assumed that each MS has two antennas placed on the same horizontal plane.
Figure 8 illustrates the description of an exemplary design, referred to here as Design I, for the IF-sampling receiver.
Figures 9a, 9b, 9c and 9d illustrate a flow diagram for a TDOA positioning strategy used for reliable position measurement. The positioning strategy consists of a number of algorithms (Least Squares, Location On the Conic Axis (LOCA), Plane Intersection) and numerous decisions. Given a set of observations, there are 4 possible outcomes: two LS position solutions (908), two LOCA position solutions (909), one LS position solution (923, 936), and no position solution (927).
Fig. 10 illustrates a possible AOA likelihood function, given a particular Strength of Arrival (SOA) difference between two antennas. The graph has a wide peak, from approximately 0° to 45°. This indicates that when a certain difference in 2o SOA of a CT transmission is observed at the two antennas, it is likely that the angle of arrival of the CT transmission at the antennas is between 0° and 45°.
Fig. 11 illustrates a second possible AOA likelihood function.
Fig. 12 illustrates one implementation of an algorithm for Maximum Likelihood Angle of Arrival (ML-AOA) estimation.
Figs. 13 and 13A are flow diagrams illustrating implementation of an algorithm for detecting CT transmissions.
Fig. 14 illustrates an exemplary embodiment of a monitoring site and Host.
Figure 15 illustrates a 2-D representation of a MS with three antennas positioned on the corners of an equilateral triangle. Figure 15 assumes, without loss of generality, that the three antennas belong to the same horizontal plane as well as a CT. Each antenna receives a signal transmitted from the CT. Such a structure is typical of a three sector CDMA cellular and PCS infrastructure.
Figure 16a plots the PDOA (Phase Difference of Arrival) between antennas 1 and 2, shown in Figure 15, with respect to the AOA of the signal transmitted by the 5 CT with respect to the line formed by joining antennae to antennae, clockwise.
Figure 16b plots the PDOA between antennae and antenna3, shown in Figure 15, with respect to the AOA of the signal transmitted by the CT with respect to the line formed by joining antennas to antennae, clockwise.
Figure 16c plots the PDOA between antenna3 and antennas, shown in Figure

10 15, with respect to the AOA of the signal transmitted by the CT with respect to the line formed by joining antennas to antennae, clockwise.
Figures 16a, b and c assume, without loss of generality, that the baseline between any two antennas (shown as d;,s,e in Figure 15) is 2/3 meters and that the wavelength of the signal transmitted from the CT corresponds to a carrier frequency 15 of 1.9GHz. Figures 16a, b and c also assume that the CT is far from all antennas with respect to their baseline, d;,,,e.
Figure 17 illustrates a 2-D (vertical) representation of a MS with two antennas separated in the z-axis, i.e. of different elevation. Figure 17 assumes, without loss of generality, that the two antennas are placed on the same vertical axis and that the CT
2o is placed on the same vertical plane as the vertical axis. Each antenna receives a signal transmitted from a Cellular Telephone (CT) with a given elevation angle. The elevation angle between a CT and a given antenna is defined as the angle between the horizontal plane of the CT and the line joining the CT and the antenna. Such a structure is typical of a vertical diversity cellular or PCS system.
Fig. 18 shows typical orientations of sectors at a sectorized cellsite, and illustrates the angle of arrival. Note that although the receiver will in theory receiver signals from all three transmitters, if the transmission antenna patterns are typical of a sectorized cellsite (as in Fig. 17), transmitter A will be received at a lower strength than transmitter G, and transmitter B will be received at an even lower strength, 3o possibly so low that the receiver cannot detect it.

Fig. 19 shows typical antenna gain patterns for cellsite with three sectors.
Figs. 20a and 24b shows the relationships between the strength of the pilot signals of sectors A and B, and the angle of arrival. Note that the relationship shown is idealized, in that actual field measurements would exhibit significant variation in strength versus time and versus angle.
Fig. 21 shows the relationship between the difference in the strengths of pilots A and B, as measured by the mobile, versus the angle of arrival. The relationship shown in idealized.
Fig. 22 illustrates multiple signal arrivals arising from the direct path and a l0 multipath reflection.
Fig. 23 shows a correlator output which might be generated as a result of multiple signal arrivals.
Figs. 24a, 24b and 24c illustrate the effect of combining two AOA likelihood distributions to produce a single, composite likelihood distribution.
Fig. 25 illustrates the structure and interpretation of a an SDOA-AOA
distribution, implemented as a two-dimensional array of numbers, which represents a two-dimensional likelihood distribution of strength difference of arrival and angle of arrival.
Fig. 26 shows a single element of an SDOA-AOA distribution. Such an 2o element corresponds to the following defining parameters:
N SDOA bins = 41, low SDOA bin = -20 dB, high SDOA bin = 20 dB, and N AOA bins = 361.
The bin values for SDOA and AOA, 2 dB and 56°, and the region associated with the distribution element, are shown. As well, two SDOA-AOA points are shown, one within the region and one outside of the region of the element.
Fig. 27 illustrates the azimuth initialization of the SDOA-AOA distribution 3o for a pair of antennas having azimuths at 120° and 240°. Note that the plot should be interpreted as being periodic with respect to angle of arrival, so that the plot shows two line segments: one labeled "front side", and another labeled "back side".
The two parts shown labeled "back side" are parts of the same line segment.
Fig. 28 illustrates an embodiment of the overall procedure for ML-AOA
operation including initialization, training, and estimation.
Fig. 29 illustrates SDOA values for a pair of receivers. Each number shown indicates the SDOA value that might be observed when the transmitter is at the position of the number, and the SDOA is computed as the difference (SOA of receiver 1 ) - (SOA of receiver 2).
to Fig. 30 shows the main physical elements of an exemplary embodiment of the MLR system. A number of receivers detected a transmission from the transmitter and report measurements to the MLR Host.
Fig. 31 illustrates the secondary search process. The secondary search focuses effort on searching for a transmission detected by the primary search.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In this patent document, the word "comprising" is used in its non-limiting sense to mean that items following the word in the sentence are included and that items not specifically mentioned are not necessarily excluded. The use of the indefinite article "a"
2o in the claims before an element means that one of the elements is specified, but does not specifically exclude others of the elements being present, unless the context clearly requires that there be one and only one of the elements. In the detailed description of the invention, there are several aspects of the invention disclosed. Wherever "the intention of the invention" or "intention of the patent" is referred to, this means that the following item is an invention of an aspect of one of the inventions and not necessarily the intention of all the inventions or the intention of all aspects on one or more inventions.
Further, where an invention is said to "consist of something in the detailed description, this particular aspect of the invention incorporates the mentioned steps or their equivalents, but this is not intended to limit a claim to the same feature.
Where an 3o element or step is said to be crucial (or like words), this refers to the element or step being crucial to the particular aspect of the invention being discussed, and may not be crucial to other aspects of the invention. Where the invention is said to "intend" to do something for a purpose, then this means that, for the particular purpose stated, it is preferred to do that thing in the carrying out of the invention. A "bin" is a counting mechanism, such as an element in a memory device, with a value or count that may be incremented under instruction from a microprocessor. A wireless location algorithm is any algorithm that may be used to locate a wireless transmitter, and includes the algorithms described in this patent document.
The following definitions take precedence over definitions for the same terms that can be found in the open literature.
Cellular Telephone (CT): is a device, which can be portable or fixed, that can consist of a transmitter alone, or both a transmitter and a receiver. It can be a regular Cellular Telephone (CT), a PCS (Personal Communication Systems) telephone, a cordless telephone, a Personal Digital Assistant (PDA), a GPS receiver, or a combination thereof. It can be a radio tag or a wireless telephone that does not contain the audio portion of the telephone. It can also be a transmitter that transmits periodically over a given channel, or a receiver that receives Radio signals, or both.
Mobile Receiver (MR): is a device, which can be portable or fixed, that can consist of a receiver alone or both a receiver and a transmitter. It can be a regular Cellular 2o Telephone (CT), a PCS (Personal Communication Systems) telephone, a cordless telephone, a Personal Digital Assistant (PDA), a GPS receiver, or a combination thereof. It can be a radio tag or a wireless telephone that does not contain the audio portion of the telephone. It can also be a transmitter that transmits periodically over a given channel, or a receiver that receives Radio signals, or both.
Base Station (BS): is a device of known location with respect to other BSs at a given time. A BS can be portable or fixed. It can consist of a transmitter alone or a receiver or both. It can be a regular cellular Base Station, a regular satellite transceiver, a PCS
Base Station, an ESMR Base Station, a Paging Base Station or any other type of transmitter/transceiver combination. Most cellular/PCS BSs use some form of diversity antennas: vertical (i.e. the antennas are separated vertically), horizontal (i.e.
the antennas are separated horizontally) or both.
Cell: is a geographical area serviced by a cellular Base Station (BS).
Sectorized cell: is a cell that is made of multiple spatially differentiated sectors. Each sector can be considered as an independent cell to be serviced by an independent cellular BS. However, sectors in a cell are usually serviced by the same cellular BS in order to minimize cost and complexity. We refer to such a BS as a sectorized BS.
Antennas belonging to a sectorized BS are usually, but not necessarily, placed on the l0 same horizontal plane.
Sector antennas: are directional cellular antennas which are used by a BS to transmit and receive over spatially differentiated regions. Each sector has a dedicated antenna (or set of antennas if diversity is applied).
Diversity Antennas: are cellular antennas which provide redundant reverse-link signals to a BS. Diversity can be accomplished by means including multiple antennas separated horizontally or vertically, or with different polarizations. In this patent, we use horizontally separated diversity antennas as a mean to estimate the horizontal Angle Of Arrival (AOA) of the received radio signal at a MS. When the diversity antennas are vertically separated, either the elevation AOA is estimated, or the received signals from all antennas at a given MS is combined using: selection combining, maximal ratio combining, co-phasing combining, equal gain combining, or other methods of combining.
Estimating the horizontal AOA of the received radio signal at a MS can be used to estimate the range between the CT and the MS as long as the altitude of the CT
is known.
Monitoring Site (MS): is a receiver that has the ability to monitor all four channels:
Access, Paging, Forward Traffic, and Reverse Traffic. It is appropriate to collocate the MS with the BS in order to take advantage of the existing cellular infrastructure.
The patent however does not require such a collocation since the MS performs all reception tasks independent of a BS. In fact, the MSs can be mobile as long as their estimated location is known in time.
Host: is a central processor to process all positional information that are received from the MSs and to transmit monitoring orders to all MSs. The host can also be 5 responsible for location services such as fleet management, location sensitive billing, etc. The Host can also be responsible for software/firmware upgradeslre-configurations of the MSs.
Access Channel: is the channel to be used by the CT to transmit control signals to the BS such as call originations, registrations, etc. This channel is analogous to the l0 Reverse Control Channel in AMPS.
Paying Channel: is the channel used by the BS to transmit control messages to the CT such as paging the CT, acknowledging a registration, etc.
Reverse Traffic Channel is the channel assigned by the BS to the CT, which the CT
uses to transmit voice data, messages, and other data to the BS, during a CDMA
call.
~5 Forward Traffic Channel: is the channel assigned by the BS to the CT on which the BS will transmit voice data, messages, or other data to the CT during a CDMA
call.
Pilot Channel: is the channel on which the BS broadcasts the pilot signal, which is used by the CT for detection of the BS, synchronization, and RSSI estimation.
Sync Channel: is the channel on which the BS broadcasts the Synchronization 20 Message, which is used by the CT for synchronization of its internal timing and states, and for configuration of some network-dependent parameters.
Ori~inations: are defined as calls initiated by a CT.
Pages: are initiated by a BS to a CT.
Reverse Traffic Mode: A step in the establishment of a call is for the CT to enter the Reverse Traffic Mode, in which the CT begins to transmit on the Reverse Traffic channel. The mobile enters this mode after the mobile has acquired (begun to receive) transmissions on the Forward Traffic channel. This is analogous to the Reverse voice channel in AMPS.
Unanswered conversation mode: is defined as an origination that is in conversation mode that has not been answered yet by the called party.

Answered conversation mode: is defined as an origination that is in conversation mode that has been answered by the called party.
Super-Resolution (SR) Algorithm: is an operation that transforms a time domain signal, s(t), to a frequency domain signal, S(f), in such a way that the frequency domain signal, S(fj, has a better resolution than the resolution offered by the Fourier transform, i.e. S(fj has a better resolution than the Fourier transform F{s(t)}, of s(t).
Vice-versa, a SR algorithm transforms a frequency domain signal, S(f), to a time domain signal, s(t), with a better resolution than the resolution offered by the inverse Fourier transform, i.e. s(t) has a better resolution than the inverse Fourier transform 1o F-I {S(fJ}, of S(fj). Examples of SR algorithms are well known in the literature and include: MUSIC/Root MUSIC, ESPRIT, Auto Regressive Moving Average, Minimum Variance, MUSIC using Higher Order Statistics, ESPRIT using Higher Order Statistics, Auto Regressive Moving Average using Higher Order Statistics, or Minimum Variance using Higher Order Statistics.
Freauency-domain Rayleigh Resolution: is the frequency-domain resolution offered by the Fourier transform.
Time-domain Raylei~h Resolution: is the time-domain resolution offered by the inverse Fourier transform.
Inverse SR algorithm: is an algorithm which processes a time domain signal in 2o order to improve its time-domain resolution over the conventional time-domain Rayleigh resolution. A preferred embodiment of the inverse SR algorithm comprises a conventional time domain correlator, a time domain window, a Fourier Transform, a frequency domain window, a frequency domain equalizer, and a processor which performs a SR algorithm in order to resolve the TOAs in the received signal at a given MR. Alternatively, an inverse SR algorithm can process a frequency domain signal in order to improve its frequency-domain resolution over the conventional frequency-domain Rayleigh resolution. In this case, a preferred embodiment of the inverse SR algorithm comprises a frequency domain correlator, a frequency domain window, an inverse Fourier Transform, a time domain window, a time domain equalizer, and a processor which performs a SR algorithm in order to resolve the FOAs in the received signal at a given MR.
Fourier Transform-Based Filters: are filters that: Fourier Transform the time domain signal, then window the transformed signal over a given band, and Inverse Fourier Transform the windowed signal.
Effective Bandwidth: is the bandwidth over which the received radio signal at a given MS has been observed during a given observation interval.
Passive Location of a CT: is the location of a CT without its bearer's knowledge.
Surface Wave Propagation: is the propagation of the Radio waves that follow the 1 o surface of the earth. Such a propagation might have a different velocity than free-space propagation.
Elevation An~le: between a CT and a given antenna is defined as the angle between the horizontal plane of the CT and the line joining the CT to the antenna.
An~le of Arrival (AOA) - the angle or direction from which a transmission arrives at ~ 5 a receiver. Except where otherwise stated in this document, the AOA and AOT are assumed to be identical.
AnEle of Transmitter (AOT) - the angle or direction at which a transmitter or group of transmitters is located with respect to a receiver. Note that the AOA and AOT are identical in many, but not all cases.
20 Cellsite - A location of multiple wireless transmitters. In the preferred embodiment of this invention, the transmitters consist of sectors of a cellsite in a cellular communications network, however, this invention may be implemented using any type of transmitters.
Azimuth - a representation of angle measured in degrees clockwise from due North.
25 Transmitter - A device which transmits wireless signals, such as a cellular phone.
This may include elements such as a power supply, electronic oscillator circuits, modulation circuits, amplifiers, and one or more antennas. A transmitter may include an integrated receiver, as is the case with a cellular phone, or it may be a transmit-only device.

Network Area - A general region in which there are receivers, and within which the locations of certain transmitters can be estimated by MLR. The network area could be the interior of a building, a city, a continent, or a region of space near or far from the surface of the Earth.
Receiver - A device which is capable of receiving transmissions from one or more transmitters, and of measuring the received signal strength or strength of arrival (SOA) of the signal. A receiver typically consists an antenna, a radio frequency downconverter, and signal processing circuitry.
Universal Transverse Mercator (UTM) Grid System - A co-ordinate system for 1o identifying locations on the surface of the Earth. There are 60 UTM zones defined by lines of longitude at 3 degree intervals. A position within a zone is defined by the distance north from the Equator ("northing"), and the distance east from a north-south reference line ("easting").
Strength of Arrival (SOA) - The amplitude or power of a signal arriving at a receiver.
Strength Difference of Arrival (SDOA) - The difference between the strengths of arrival of one signal at two difference receivers, or the difference between the strengths of arrival of two signals at one receiver.
dBm - A logarithmic measure of signal power, obtained by multiplying the logarithm of power in milliwatts by 10.
The principles of locating a mobile transmitter, eg a CT, using AOA are illustrated in Figs. 1-4.
Fig. 1 illustrates transmission by a CT (101) of a signal s(t) (103). When the CT is IS95-based, it transmits a signal either over the Access channel or over the Reverse Traffic channel. In either case, the transmission is intended for a specific Base Station (BS) (102). Fig. 1 assumes that the BS (102) has two antennas that belong to the same horizontal plane.
Fig. 2 illustrates the transmission of the signal s(t) by the CT at Time 'io' and its reception by the k'~' antenna at the i'h Monitoring Site (MS) (201 ) at Time of 3o Arrival: i;,k. In order to solve for the horizontal coordinates (x,y) of the CT (202), a minimum of three MSs (with a minimum of one antenna per MS) are required using TDOA positioning, or a minimum of two MSs (with a minimum of two horizontally spaced antennas per MS) using Angle Of Arrival (AOA) positioning. In either case, it is possible to take advantage of the cellular infrastructure by locating the MSs at the BS sites, thereby using their:
1. directional antennas (either diversity or sectored) with good Rf coverage and appropriate RF front end, 2. high speed link to the Mobile Switching Center (MSC) using either a T1-Link or a wired telephone link (Plain Old Telephones (POTS)), and 3. convenient weather-proof temperature-regulated housing with regulated power supply.
It is however possible to place the MSs at locations that are independent from the cellular BSs since the method of the invention does not require any assistance from the BSs or from the MSC. In Fig. 2, each MS (201) has two antennas.
Fig. 3 illustrates a three MS system which receives a signal transmitted from a Cellular Telephone (CT) located at (x,y). In Fig. 3 each MS has two antennas placed essentially on the same horizontal plane. In Fig. 3, when the CT is far from each MS
with respect to the baseline between the two antennas at each MS, the received wavefront is planar i.e. y;,~ - y;,2 - Y;, where:
2o ~ y~,i is the Angle Of Arrival (AOA), at the first antenna of the i'h MS, ~ Y;,2 is the AOA at the second antenna of the i'h MS, and ~ y; is defined as the angle formed between:
1. the line joining the CT (301) and the i'h MS (which we refer to as line,;) and, 2. the line joining the two antennas at the i'h MS (which we refer to as line2,;);
in a clockwise manner from lines,; to line2,; , where i=1, 2, 3. In Fig. 3, liner,; and line2,; , for i=1, 2, 3, are all on the same horizontal plane, when the elevation of each antenna is much smaller than the distance between the antenna and the CT.

Fig. 4 illustrates the Direction of Travel (DOT) 'cp' (401 ) relative to Northing (in a clockwise manner from Northing) and the speed v (402) of the CT (404) of coordinates (x,y) which together represent the velocity v of the CT. The kt"
antenna at the it" MS (403) of coordinates (x;,k,y;,k,z;,k) receives the signal r;,k(t), processes it 5 and transfers the positional information regarding the CT to a central processor, where i=l, 2, 3. In Fig. 4, each MS may have two antennas placed on the same horizontal plane and the CT and all antennas are also placed on effectively the same horizontal plane.
Figure 5 illustrates the two-dimensional (horizontal) Locus of Position (501 ) for TDOA2,~,k,", which is defined as TDOA2,l,k,m = ~2,k - ~l,m - ~~2,k - To ~ - ~~I,m - ~o ~X2,k - X~2 + \Y2,k - 5'~2 - C ~Xl,m - X~2 + ~yl,m - 5'~2 (1) where c is the speed of propagation, ~Xt,m ~ Y~,m ~ Zl,m ~ are the coordinates of the mtn 15 antenna at MS1, ~X2,k ~ y2,k ~ Z2,k ~ are the coordinates of the k'n antenna at MS2~ and (x,y) are the coordinates of the CT (502). This is achieved using Time Difference of Arrival (TDOA)-based Hyperbolic Multi-lateration (as shown in Turin, G. L. et al., "A Statistical Model of Urban Multipath Propagation," IEEE Transactions on Vehicular Technology, Vol. VT-21, No. l, February 1972, and as shown in Smith, 2o J.O. et al., "Closed-Form Least-Squares Source Location Estimation from Range-Difference Measurements," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, No. 12, December, 1987). In the case where the three-dimensional coordinates of the CT are required, we have to solve for (x,y,z) using TDOA2 l,k,m - ~2,k - ~l,m - ~~2,k - ~o ~ ~21,m - ~o ~X2,k - X~2 + lY2,k - y~2 + ~Z2,k - Z~2 ~Xl,m - X~2 + \Yl,m Y)2 -+' (Zl,m - Z)2 (2) Figure 8 illustrates the description of Design I (discussed below) for an exemplary IF-sampling receiver for use in locating a mobile transmitter with precision, and which may then be used in training the MLR process. The received RF
signal r;,k(t) at the kt" antenna of the i'" MS is initially filtered by an RF
Band Pass Filter (BPF) (802), amplified by an RF amplifier (803), and down-converted to the Intermediate Frequency (IF) by a Mixer (805). The IF signal is amplified by an IF
Amplifier (806), filtered by a Band Pass Filter (807), amplified by an IF
Amplifier (808) to form the IF output. The IF output is sampled by an A/D (809) and then processed by a Digital Signal Processor (810). A Frequency Reference signal (811 ) is provided to the RF synthesizer. A preferred source for the reference signal is one that is common to all MSs such as a Global Positioning Systems (GPS) signal, or one that is derived therefrom.
In Fig. 10, the graph has two peaks, at 30° and 150°. This indicates that when a certain difference in phase of arrival of a CT transmission is observed at the two antennas, it is likely that the angle of arrival of the CT transmission at the antennas is either 30° or 150°.
Fig. 11 illustrates a possible AOA likelihood function, given a particular 2o Strength of Arrival (SOA) difference between two antennas. The graph has a wide peak, from approximately 0° to 45°. This indicates that when a certain difference in SOA of a CT transmission is observed at the two antennas, it is likely that the angle of arrival of the CT transmission at the antennas is between 0° and 45°.
Figure 12 illustrates one implementation of an algorithm for Maximum Likelihood Angle of Arrival (ML-AOA) estimation. The algorithm is initiated when a MS is apprised of a CT transmission (1201). This may be accomplished by the MS
itself detecting the CT transmission, or by the MS being notified of the CT
transmission. In the latter case, it is preferable that the MS also be given an approximate TOA of the transmission and an information on the content of the transmission, to aid the MS in detecting the CT transmission.
The MS attempts to detect the CT transmission on some or all of the receive paths available to the MS associated with different antennas or antenna elements (1202). For each instance of the received transmission that the MS detects, the MS
measures the SOA and/or POA (1203). For each pair of SOAs, the MS retrieves a likelihood function for AOA conditional on a function (such as ratio) of the observed SOAs. For each pair of POAs, the MS retrieves a likelihood function for AOA
conditional on a function (such as ratio) of the observed POAs (1204).
The MS combines the likelihood functions for AOA by taking their product (1205). The ordinate of the maximum of the resulting likelihood function is taken as the AOA estimate (1206, 1208). Information from other sources (1207), such as AOA likelihood functions from other MSs, may be combined with the other likelihood functions.
Figure 13 illustrates an implementation of an algorithm for detecting CT
transmissions. A correlation/combining function z~'t, F~ is evaluated at trial values of ~ and F. The ordinates (~, F~ of the maximum of z(~, F~ are taken as initial estimates of the TOA and Frequency of Arrival (FOA), respectively. A threshold for this maximum value may be used to determine whether or not a transmission has been detected.
Figure 14 illustrates a possible embodiment of a MS and Host. The antenna (1403) and RF Downconverter (1405) receive forward link transmissions (1401).
The DSP Board (1407) converts the downconverted RF signal to digital signals and processes them to detect BS transmissions, measure their TOA, POA, SOA, and FOA, and decode messages transmitted by the BS.
The antenna (1404) and RF Downconverter (1406) receive reverse link 3o transmissions (1402). The DSP Board (1408) converts the downconverted RF
signal to digital signals and processes them to detect CT transmissions, measure their TOA, POA, SOA, and FOA, and decode messages transmitted by the CT.
A Communication Controller ( 1409) interfaces between DSP Boards ( 1407, 1408) and some interface ( 1410) to the Host ( 1411 ). 1401 - 1409 comprise a MS.
The Host comprises one or more computers that receive information from MSs and estimate the location, speed, and DOT of a CT. Although not explicitly shown on Figure 14, the Host also sends information and orders to the MSs via the interface.

In a WLS, many factors affect the system performance, RF shadowing and flat fading, frequency offsets (including LOs drift and Doppler Shifts), clock errors, time delays, noise, multipath (selective fading), interference; geographical geometry of the MSs relative to the intended CT, and power control (of the CT's transmit power) Each factor degrades the estimated location of the CT depending on the technology employed for extracting the independent equations required for location.
RF Transmission: More specifically, the Low Pass (LP) equivalent transmitted signal, s (t), can be modeled as S (t) = e-.12'~(f~ +ofo )TO e.l(Z~ofoc+~o ) p(t - 'Co ) (3) and the RF transmitted signal, s(t), (see Figure 1 ) can be expressed as s(t) = Re{ e~2~'f°t s (t) } (4) where ~ Re { . } denotes a real part operation;
~ f~ is the nominal carrier frequency, ~ Ofo is the frequency offset from f~ (usually unknown to the CT or BS since it is essentially an error in the frequency reference of the CT or BS), io is the time of transmission (also unknown to the MSs), ~ ~o is the phase offset of the transmitted carrier frequency f~ + Ofo (also unknown to the MSs), ~ j=~ and ~ p(t) is a band-limited baseband signal.
The signal s(t) may be transmitted by a BS or a CT, since both types of signals may contain information of interest in determining the location or velocity of a CT.
RF Reception: Then, the LP equivalent received signal, ~,k (t) , through the k't' antenna at the i''' MS can be modeled as k (t) = G R-° eJ~ei,k +~o ) eJ2'~ Ofo +8f;,k ) t t _ ,~ _ Ot i,k i,k 1~( i,k i,k~
_ (5) + W i k (t~ + MPi k (t~ + li~ k (t~
and the RF received signal, r;,k(t), (see Figure 2) can be expressed as ri,k (t) = Re~ e~2~f~t r'k (t) (6) 5 where Re { . } denotes an operation which returns the real part of a complex number . G;,k represents the gain (complex) due to the transmitting and receiving antennas from the CT to the k'" antenna of the i'" MS (a function of the two antenna patterns respectively), 10 . R ~, k represents the attenuation (real) due to the propagation channel, where n is a real number (usually between 2 and 4) that depends on the channel and R;,k is the range between the CT and the k'" antenna of the i'" MS, 0;,k = { -2~( f~ + ~fo + 8f;,k ) (i;,k + Ot;,k ) } mod 2~
15 ('7) is the phase of the received RF signal at the k'" antenna of the i'" MS (more specifically at the connector of the k'" antenna of the i'" MS), where:
8f;,k is the frequency offset due to the Doppler shift over the propagation 20 channel (a function of speed, v, and Direction Of Travel (DOT), cp).
i;,k is the Time Of Arrival (TOA) of the signal r;,k(t) at the k'" antenna of the i'" MS (a function of the range R;,k), ~t;,k is the overall group delay through the antenna of the CT to the k'"
antenna of the i'" MS (usually a function of frequency), w;,k(t) represents the Additive White Gaussian Noise (AWGN, complex) due to thermal noise at the k'" antenna of the i'" MS (a function of temperature and bandwidth), . MP;.k(t) represents all multipath components (complex) at the k'" antenna of the i'" MS (a function of the environment and of the elevation of the antennas), and I;,k (t) represents all low-pass equivalent interferences (both in-band and out-of band) at the k'" antenna of the i'" MS.
Total RF Retention: In IS-95, a number of CTs transmit simultaneously over the same reverse link frequency band. In this model of a CDMA system, I~ (t) represents all such CDMA signals excluding ~ (t) .
Baseband Reception: One or more IF stages down-convert the received RF signal, r;,k(t), to an analog baseband signal, r~, k (t) , which is equivalent to performing the following operation:
r''k (t) - a j2~f~t r' k (t) e-j2~(f~ +of;,k )t a J~~,k - ~'k (t) e- j2~ of;,k t e-j~~,k (8) where ~ Of;,k is the frequency error between the Local Oscillators (LOs) in the k'"
receiver at the i'" MS and the carrier frequency f~; and ~;,k is the carrier phase of the LOs in the k'" receiver at the i'" MS.
From equations (5), (6) and (8), one can refer to:
~ "yJ;>k = 6;,k - ~;,k + ~o" as the Phase Of Arrival (POA) of the received signal, r~,k (t) ; and "f;,k = 8f;,k - Of;,k + Ofo" as the Frequency Of Arrival (FOA) of the received signal, ri,k (t) .
~ SOAi,k = Gi,kRi,k as the Strength of Arrival (SOA) of the received signal, ri,k(t~
~ TOA i, k = ~ i, k + Dt i, k as the Time of Arrival (TOA) of the received signal ri, k (t) .
Additionally, we define w' (t ) _ [w i, k (t ) + MPi, k (t ) + Ii, k (t ),e-~2~'f~ t as the received and downconverted noise, interference, and multipath. In other words, ri,k (t)= SOAi,k ~ exp(jWi,k + .l2~fi,kt)~ p(t - TOAi,k )+ w'(t~
(9) There are various known means of extracting the complex baseband signal from a passband or IF signal, such as subsampling followed by digital quadrature demodulation.
Digital Receution: Finally, an Analog-to-Digital (A-to-D) Converter converts the baseband signal, ri, k (t) , to a digital signal, ri,k (m ) , which is equivalent to performing the following operation:
ri,k (m) = ri,k (t) t-m TS + qi,k (m) where TS is the sampling interval, m is the integer discrete-time index, and q;,k(m) is the quantization noise, which depends primarily on the number of bits and scaling of the A-to-D.
Five Steps for Positioning a CT using a network-based WLS:

1. Induce, Identify and categorize activity of a CT:
In some applications, activity of a CT will trigger the requirement for that CT to be located. For example, in the application of this invention to E911 services, the act of a CT originating a 911 call will trigger the need to locate that CT. Hence, the WLS
System must monitor the activity of a CT' for such a trigger.
In other applications, a powered-up CT has to be located passively, such as in the case for fleet management. This can happen based on the periodic registrations that the CT performs with a BS, or by active positioning. In the latter case, the Host can call the CT, receive its response through a number of MSs, then drop the call.
2. Detection:
There are generally two sources of information to be used to locate a CT using a network-based WLS: The Reverse Control/Access Channel and the Reverse Voice/Traffic Channel. When using the Reverse Control/Access Channel to locate a CT, the CT accesses the radio channel using a Random Access technique such as Aloha in AMPs and in IS-54, and slotted Aloha in CDMA, IS-136 and GSM.
The difficulty with locating over the Reverse Control/Access Channel is that a number of MSs must be able to detect the CT transmission even at low signal power.
This problem is compounded when power control is activated at the CT, since in this case remote MSs receive the CT transmission well below the received signal at the serving BS. Several detection algorithms have been suggested in the literature such as Coherent combining, and Non-coherent combining.
Both techniques are sometimes unsuitable for WLS due to errors in the frequency estimation of the received signal. A novel detection is proposed in this patent that circumvents the errors in the estimated frequency: Group-coherent combining.
3. Measurement of Signal Parameters:

arious signal parameters exist in equation (9) that can lead to independent equations regarding the static location of the CT, i.e. regarding the coordinates, (x,y), of the CT location of the CT, such as ~ the Strength of Arrival (SOA), SOA ~ k , of the carrier;
~ the Phase of Arrival (POA), yr;,k, of the carrier;
~ the baseband Waveform of Arrival (WOA), p(t - TOA;,k); and ~ the message content.
In addition, there is one source of information where one can extract an independent equation from equation (9) regarding the kinematic location of the CT, i.e.
regarding the velocity, v , namely:
~ the Frequency of Arrival (FOA), f;,k, of the carrier.
4. Estimation of Location Parameter:
Based on the measured signal parameters of the CT, one can estimate the location parameters of the CT. For example:
~ the SOA, SOAK k , can be used to estimate the range of the CT;
~ the POA, y~;,k, can be used to estimate the AOA of the CT (Solution I);
~ the WOA, p(t - TOA;,k), can be used to estimate the TOA, TOA;,k, of the CT
(Solution II, III & IV);
~ the FOA, f;,k, can be used to estimate the velocity of the CT (Solution V);
~ the combination of SOA, SOA~,k, and POA, y~;,k, can be used to estimate the AOA of the CT (Solution VI).
5. Positioning of the CT:
Based on the estimated location parameters of the CT, one can estimate the location of the CT. Location examples include TOA/Range Positioning (Circular Multilateration); TDOA Positioning (Hyperbolic Multilateration); Hybrid TDOA
Positioning (Circular Multilateration with TDOAs); AOA Positioning; AOA/TDOA
Positioning; and Speed and Direction of Travel. Topics in Positioning of a CT

include: Effect of Geometry; Weighting of Observations; Blunder Detection; and Multiple Solutions. In the following sections, we expand further on the five steps for positioning a CT using a network-based WLS.
5 1. Induce, Identify and catesorize activity of a CT:
1.1 Active CT:
In some applications, activity of a CT will trigger the requirement for that CT to be located. Hence, the WLS must monitor the activity of CT's for such a trigger. For example, in the application of this invention to E911 services, the act of a CT
10 originating a 911 call will trigger the need to locate that CT. Another example is the case of a road accident where the airbag is inflated. In this case, the CT can be a simple transmitter that transmits a specific alert signal over the cellular bands.
MSs will monitor Access channel messages, identify Access channel origination messages, and extract the dialed number, the calling number, and possibly additional 15 parameters. Selection criteria will be used to determine if the CT
originating the call is to be located.
In order to identify activity of a CT, it is necessary to detect transmissions involving the CT. Both forward and reverse link transmissions may be of interest.
Following detection of a transmission, its message content may be decoded and 20 examined.
1.2 Passive CT
In some cases desirable to locate a CT that is not currently transmitting.
There are two alternatives for locating such a CT: Passive Positioning; and Active Positioning. n passive positioning, the CT can be located as it performs regular tasks 25 such as periodic registrations with a serving BS if the CT is stationary or registrations with new serving BSs as it enters new cells. In passive positioning, the timing of the last location fix is not crucial. It could be minutes or even hours in the past. Such a positioning is limited to some specific applications such as: RF Planning;
Traffic Monitoring; and Fleet management.

In active positioning, the timing of the last fix is crucial. Such a positioning is important in applications such as: Recovery of stolen vehicles; Prevention of crimes;
and Recovery of lost persons and pets.
In active positioning, the CT can be induced to produce transmissions that can be monitored by one or more MSs in order to determine the location of the CT.
A CT
can be induced to transmit on the Access channel by the Host initiating a call, through a telephone network connected to the cellular network, to the CT. This induces one or more BSs to transmit an Origination Message (see IS-95) addressed to the CT, on the Paging channel. If the CT is powered up and functional, it will respond by transmitting a response on the Access channel. In addition, a particular CT
can be induced to transmit on the Access channel by transmitting a Paging message addressed to that particular CT with the VALID ACK field of the Paging message set to 1, indicating to the CT that it must respond to the Paging message.
CTs can be configured, by an appropriate System Parameters Message from the cellular network, to transmit a Registration Message on the Access channel whenever some or all of the following events occur when the CT powers up, when the CT
powers down, when the CT reaches a specified distance from the location of its last registration, and when a specified interval of time passes since the CT's last registration.
Some BSs could be configured to transmit a particular System Parameters Message content in order to induce CTs to transmit a Registration Message when in certain regions of the network. A CT can be induced to transmit on the Reverse Traffic channel by the Host initiating a call to the CT, and allowing the call to proceed to the point where the CT begins transmission on the Reverse Traffic channel.
The Host may release the call after a specified interval of time, or after the CT's Reverse Traffic channel transmission have been detected by one or more MSs.
The Host may provide MSs with information to assist them with detecting MS
transmissions, such as an approximate or estimated TOT, TOA, andlor FOA, or mobile ESN or message content of CT transmissions.

In both active and passive positioning, the CT could be a simple (miniaturized) transceiver, without the audio portion, which can emulate a cellular telephone in terms of transmitting over the reverse channel. In this case, the CT can be hidden in articles that would be normally carried by their corresponding transportation vehicle such as: Bracelets for persons; Collars for pets; and Black boxes under the hood/trunk of cars and trucks.
2. Detection and Acguisition There are generally two sources of information to be used to locate a CT using a network-based WLS: The Reverse Control/Access Channel and the Reverse Voice/Traffic Channel. When using the Reverse Control/Access Channel to locate a CT, the CT accesses the radio channel using a Random Access protocol such as:
Aloha in AMPs and in IS-54, and slotted Aloha in CDMA, IS-136 and GSM.
The difficulty with locating over the Reverse ControUAccess Channel is that the same CT transmission must be detected and acquired by a minimum of three MSs in order to perform hyperbolic trilateration. This problem is compounded when power control is activated at the CT, since in this case remote MSs receive the CT
transmission well below the received signal at the serving BS. This problem causes the probability of locating a CT to be less than 1.
On the other hand, when locating a CT using the Reverse Voice/Traffic Channel there are no detection problems to resolve. This is due to the fact that when the CT makes a call over a specific Reverse Control/Access Channel, such a request is monitored by a MS dedicated to monitor all activities over such a Reverse Control/Access Channel. The assignment of the Voice/Traffic Channel is performed by the serving BS over the Forward Control/Access Channel and is also monitored by the same MS. The MS transfers such information to the Host in order for the Host to decide whether to locate such a CT or not. In case the Host decides to locate such a CT, it notifies a minimum of three MSs to monitor the transmission of the CT
over the Reverse Voice/Traffic Channel with enough side information regarding the CT

transmission. The side information allows the notified MSs to avoid (or at least to minimize) the need for detecting the CT transmission. In other words, the probability of locating a CT can be equal to 1.
In case the MSs must detect the CT transmission, several detection algorithms have been proposed.
2.1 Detection Model The detection algorithm has at its disposal the received, down-converted, and sampled signal r~,k (m), as defined in the following equation:
ri,k (m)= SOA;,k ~ exp(jyr~,k + j2nf;,kmTs ~~ p~mTs - TOA;,k )+ w'~m)+ q;,k (m) over the observation interval, 0 <_ t <_ T;,k where, without loss of generality, p(t) is assumed to be an Access probe.
2.2 Detection Algorithm The objective of the detection algorithm is to determine if the sought signal p(t) is extant and resolvable in the received signal r~,k (m), and if so, to provide coarse estimates of TOAi,k,and f~,k denoted as ~ and F respectively. Figure I3 illustrates the detection algorithm at a high level. A correlation/combining function z(~, F) is used as a measure of the correlation between the desired and received signals. z~'L, F) is evaluated over a set of ordinates called the trial values, C~ ~ , F~ ~.
Specification of the algorithm requires defining the correlation/combining function and selecting trial values ~~i,Fj~.
2.3 Selection of Trial Values Prior to detection, it is assumed that upper and lower bounds (denoted by subscripted "start" and "end") on TOAD k and F~,k are known, hence it is only necessary to use trial values for ~ and F within the bounds of the following inequalities:
~ start ~ TEA i, k ~ ~ end Fstart ~ Fi, k C Fend It is only necessary to use trial values for 't and F within the bounds of the above inequalities. Next, there is the question of the number and distribution of trial values within the above bounds. As it is known that the CDMA baseband signal is bandlimited to approximately one half of the chip rate, a uniform spacing of one-half or one-quarter chip will be sufficient for trial values of ~ . Hence, preferred values for spacing of ~i are 0~ = 0.407 ~s or 0.203 ~.s and the trial values of ~ are ~k = start + k 0~ , k = 0,1, 2,..., NT , N __ T end ~ start T
where rxl denotes rounding to the nearest integer, and if equidistant between integers, rounding up.
To maintain a specified degradation due to frequency error, the spacing of trial values for F should be inversely proportional to the observation interval Ti k . The preferred value for ~F , the spacing of trial frequencies, is QF = 0.1 Ti, k The trial values of F are Fk = Fstart + k ~F , k = 0,1,2,..., N F , NF = Fend - Fstart ~F

The trial values ~~ ~ , Fj ~ consist of all possible pairings of ~ i and Fj ;
there are NT ~ N F such pairs in total. Hence, z~~i , Fj ~ will be evaluated NT ~ N F
times in order to search for a particular transmission.
5 2.4 Definition of Correlation/Combining Functions Three candidates for the correlation/combining function are:
~ z 1 (~, F) , coherent correlation, ~ z2 ('c), noncoherently combined correlation, and 10 ~ z3 (~,F), the grouped coherent combined correlation.
The grouped coherent combined correlation is the preferred combining function for use in this invention.
2.4.1 Coherent Correlation 15 The coherent correlation is defined as T~'k ; Ts * - j2~tFmTs 2 Zl~'~~F)= ~ r~,k~m-i~Ts~ (mTs~
m =0 The magnitude-square of the sum is taken in order to remove the effect of the unknown and arbitrary phase shift of the received signal and correlation result.
The performance of coherent correlation will equal or exceed the performance 20 of the other two methods. The main drawback of coherent correlation is its computational complexity. As T~ k increases, OF must decrease linearly, which results in a corresponding increase in the number of trial values of F (see Equation ~F = T ~ 1 ). At the same time, the complexity of computing each value of zl (~, F) ~,k also increases linearly. Hence, the overall complexity of the time-frequency search in the detection algorithm is a quadratic function of Tl k .
2.4.2 Noncoherent combining The complexity of computing zl ~~, F) over multiple values of F can be avoided by correlating over subintervals of T~, k , each of duration Tgroup , and combining these subinterval correlations noncoherently to yield z2 ~~~
~T /Tg p i,k ~ rou C(n ~) 2 l ~
n=0 The correlations over the subintervals, c~n, ~), are referred to as subcorrelations:
~~n+1)Tgroup ~Ts ~1 c~n,i)= ~ r;,k~m-i/Ts~*~mTs~
m= nTgroup ~Ts An optional step which reduces the effect of noise is to filter the sequence of subcorrelation results prior to noncoherent combining to remove signal components outside of the range of expected frequency offsets, Fstart < F <- Fend . The preferred embodiment is a transversal filter with taps h~n), - Nh ~2 <- n <_ Nh ~2 , having a passband between the frequencies 27~FStartTgroup and 27LFendTgroup din radians per sample).
Evaluating the incoherent combining function over the trial values of ~ will yield a TOA estimate, ~ . In order to obtain the FOA estimate F , the coherent combining function z 1 ~~, F) is then evaluated at ~ and over the trial values Fk . The trial value Fk which maximizes zl ~~, Fk ) is taken as the FOA estimate F .
2.4.3 Grouped Coherent Combining This third approach is capable of achieving detection performance close to that of coherent integration, with significantly reduced complexity.
Subcorrelations c(k, ~) are computed as described for incoherent combining, and are then coherently combined at the trial values of F .

T~~ki T~oup -j2~CFriTgroup z3 (i, F) _ ~ c(n, i) ~ a ri=o In some circumstances, it may be computationally efficient to compute z3 (~, F) by taking the Fast Fourier Transform (FFT) of c(n, ~) over n. In this case, the frequency spacing of the FFT samples is ~FFFT = l~Ti,k ~ This spacing can be reduced to meet the criteria of Equation OF = T ~ 1 by zero-padding c(n, ~~
before ~,k computing the FFT.
3. Measurement of Signal Parameters 3.1 Measurement of TOA and FOA
In this section, the coarse estimates of TOA and FOA, i and F , will be referred to as ~oo~.se and Fcoarse ~ These estimates are refined by recomputing the subcorrelations with a frequency offset of F~oarse Lm+1)Tgroupj Ts J-1 * -j2~Feoai.semTs c(n, i) _ ~ r;, k (m - ~/Ts ~ ~mTs m vn Tgroup % Ts and repeating the detection algorithm with a finer spacing of trial values localized around the coarse estimates coarse ~d Fcoarse ~ The preferred fine trial values are:
~F 0.25 0'tfine = 0.102 ~.,~s , fne =
Ti, k ~k = coarse + k 0.102 E.t.s~, k = -16,-15,...,16 0.025 Fk = Fcoarse + k , k = -8,-7,...,8 Ti, k Evaluation of z3 ~~, F~ takes into account that the subcorrelations are offset by Fcoarse T~ k /Tgroup j2~~F-Fooarse ~Tgroup Z3, fine ~~~ F~ _ n=0 This refined TOA estimate, like the coarse TOA estimate, is a measurement of the peak of the received signal. It is desirable to measure the leading edge or first arrival for the purpose of position estimation. This can be done by applying rising-edge detection or Super-Resolution to the refined correlation results. If desired, the FOA estimate can also be improved by Super-Resolution.
3.2 Measurement of POA
An appropriate correlation/combining function is applied to the received signal, without the final step of magnitude-squaring as is used in detection, and the phase of the result is taken as the POA of the desired signal.

3.3 Measurement of SOA
The magnitude of the correlation/combining function evaluated at the best available estimates of TOA and FOA may be used as an estimate of the SOA. The uncorrupted SOA is SOA; k = G;,kRi,k . We may estimate the SOA as SOA;,k = z~i, F~ measured at antenna k of ith BS.
This estimate of SOA will be corrupted by noise, interference, and errors in other estimated parameters such as POA, FOA, and TOA.
3.4 Message Decoding Message identification and fields are defined by applicable standards (IS-95, J-STD-008). The received signal can be decoded according to these published standards. Certain messages contain information which can be used to estimate the mobile location.
3.4.1 Pilot Strength Measurement Messase The Pilot Strength Measurement message is transmitted by the CT over the reverse traffic channel, and for one or more pilots, contains the following information PILOT PN PHASE This identifies the TOA of the pilot signal measured at the mobile to a resolution of one chip. The pilot PN phase offset (in units of 64 chips) can be determined from this number, in order to identify the BS transmitting this pilot signal.
PILOT STRENGTH This is the CT's estimate of the SOA of the pilot signal at the CT. As the forward and reverse link path losses will generally be close in value, this SOA estimate can be used in the same manner as reverse link SOA estimates to aid in estimating the CT location.
_._. _. -Multiple PILOT PN PHASE measurements can be processed as TOA signals to obtain a TDOA position estimate for the CT.
3.4.2 Access Channel Messages 5 The IS-95B standard allows for a CT to include PILOT PN PHASE and PILOT PN-STRENGTH information for one or more pilots in Access channel messages. These messages can be decoded by a MS and used in the same manner as described above for the Pilot Strength Measurement Message.
10 4. Estimation of Location Paramters:
4.1 SOA:
4.1.1 SOA;,k = G;,kR~,k to estimate Range, R, In the static case, the first source, SOA ~, k = G i, k R ~, k , can be used to estimate the range R;,k. However, the estimation of R ~, k from G ~, k R i, k is unreliable, even if 15 G;,k is known, due to the nature of the radio channel where RF shadowing and flat fading can deviate the value of "n" in "R~-k" from 2 (for Line Of Sight (LOS)) to 4 (for an urban environment, as shown in Hata, M., "Empirical Formula for Radio Propagation Loss in Land Mobile Radio Services," IEEE Transactions on Vehicular Technology, Vol. VT-29, No. 3, August 1980), or even 6 in heavy urban environments. Hence, unless LOS is guaranteed between the CT and the k'h antenna at the ith MS, R~,k can only offer an accuracy of a few kilometers for R;,k. In the case when LOS is guaranteed (e.g. in a flat environment such as in the sea or over a lake) and G;,k is known to the ith MS, then "n" can be chosen to be 2.
4.1.2 SDOA (Strength Difference of Arrival):

As the absolute transmit power level of the CT will in general be unknown to the MS, multiple measurements of R;jk from different MSs may be compared to estimate the relative distance of the CT from each MS. In other words, assuming that "n" is constant for some MSs, one can use SOA combined with the knowledge of the antenna gain patterns (i.e. the variation of G~,k with the AOA y~ ) to estimate the AOA of the signal transmitted from the CT to the MS. The current patent application introduces a novel method of measuring the relative gain patterns between antennas, and estimating AOA. The assumption for "n" being constant for some MSs is valid when the antennas at the MSs are closely spaced and elevated relative to the antenna of the CT.
Due to the nature of IS-95 and J-STD-008 forward link power control, a MS can estimate the forward link path loss from the power level of the forward traffic channel. This may be used independently of observations from other MSs to estimate R;,k. However, this estimation is subject to the same unreliability as the reverse link path loss range estimation.
4.2 POA:
4._ 2~1 ~r; k to estimate AOA:
The second source, the POA
yr;,k = { -2n( f~ + 4fo + bf;,k )(i;,k + ~t;,k ) + ~~;,k } mod 2~ ( 10) can be used to estimate the AOA, y;,k, where ~~;,k is defined as ~o - ~;,k.
The relationship between the POA, yr;,k, and the AOA, y;,k, is explained as follows.
For simplicity of notation we first assume that:
~ the k'" antenna at the it" MS is antennas, while ~ the m'" antenna also at the it" MS is antennae.

We further assume that the CT is far from the it" MS with respect to the baseline, d;,1,2, between antennas and antennae. Such an assumption implies that the received wavefront is planar, i.e. y;,~ - y;,2 - y;, where:
~ y;,; is the Angle Of Arrival (AOA) of r;,~(t) at antennas, ~ y;,2 is the AOA of r;,2(t) at antennae, and ~ y; is defined as the angle formed between:
~ the line joining the CT (301) and the i'" MS and, ~ the line joining the two antennas at the i'" MS;
in a clockwise manner from the line formed by the CT and the it" MS to the line formed by the two antennas.
This in turn implies that the Phase Difference of Arrival (PDOA), (W;,~ -y;,z), is related to the angle y; through the following relation:

2~d;, ,2 cosy; ) _ (tV;, i - W i,2 )mod 2~ ( 11 ) where:
~ yr;,i is the Phase Of Arrival (POA) of r;,~(t) at antennas; and ~ yr;,2 is the POA of r;,2(t) at antennae.
The solution for y; in (11) is y; _ ~ cos-1 ~ ((~V;,1 - W;,2 )mod 2n + 2~ k) 2~ d;,i,2 (12) where k in (12) is an integer that has to satisfy the following condition:

-1 ~ ~ ~W~n -W~,a)mod2~ +k ~ 1 (13) d~a,2 2~c For example, when d;,,,2 = 7~, we have the following possible solutions for k:
2 ) mod 2~
~W ~a - ~V ~

when , - -1, we have k = 0,1 or 2;

2~

2 ) mod 2~
(tV;
, - y~;

when > = + we have k = 0, -1 > 1, or - 2;

2~

~ -Wa2)mod2~
~~V~

when , - -1 we have k = 0 or /2, 1;

2~

2 ) mod 2~
~W ~
i - W;

h , = + h k = 0 , 1 1 w , ave or -en we ;

2~

2 ) mod 2~
1 - iV ~
(W, when , = 0, we have k = 0,1 or , -1;

2~

(14) Some of the solutions in (14) are trivial. As d;,;,2 becomes larger than ~,, we have more nontrivial solutions. Even though having more than one solution implies ambiguity, it is possible to resolve the ambiguity using redundant observations based on Least-Squares Techniques as explained later.
4.22 iy; k to estimate TOA:
It is also possible to use the POA, yr;,k, in equation (10) to estimate i;,k.
A
drawback in using yr;,k to estimate i;,k is the "mod 2~" operation in (10) which implies that there can be a large integer ambiguity in such an estimation. For example, in TDOA positioning, a pair of TOAs, i;,k+Qt;,k and i~,",+Ot~,m, is needed per independent equation. In this case, the amount of ambiguity is a function of the baseline between the two receiving antennas, i.e. between ~ the kth antenna in the ith MS and ~ the m'h antenna in the j'h MS
with respect to the wavelength corresponding to the frequency: f~ + Ofo +
Sf;,k in (10).
This is shown in equation (15):
~i,k - ~J.m ' ~ (~i,k - ~J.m) - (D~i,k -O~J,m) + 2~L n}/27Lf~ - (~t;,k -~t~,m) + extra term (15) where ~ i;,k corresponds to the TOA at the k'h antenna of the i'h MS;
~ i~,m corresponds to the TOA at the m'h antenna of the j'h MS;
~ n is the integer ambiguity; and ~ the extra term in (15) is due to the existence of ~ Ofo in (10) which depends on the error in the CT LOs relative to f~;
and to ~ 8f;,k in (10) which depends on the velocity v of the CT and the wavelength ~, corresponding to f~.
In the IS-95 and J-STD-008 standards, the CT frequency, f~ + Ofo, can deviate by up to 0.05 parts per million (i.e. by up to 95Hz for a 1900MHz carrier frequency).
Furthermore, in cellular telephony in North America, the carrier frequency, f~, can take values around 800MHz (with a wavelength ~, of around 37.Scm) or values around 1.9GHz (with a wavelength ~, of around 15.8cm). This implies that for a velocity of 100km/hr 8f; corresponds to:
-40Hz > 8f; >40Hz for f~ = 800MHz, or to -95Hz > 8f; >95Hz for f~ = 1.9GHz.
In conclusion:

1. f~ » 8f;,k and f~ » Ofo, i.e. the extra term in (15) is negligible; and 2. the amount of ambiguity in (15) can be potentially large unless the baseline between the two receiving antennas is small with respect to the wavelength, ~,, corresponding to the frequency: f~. We refer to such a solution as Solution I.

Solution I: When the baseline between the k'" antenna at the it" MS and the mtn antenna at the jt" MS is small relative to the wavelength, ~,, we assume without loss of generality that the two antennas belong to the same MS. When the MS is collocated with a BS, the two antennas can be:
10 ~ cellular diversity antennas;
~ cellular sector antennas; or ~ any other types of antennas, deployed solely for location. Such types include:
~ indoor antennas located inside the BS housing;
15 ~ outdoor antennas located on the roof of the BS housing; and ~ outdoor antennas located on the cellular tower.
In this case, it is possible to generate a solution using either TDOA or PDOA.
The TDOA solution between the two antennas is a hyperbola while the PDOA solution between the two antennas is a line. Both solutions approximate the exact solution and 20 coincide asymptotically, i.e. the PDOA line and the TDOA hyperbola coincide at infinity.
In processing yr;,k to estimate either i;,k or y;, we have the following sources of errors:
~ The effect of noise, w, k(t), on Y;:
When using a linear array of antennas to estimate the AOA of an RF signal 25 approximated as a planar wavefront (i.e. assuming a distant RF source), the Cramer-Rao Lower Bound on the variance, vary; ) , of the estimated AOA, y; , is equal to 12c2 ''~(y~ ) Tone ~ SNR;,k x 4~2 x M x (M2 -1) x d2 x sin 2 y; x fm Tone ( 16) where ~ vary; ) Tone is the variance of the estimate y; of the bearing y;
~ SNR; k = A? k /(26n ) , Tone ~ A;,k is the amplitude of the tone ~ 6n2 1S the noise variance, ~ M is the number of elements in the antenna array, ~ d is the distance between antenna elements, ~ fm is the frequency of the tone, and ~ c is the speed of light.
~ The effect of noise, w;_k(t) on i ; i The Cramer-Rao Lower Bound provides a lower bound on the effect of AWGN
on the variance, var(iV;,k ) , of the estimate, iV;,k , of the phase y;,k for a Tone tone of frequency fm _ _ C
var(R; k )ITone vary; k ) 2~t SNR;.k x N;,k x 4~c2fm2 Tone Tone (17) where ~ var(R;,k) is the variance of the estimate, Ri,k, of the range Tone Ri,k ~ ~, is the wavelength of the tone, ~ fm is the frequency of the tone corresponding to 7~ (i.e. fm=c/~,), ~ SNR;,k = A2k /(26n ) where SNR;,k is the Signal-to-Noise Tone Ratio at the k'" antenna of the i'" MS, ~ A;,k is the amplitude of the tone at the k'" antenna of the i'" MS, ~ 6Z" is the noise variance, ~ N;,k is the number of samples (which is directly related to the observation interval T;,k through T;,k=N;,k/fs where fs is the sampling frequency), ~ c is the speed of propagation.
~ Phase offsets:
The phase of the tone fm is shifted by O~;,k . In other words, O~;,k has to be estimated otherwise the phase yr;,k is distorted.
~ time delays, ~t;,~:
The propagation delay i;,k is affected by Ot;,k which represents the system delay through the antenna, cables, filters, amplifiers, etc. Ot;,k has to be estimated otherwise the propagation delay can be prolonged significantly.
~ multipath, MPi(k t):
In TDOA, the multipath MP;,k(t) is equivalent to extra delay over the propagation channel and has to be either estimated and removed, or mitigated.
In the case where the phase estimate is used to solve for the AOA of the received signal r;,k(t), the effect of multipath is to shift the AOA of r;,k(t) by some amount depending on the AOA of MP;,k(t) and its magnitude.
~ interference, I;,k (t) Depending on the level of interference, I~,k(t) can have a drastic effect on the accuracy of the estimated phase and may saturate the RF front end of the receiver. Its effects can be mitigated with both analog and digital hardware, as well as adequate software, whether it is in-band or out-of band.
_ __ 4.3. WOA
4.3.1 n(t - TOA;_k) to estimate TOA:
The last (and most common) source of information one can use to extract an independent equation for the static location of the CT is p(t - TOA;,k) ( 18) which can be used to estimate the TOA, TOA;,k.
Solution II: The most common method for estimating the TOA from p(t - TOA;,k is to cross-correlate p(t - TOA;,k) with p(t) (i.e. to cross-correlate r;,k(t) with p(t)).
Equivalently, one can estimate the TDOA, TOA;,k - TOA~,m, between TOA;,k at the k'" antenna of the i'" MS and TOA~,~" at the m'" antenna of the j'" MS by cross-correlating: p(t - TOA;,k) with p(t - TOA~,m), i.e. to cross-correlate r;,k(t) with r~,",(t). When the i'" MS and the j'" MS do not exist in the same location, one has to transfer both r;,k(t) and r~,~"(t) to the same location. This can be costly and time consuming depending on the size and bit resolution of r;,k(t) and r~,m(t).
Moreover, both p(t - TOA;,k) and p(t - TOA~,m) are obtained from r;,k(t) and r~,m(t) respectively, i.e. they are both noisy. A more efficient and less noisy method is to cross-correlate p(t - TOA;,k) with p(t) at the i'" MS, as mentioned above, then transfer the estimated value of i;,k to the host. In this case, p(t) has to be known at the i'" and j'" MSs which places a constraint on p(t).
Once the TOA, TOA;,k, is estimated using Solution II above, the range, R;,k, between the k'" antenna at the i'" BS, and the CT can also be estimated through equation ( 19):
R~>k = (i~,k - io) c ( 19) where c is the speed of propagation. The time of transmission, io, in (11) is usually unknown to the MSs. One may either:
1. estimate it, then use the estimated value in TOA positioning, or 2. remove it using TDOA positioning.
Both TOA and TDOA positioning are explained later in the patent.

In TOA positioning, a possible method to estimate io is to estimate the Round Trip Delay (RTD) between: the transmission from an active BS to a CT and the response of the CT to the transmission of the active BS.
In this case, 2R;,k = (2T;,k - iss) c (20) where iBS is the time of transmission from the BS to the CT and 2i;,k is the TOA of the response of the CT to the BS.
In TDOA positioning, the time of transmission, io, is removed using an extra independent equation.
It is also possible to estimate the TOA, i;,k, from phases of tones generated from p(t - i;,k - tp - ~t;,k). We refer to such a solution as Solution III which is particularly useful when p(t - i;,k - ip - Ot;,k) is either periodic or cyclo-stationary.
When p(t - i;,k -To - Ot;,k) is periodic, its Fourier series representation would reveal such tones. When p(t - i;,k - io - ~t;,k) is cyclo-stationary, performing a nonlinear operation on it would reveal such tones. In IS-95B, p(t - t;,k - io - Ot;,k) is neither periodic nor cyclo-stationary (except between chips). On the other hand, p(t - i;,k - io - ~t;,k) is cyclo-stationary: in GPS, in both TDMA standards: IS-136 and GSM, and in wideband CDMA (3G CDMA).
Solution III: When i;,k is estimated indirectly based on the phases of tones generated from p(t - i;,k - io - Ot;,k), an integer ambiguity can still exist in the solution unless the wavelength of the selected tones is large with respect to the range between the CT and the k'" antenna at the i'" MS. The selected tones are discussed below where a solution for the integer ambiguity is presented.
It is also possible to use the estimated TDOA solution, i;,k - i~,m, to estimate the AOA, y;~. We refer to such a solution as Solution IV.
Solution IV: In order to estimate y;~ from the TDOA solution, i;,k - i~,m, it is assumed that the CT is far from both the k'" antenna at the i'" MS and the mt" antenna at the jt"
MS with respect to their baseline, d;~,k,",. As mentioned previously, such an assumption practically implies that:

1. Both antennas exist at the same MS.
2. The received wavefront is planar, i.e. y;,, - y;,2 = y;, where ~ y;, i is the Angle Of Arrival (AOA), at antennas of the it" MS, ~ y;,2 is the AOA at antennae of the i'" MS, and 5 ~ y; is defined as the angle formed between:
~ the line joining the CT (301) and the ith MS and, ~ the line joining the two antennas at the it" MS
in a clockwise manner from the line formed by the CT and the it" MS to the line between the two antennas.
10 3. Equation (21 ) relates the angle y; to the Time Difference of Arrival (TDOA), i;, i - i;,z, as follows d;>>,z cos(Y; ) = i;.l - ~~,z (21) c where 15 ~ d;,~,z is the distance between the first antenna at the i"' MS and the second antenna at the it" MS; and ~ c is the speed of propagation.
The advantage in estimating the AOA, y; , using p(t - i;,k - io - Ot;,k) in equation (18) from equation (22):
C
20 Y; _ ~ cos-1 ~i;u ' i;,z ) (22) d~,l>z instead of using yr;,k in (10) from equation (23):
Y; _ ~ cos-1 ~ OV;n - W;,z + 2~ k) (23) 2~ d;,,,z is the fact that there are no ambiguities in equation (22) except for the ~ in the solution of y;, while equation (23) can have a number of ambiguities depending on the 25 value of the integer k.

The disadvantages in estimating the AOA y; using p(t - i;,k - io - ~t;,k) in equation (18) instead of using y;,k in (10) are:
1. a small baseline is required between the two antennas; and 2. the noise affects the variance, var(~;,k ) , of ~;,k more p(t) substantially than it affects the variance, vary;, k ) , of yl;, k .
The second disadvantage can be explained by comparing the Cramer-Rao Lower Bound for ~;,k var(y,k ) ~ (24) 2~ SNR x N x 4~2f 2 Tone ~>k Tone >>k m with the CRLB for ~;,k :

CZ Var('C;,k) > C (25) SNR;,k x 4~2BW2 p(t) Assuming that SNR;,k Tone x N~~k in (24) is equal to SNR;,k p(t) in (25), then the difference between (24) and (25) is fm2 in (24) compared to BW2 in (25).
In IS-95 and J-STD-008 the BW is approximately equal to 1.23MHz while fm can be equal to the carrier frequency f~, i.e. either 800MHz or 1.9GHz. The ratio between the two values in dB is 56.26dB for f~ 800MHz and 63.77dB for f~ 1.9GHz. In both cases, the difference is large. Nonetheless, p(t - i;,k - ~t;,k) in (18) is suitable for TDOA
positioning while yr;,k in (10) is suitable for AOA positioning as explained here:
~ Using W;,k in (10) to estimate the AOA, y; , we have a lower-bound of 5 x 10 5 radians2 for a SNR, SNR;,k x N~,k , of 30dB and for a distance, Tone d;,,,2, of one wavelength, i.e. 0.375m. This is equivalent to having a standard deviation for y ~, of 7.07 x 10 3 radians, which corresponds to a range error of 7.11 meters for every kilometer range between the MR and the antennas.
~ On the other hand, p(t - i;,k - io- ~t;,k) in (18) is suitable for TDOA
positioning since in this case the baseline between antennas does not have to be small.
For example, assuming the SNR, SNR , in equation (25) to be lOdB for IS-~'k P(t) 95, the range R;,k has a variance of 150.69meters2 or equivalently R;,k has a standard deviation of 12.28meters.
In processing p(t - i;,k - io - ~t;,k) to estimate i;,k , we have the following sources of errors:
~ noise, wi(k t):
The Cramer-Rao Lower Bound provides a lower bound on the effect of AWGN
on the variance, var(i;,k ) , of the estimate of the delay i;,k:
p(t) c2 var(R;,k ) = c2 var(i k ) >_ P(t) ~' P(t) SNR X 4~2BW2 ''k P(~) (26) where ~ var(R ~,k ) is the variance of the estimate, R ~, k , of the range R;,k P(t) ~ BW is the RMS bandwidth of p(t), S~''k P(t) - 2E;,k / No ~ E;,k is the energy of r;,k(t), ~ No is the noise Power Spectral Density, and ~ c is the speed of light.

~ The effect of Bandwidth, BW:
Equation (26) demonstrates that the bandwidth of the signal plays an important role in the accuracy of the wireless location system. In IS-95, the radio frequency (RF) channels are spaced by 1.23 MHz which is a comparable BW relative to systems designed primarily for location such as Global Positioning Systems (GPS) with a BW
of IMHz over Standard Positioning Services (SPS) channels. The preferred embodiment of location system, including host, according to the current patent application is network-based while GPS is handset-based. In GPS, the location system initially uses a conventional sliding correlator (similar to Solution II) in the handset to obtain a set of pseudo-ranges (one pseudo-range per satellite) (see e.g.
Spilker, J.J., "GPS Signal Structure and Performance Characteristics," Global Positioning System, Volume I, The Institute of Navigation, Washington D.C., 1980). The pseudo-ranges are then used in mufti-lateration to obtain a position fix of the GPS
receiver. A typical accuracy for a commercial one point (i.e. no differential reception) GPS
receiver with SPS is around 30m RMS without Selective Availability (SA).
In order to achieve a comparable accuracy using IS-95 (assuming no multipath), Solution II suggests that a conventional sliding correlator is required at each MS with 8 samples per chip. The sliding correlator provides a TOA estimate of the transmitted radio signals which is followed by a hyperbolic (differential) mufti-lateration of all the TOA estimates at some central site. The reason for requiring 8 samples per chip is that the correlation function from which a TOA may be estimated has a resolution which is limited to that of the Fourier transform. The traditional resolution bound on Fourier-based methods is the Rayleigh resolution criterion as shown in Haykin, S., "Adaptive Filter Theory, " 2nd Edition, Prentice Hall, Englewood Cliffs, NJ, 1991.
In order to reduce the required number of samples per chip, while maintaining good accuracy (even with multipath), further processing using SR algorithms often yields a result with higher resolution. This was shown by Dumont, L.R., et al., "Super-resolution of Multipath Channels in a Spread Spectrum Location System,"
IEE Electronic Letters, Vol. 30, No. 19, pp. 1583-1584, September 15, 1994 and as shown by Fattouche et al., U.S. Patent No. 5,570,305 issued Oct., 1996, and as shown by Ziskind, I. et al., "Maximum Likelihood Localization of Multiple Sources by Alternating Projection," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-36, No. 10, October, 1988.
~ The Effect of the Observation Interval, T; k:
The Observation interval, T;,k, is directly related to the energy E;,k in the received signal r;,k(t) at the k'h antenna of the ith MS since T~.k 2 E;,k = f Ir;,k fit) dt (27) It is also related to the steady state response of a filter in such a way that the response of the filter reaches its steady state as long as T~, k >
BW;>k (28) where BW;,k is the bandwidth of the filter in the receiver corresponding to the k'h antenna of the i'h MS.
~ time delays, ~t;~:
The propagation delay i;,k is affected by Ot;,k which represents the system delay through antenna, cables, filters, amplifiers, etc. ~t;,k has to be estimated otherwise the propagation delay can be prolonged significantly.
~ interference, Ii( Depending on the level of interference, I;,k(t) can have a drastic effect on the accuracy of the estimated phase and may saturate the RF front end of the receiver. Its effects can be mitigated with both analog and digital hardware, as well as adequate software, whether it is in-band or out-of band.

~ The effect of Multipath, MPs(k t):
When multipath is considered, the accuracy of the IS-95 land-based WLS could potentially degrade beyond the 30m accuracy even with the required 8 samples per 5 chip. The reason is that it is not always possible to resolve the multipath component from the direct path component when both components arrive within one chip from each other. The cellular frequency bands are in the mid-800MHz band and in the mid-1.9GHz band, and the propagation characteristics at these UHF frequencies will have a significant impact on positioning by multilateration as shown in Parsons D., "The 10 Mobile Radio Propagation Channel, " John Wiley & Sons, New York, 1992. That the ranges measured correspond to Line Of Sight (LOS) distances is a major assumption made when estimating position by multilateration. Although the dominant transmission mode in this band is LOS, reflections from natural and man-made objects as well as diffraction around said objects are also possibilities.
Multipath and 15 diffraction allow the cellular signal to propagate in heavily built up areas as well as indoors. However, they also cause the measured ranges to be longer than the true LOS distance which introduces error into the multilateration process. In addition, the propagation distance at UHF is relatively short. This allows frequency reuse in the cellular system but limits the number of observables in the multilateration process.
20 For instance, in a dense urban environment with a delay spread of 3 microseconds (as shown in Hata, M., "Empirical Formula for Radio Propagation Loss in Land Mobile Radio Services," IEEE Transactions on Vehicular Technology, Vol. VT-29, No. 3, August 1980) multipath causes the location accuracy to degrade. Once again, the reason for this is that the correlation function from which the multipath may be 25 estimated has a resolution which is limited to that of the Fourier transform which implies that any multipath within such a resolution is unresolvable using traditional methods. Further processing using an inverse SR algorithm often yields a result with higher multipath resolution as shown by Dumont, L.R., et al., "Super-resolution of Multipath Channels in a Spread Spectrum Location System," IEE Electronic Letters, Vol. 30, No. 19, pp. 1583-1584, September 15, 1994 and as shown by Fattouche et al., U.S. Patent No. 5,570,305 issued Oct., 1996, and as shown by Ziskind, I.
et al., "Maximum Likelihood Localization of Multiple Sources by Alternating Projection,"
IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-36, No.
10, October, 1988. Another approach to multipath resolution is due to Morley, G.D. et al., "Improved Location Estimation with pulse-ranging in presence of shadowing and multipath excess-delay effects," Electronics Letters, Vol. 31, No. 18, pp.
1609-1610, 31 st Aug. , 1995.
4.3.3 Choices of p(t):
The choice of p(t) depends on the radio signal generated by the CT. Several standards are of interest to us such as CDMA, AMPS, TDMA, wideband CDMA, ESMR, two-way paging, etc.
4.3.3.1 CDMA Channels:
Regarding the types of CDMA channels to monitor, there are essentially two types: the access channels and the reverse traffic channels.
4.3.3.1.1 The Access Channels:
CDMA CTs may transmit messages on the Access channel when not communicating on a traffic channel. A CT may transmit on the Access channel in response to input from the CT user (such as dialing a call), in response to Paging messages received, or in response to other conditions (such as expiry of a registration timer).
Preamble and Capsule An Access probe is a CT transmission consisting of a preamble and message capsule containing a complete message. The number of preamble and capsule frames in each access probe are determined by network configuration (PAM SZ and MAX CAP-SZ, respectively). A CT will transmit an Access probe (with identical message content) multiple times at varying power levels, until it receives a response from the cellular network or a specified number of probes have been transmitted.

EncodinE and Modulation The message types, structure, encoding, and modulation of the access capsule are described in the applicable CDMA standards (IS-95, J-STD-008). The bits comprising the message are processed with the following steps:
1. A message length (MSG LENGTH in J-STD-008 section 2.7.1.2.1) field is prepended to the capsule message bits (J-STD-008 section 2.7.1.3).
2. A 30-bit CRC is computed and appended to the message length and message body fields (J-STD-008 section 2.7.1.2.2).
3. The capsule message bits are zero-padded to the maximum capsule length, which is 3 x 88 x ~MAX-CAP-SZ + 3~.
4. The capsule bits are divided into frames of 88 information bits each.
5. An 8-bit encoder tail (zero-valued bits) is appended to each group of 88 bits.
6. Each frame of 96 bits is convolutionally encoded. The code rate is 1~3 with a constraint length of 9, with generator functions g p = 5 5 7 , g 1 = 663, and g2 = 771 (all in octal). The encoder tail allows the shift registers to reset to zero-state between frames.
7. Each code symbol is repeated once, so that if the encoder output is (a, b, c, d,...) the repeated outputs are (a, a, b, b, c, c, d, d,... ).
8. Each frame of code symbols is interleaved. Symbols are written by columns into an array of 32 rows by 18 columns. Symbols are read from the array by rows in this order:

9. The interleaved symbols are separated into groups of 6, and each group of 6 translated into a 64-chip Walsh code.

10. Each chip output from the previous stage is modulated by 4 chips from the long code (J-STD-008 section 2.1.3.1.8), which has a rate of 1.2288 Mcps.
The long code mask, hence the long code phase, is determined by the network identification of the base station towards which the Access probe is directed.

11. The output from the previous stage is modulated by the I-channel and Q-channel short codes (J-STD-008 section 2.1.3.1.9).

12. The Q-channel signal is delayed by one-half of a chip, or 405.9 ns.

13. The I and Q-channel signals are converted into analog filters with a pulse-shaping function having specified properties (J-STD-008 section 2.1.3.1.10), and are upconverted to the appropriate frequency channel.
The preamble is generated by composing a frame of 88 zero-valued bits for each preamble frame, and applying steps 5-13 described above for the capsule bits.
Note that since the preamble bits begin as zeros, steps 3-7 will have no effect beyond increasing the number of '0' bits or symbols. Thus, an alternative definition for the preamble content is a signal consisting of the long and short codes only. The deterministic nature of the preamble facilitates detection of the probe by receivers.
Slotted Transmission Access probes are slotted. The slot width is the length of one access probe, which is determined by the network configuration (PAM SZ and MAX CAP_SZ).
CDMA system time (which generally coincides with GPS time) is the time base for these slots.
PN Randomization A CT will delay the transmission of an Access probe by a duration computed from a network configuration parameter (PROBE PN RAN) and the CT's ESN. The phases of the long and short codes applied to the probe are not affected by this delay.
This delay will not affect TDOA positioning. For RTD positioning, a MS or host must apply a correction for the PN Randomization delay to the measured TOA of an Access probe.
4.3.3.1.2 The Reverse Traffic Channels:
In most cases, CT transmissions on a Reverse Traffic channel will consist of the following stages:
1. The CT transmits the Reverse Traffic Preamble.
2. The CT transmits a mixture of null traffic and messages.
3. The CT transmits a mixture of voice traffic and messages.
The Reverse Traffic preamble consists of a datastream of all zeros modulated by the long and short codes only. The deterministic nature of this preamble aids in the acquisition of the reverse traffic signals by BSs and MSs. A CT transmits Reverse Traffic preamble frames upon initiating transmission on a Reverse Traffic channel, and continues to do so until an acknowledgment is received from a BS
indicating successful acquisition of the preamble, or a time limit is reached.
In the second stage, following the preamble, the CT transmits message frames related to the negotiation of service options and in response to messages from the BS.
The CT transmits null traffic frames when not transmitting message data.
In the third stage, the CT transmits variable-rate frames containing either messages or voice data.
MSs can detect Reverse Traffic transmissions from any of these three stages in order to locate the CT. In all cases, it is necessary for a MS to reconstruct the CT
transmission in order to correlate with the received signal. A MS situated near a serving BS can decode Reverse Traffic frames and relay their content to other MSs, so that the other MSs may reconstruct the Reverse Traffic signal and detect it within their received signals.
4.3.3.2 AMPS Channels:

Regarding the types of AMPS channels to monitor, there are essentially two types: the reverse control channels and the reverse voice channels.
4.3.3.2.1 The Reverse Control Channels:
5 The reverse control channel is digital in nature and is therefore cyclo-stationary with a cycle corresponding to one half of a symbol (Manchester encoded).
4.3.3.2.2 The Reverse Voice Channels:
The reverse voice channel is analog in nature with inherent tones (the 10 Supervisory Audio Tone (SAT), the Signaling Tones (ST) and harmonics of the pitch of the speech).
4.3.3.3 TDMA/GSM Channels:
Regarding the types of TDMA/GSM signals to monitor, there are essentially 15 two types: the reverse digital control signals and the reverse digital traffic signals.
Both signals are digital in nature and therefore are cyclo-stationary with a cycle corresponding to one information symbol. Both signals can therefore be used to generate tones at given frequencies after performing a nonlinear operation on them.
20 4.3.3.4 Wideband CDMA Channels:
For wideband CDMA, p(t) is selected from a family of finite-duration Pseudo-Noise sequences that have good autocorrelation properties and good crosscorrelation properties. The PN sequences are used to spread the information sequence and therefore p(t) is inherently cyclo-stationary with a cycle corresponding to the duration 25 of one PN sequence. Suggested bandwidths are SMHz, IOMHz and lSMHz. The practical description of the patent will describe methods and apparatus to estimate i;,k and to mitigate its sources of errors.

4.4 FOA:
4.1 f;_k:
In the kinematic case where the CT moves with respect to the MSs, the speed and Direction Of Travel (DOT) of the CT may be of interest. The only source of information one can use to extract an independent equation for the speed and DOT of the CT is f,,k = 8f;,k - ~f;,k + ~fo (34) which can be used to estimate the Doppler shift 8f;,k . This is explained in Figure 6 which assumes a three antenna system: the m'n antenna at MS ~ with coordinates (xi,",,y~,",,z,,m), the k'n antenna at MSZ with coordinates (X2,k,y2,k~z2,k) and the n'n antenna of MS3 with coordinates (X3,n,y3,n~Z3,n)~ In this case, the FOAs:
f~,",, f2,k and f3,~
are related ~ to the Direction Of Travel (DOT), cp, relative to Northing (clockwise), ~ to the speed of travel, v, and ~ to the frequency offsets Of;,k, as follows:
f,,m = 8f~,m- Of~,m+ Ofo = v/~, cos(cp-A~,m) - ~fl,m + Ofo (35a) f2.k = BfZ,k - ~f2,k + Ofo = v/7~ cos(cp-AZ,k) - Of2.k + Ofa (35b) f3,~ = bf3,n - ~f3,n + Ofo = v/~, cos(cp-A3,n) - Of3,n + ~fo (35c) where ~ A,,m is the clockwise angle from Northing to the line formed by (x~,m,y~,m) and (x,y), ~ AZ,k is the clockwise angle from Northing to the line formed by (X2,k,yZ,k) and (x,y), ~ A3,n is the clockwise angle from Northing to the line formed by (x3,n,y3,n) and (x,y), and ~ (x,y) are the 2-D (horizontal) coordinates of the CT.
In other words, there are three equations (35a, b and c) with 6 unknowns: cp, v, Of,,m, Of2,k, Ofs,n and Ofo. This is a problem that can be resolved if the frequency offsets Of;,k are made equal to one another, i.e.
if Of~,r,, = OfZ,k = Of3,n = ~f.
In this case, we have two equations with two unknowns: v and cp after using Frequency Difference Of Arrival (FDOA):
-fl,m + f2,k = v/7~ cos(cp - A,,m ) - v/~, cos(cp - AZ,k ) (36a) -f2,k + f3,n = v17~ cos(cp - A2,k ) - v/~, cos(cp - A3,n ) (36b) We refer to such a solution as Solution V. Note that in Solution V the position of the CT (x,y) must be known (or estimated) prior to estimating the speed and velocity of the CT, in order to be able to know A,,m, A2,k and A3,n in equations (36).
I 5 In processing f;,k to estimate 8f;,k , we have the following sources of errors:
~ noise, wi(k t):
The Cramer-Rao Lower Bound provides a lower bound on the effect of AWGN
on the variance, var(8f;, k ) , of the estimate of the frequency 8f; of a tone:
Tone var(8f >_ i,k)Tone SNR;,k x N;,k x (N;,kz -1) x 4~2 Tone (37) where ~ var(8f;, k ) is the variance of the estimate, bf~ k , of the frequency 8f;,k, Tone ' ~ SNR~,k = A2k /(26n ) is the SNR of the tone at the k'" antenna of Tone the i'" MS, ~ A;,k is the amplitude of the tone at the k'" antenna of the i'" MS, ~ a"2 is the noise variance, and ~ N;,k is the number of samples (which is directly related to the observation interval T;,k).
~ freguency offsets, Of;~, As mentioned above, there are three equations (35a-35c) with 6 unknowns:
cp, v, Ofl,m, Of2,k, Of3,n and Ofo. This problem can be resolved if the frequency offsets Of;,k are either removed or made equal to one another, i.e. if Of~,m =
~f2,k = Of3," _ ~f. It is more realistic to have af~,m = ~f2,k = ~f3," = 4f than to estimate and remove the frequency offsets.
~ multipath, MP;.k(t):
The effect of the multipath, MP;,k(t), in this case is to add some Doppler shift to 8f;,k due to dynamic (non-stationary) reflectors such as cars, buses, trucks, etc.
~ interference, Ii(k t):
In this case, I;,k(t) plays the same role in distorting the estimate of the frequency 8f;,k as in distorting the estimate of the phase ~;,k except that its effect can be reduced more significantly.
~ Error in Estimating (x,y):
In equations (36) it is assumed that the position, (x,y), of the CT is known prior to estimating its speed and DOT. This is usually not true and (x,y) needs to be estimated first. The estimation of (x,y) is imperfect, implying that it will contain errors that can affect the estimation of the speed of the CT and its DOT. The practical description of the patent will describe methods and apparatus to estimate Sf~,",, 8f2,k and Sf3," and to mitigate its sources of errors.
4.5 Combination of SOA;_k and iu;_k:
Solution V: Maximum Likelihood An~le of Arrival Estimation (ML-AOA) This section presents a unique means of estimating AOA of radio signals transmitted by a CT. This novel method addresses the problem of site-dependent variations in antenna gain and phase patterns.
__ _. _ ..~_ __ 4.5.1 Conventional Approach to AOA
This "conventional" approach to AOA is briefly described in order to highlight the differences in the novel approach to adaptive maximum likelihood AOA
estimation.
4.5.1.1 Estimating AOA from POA
The POA of a mobile transmission (assumed without loss of generality to be an Access probe in a CDMA system) is measured on two (or more) antenna elements.
Their difference y~;,,-yr;,2 is computed. A closed-form solution for the AOA
is evaluated using W;,~-yr;,2 based on equation (12), the separation, d;,1,2, between the two antennas, and the wavelength, ~,, of the radio signal. There may be multiple solutions.
The solutions) for AOA are incorporated with other information and algorithms, such as least-squares and sector information, in order to arrive at an estimate of position.
4.5.1.2 EstimatinE AOA from SOA
As many antennas have a gain pattern which varies with the physical angle of arrival, the SOAs of CT transmissions measured at different antenna elements can be used alone or in conjunction with POA in order to estimate AOA. U.S. Patents 5,541,608 and 3,824,595 describe AOA measurement systems which incorporate both POA and SOA measurement.
4.5.2 Maximum Likelihood AOA
Maximum likelihood AOA begins in the same way as the conventional approach described above. The POA, W;,k, and SOA, SOA;,k, of the access probe is measured for each antenna element on which the probe can be detected. For a pair of antenna elements, the phase difference and gain difference, or SOA ratio, are computed.

SOAi, l ~Wi,l,2 - Wi,W Wi,2 ~SOAi,l,2 -SOAi,2 For the phase difference OWi,~,2, we can construct py~ ~yi ~ ~Wi,l,2~~ a likelihood function for yi , the AOA at the ith MS. If the conventional closed-form solutions for yi were 30° and 150° then the likelihood function would probably look 5 something like Fig.10.
As long as the model of the conventional method is accurate, the likelihood function by itself does not really give us more information than the closed-form solution for AOA. The benefit of the maximum likelihood method is accrued in the combining of POA/SOA information, in its flexibility in accommodating real-world 10 variations from the conventional model, and in the ease of adaptive training, as described in the following.
Suppose that in addition to py~ ~yi ~ OWi,l,2 ~, we also construct py~ ~yi ~ OSOAi,l,2~, the likelihood function of AOA at the ith MS given the observed relative signal strengths measured on antennas: antennas and antennae. In 15 this case, suppose that these two antennas are from different sectors, and that Figs. 10 and 11 illustrate the likelihood functions py~ ~y; ~ ~Wi,l,2 ~ ~d py; ~Yi ~
OSOAi,l,2 respectively. Qualitatively, py; ~yi ~ OWi,l,2 ~ and py; ~Yi ~ OSOAi,l,2 ~
indicate that the AOA is probably very close to 30° or 150°. py~ ~yi ~
~SOAi,l,2 ~ indicates that the AOA is probably from about 0° to 45°. It is apparent that a good estimate for the 20 AOA is then 30°.
Some sort of monotonic combining function is required to combine the two likelihood functions. Multiplication is intuitively satisfying because of the relationship for independent joint probability:
py; ~Yi I OWi,l,2 ~~SOAi,l,2 ~= Py; ~Yi ~ ~Wi,l,2lry; ~Yi ~ ~SOAi,l,2 ~, although this is not necessarily applicable since the POA and SOA differences are not necessarily independent. Other possibilities include addition (x+y) or more complex functions (such as x2 + l Oxy + y2 ).
In effect, we are approximating the joint conditional pdf/likelihood function py; ~Yi ~ ~Wi,l,2 ~OSOA;,1,2 ~ by combining pY~ ~y; ~ ~Wi,t,2 ~ and pY~ (Yi ~ ~SOAi,l,2 ~. A alternative approach is to somehow obtain and use the joint conditional pdf/likelihood function pY~ ~Yi ~ ~Wi,l,2~OSOAi,l,2~~
Once the likelihood function for yi is synthesized from the available observations, yi can be estimated by the first moment of the distribution (the mean), the ordinate of the maximum of the distribution, or by some other appropriate means.
Various measures of spread, such as the standard deviation of the distribution, can be used as measures of confidence in the estimate. In general, the less the spread of the distribution, the greater the confidence.
This method requires that we somehow obtain the likelihood functions. While we could construct the functions based on expressions for AOA, the distance between antennas, antenna phase patterns, and antenna gain patterns, the resulting model would be quite sensitive to errors or changes in the measured parameters. It is desirable to adopt some kind of adaptive or self training approach.
Figure 12 illustrates the high-level steps involved in ML-AOA (Maximum Likelihood Angle of Arrival estimation).
Adaptive Training The likelihood functions may be constructed by collecting known AOAs along with accompanying POAs and SOAs. These known AOAs may be computed from CT locations previously known, or measured by other means such as ~ Global Positioning System (GPS);
~ the "Russian GPS" system; and ~ TDOA location by the WLS.
The WLS constructs the likelihood function pY~ ~y~ ~ OWi,~,2 ~ bY defining bins covering the expected ranges yi and D ~ i,1,2 . When a CT transmission is detected with known y i and measured ~ y i,1,2 , the bin whose range includes ( yi , 4 W i,1,2 ) is incremented. Alternatively, that bin may be increased by a value related to the estimated confidence in yi and OWi,l,2 ~ As this training procedure is repeated a sufficient number of times, the values in the bins will approximate p,~~ ~yi ~
OWi,l,2 ~~
The likelihood functions for SOA ratio, or for both POA and SOA, may be similarly constructed.
It may be desirable to apply additional processing, such as smoothing, to these empirical likelihood functions. Also, extra bins may be defined for each pair of antennas to count occurrences in which the CT transmission is detected at one antenna and not another.
The WLS will have opportunity to train not only from TDOA locations of E911 or fleet management services, but from all call originations on the CDMA
carrier.
When a WLS subsystem and host resources are idle, they can attempt to locate all call originations by TDOA. Any such location which is deemed sufficiently reliable can then be used to train the likelihood histograms.
The histograms may be initialized with estimates of the likelihood functions prior to training. The histograms may be smoothed by convolution with an appropriate smoothing function prior to use in estimation of AOA.
5. Positioning Technoloeies:
5.1 TOA/Range Positioning (Circular Multilateration) In a 2-D (horizontal) location system it is possible to estimate the position of a CT from the range of the CT to at least two MSs. The CT horizontal position estimate is simply the intersection of two horizontal circles with radii equal to the ranges and centered at the MSs. This method of positioning may therefore be called circular multilateration. Ranges may be calculated by subtracting the known time of transmission~o of signal s(t) from the measured TOAs, i;,k, of signal r;,k(t).
There are three possible solutions:
1. When the Time of Transmission, ~o , is known, we refer to the positioning technique as Range positioning.
2. When the time of transmission, ~o , is unknown, and to be estimated, we refer to the positioning technique as TOA positioning.
3. When the time of transmission, ~o , is unknown, and to be eliminated using TDOA, we refer to the positioning technique as TDOA positioning (which is discussed in the following two sections).
In Range positioning, one way of determining the time of transmission, ~o, is to use the RTD between the BS transmission and the reception of the CT's response to the BS transmission. In this case, a minimum of two independent equations is required to solve for the two unknowns x and y.
In TOA positioning, there are now three unknowns: x, y and ~o . TOAs from three MSs are required and the equation for the k'" antenna at the i'" MS is 1 ( l 2~ Ti k -'Lo -C (x-xi,k~ +~y yi,kl2 -where ~ ~;,k is the Time Of Arrival of signal r;,k(t) at the k'" antenna of the it" MS, ~ ~o is the time of transmission of signal s(t) from the CT, ~ (x, y) is the best known 2-D position of the CT, ~ (x ~, k , y ~, k ) is the known 2-D position of the k'h antenna at the ith MS where i=1, ..., N.
When more than the minimum number of MSs, as explained above, are available, redundancy is said to exist. If a redundant set of measured TOAs contain errors, the TOAs must be adjusted in order to obtain a unique solution to the unknowns.
The amount by which each TOA is adjusted is called the residual. Several methods of adjusting the observed TOAs such that the sum of the squares of the residuals is a minimum are available including: General Minimum Variance Unbiased Estimation, Best Linear Unbiased Estimation, Maximum Likelihood Estimation, Least Squares Estimation, Method of Moments, General Bayesian Estimation, Linear Bayesian Estimation, Kalman Filtering, etc. In this patent, a preferred embodiment of the method to adjust the observed TOAs such that the sum of the squares of the residuals is a minimum is Least Squares Estimation.
5.1.1 Effect of Geometry on TOA Positioning In a location system, geometry (that is the relative positions of the MSs with respect to each other and the CT to be positioned) plays an important role as shown in equation (39) std(position) = DOP x std(R~,k ) (39) where ~ std( R~, k ) is the standard deviation of the range estimate R ~, k obtained from equations ( 19) or (26), and ~ DOP is Dilution Of Precision which is a measure of geometry.
In a 2-D location system, it is common to refer to the Horizontal DOP (HDOP) which is defined as HDOP = ~/EDOP2 + NDOP2 (40) where ~ EDOP is the East DOP and is defined as the square root of the element in the 1 S' row and 1 S' column of CTOA, ~ NDOP is the North DOP and is defined as the square root of the element in the 2"d raw and 2"d column of CTOA, ~ CTOn is an unscaled matrix defined as CTOa = [A Ci ~ C ~ is the unscaled measurement covariance matrix (the 10 identity matrix of appropriate dimension), ~ A is the design matrix for the model of equation (38) and is defined as X-X1 k y-yl,k -_ dl,k -C
dt,k X X2,k y - 5'2,k A= - - -c d2 d2 (41) k k C . , X - XN y yN,k k -_ dN,k -C
dN,k and d;,k is the best derived distance (range) between the CT and the k'"
antenna at the it" MS.
5.1.2 Wei~htin~ of the TOA Observations In the position estimation process, not all TOA observations need carry the same weight. TOA observations thought to be more reliable may be weighted more heavily than those that are deemed less reliable. This is accomplished through the observation covariance matrix. The inverse of C~ is the weight matrix. Larger values on the diagonal of C ~ ~ correspond to heavier weighting for the corresponding TOA observations. In the context of cellular telephone positioning, RSSI at each MS
is one method of assigning weights to the TOAs. A high RSSI at a MS implies a reliable TOA. This is due to two facts:
1. The RSSI at a MS usually consists of received signal power + received noise power. The noise in the receiver is mainly thermal noise which is a function of bandwidth and temperature. When two MSs have comparable temperatures and bandwidths, the received noise power is approximately the same in both MSs. Thus, a high RSSI implies a high received signal power, which in turn implies a high SNR. This is desirable.
2. Furthermore, a higher RSSI usually implies less shadowing than a lower RSSI, which in turn implies less multipath. This is also desirable.
5.1.3 Blunder Detection in TOA Positionin Blunders are gross errors in the TOA observations. This can be caused by large signal level fluctuations due to either flat fading or sudden in-band interference. If unremoved, blunders cause large errors in the estimated position. It is possible to detect observations containing blunders by observing the misclosure of each observation during the iterative Least Squares process. Misclosure is defined as the value of the position model (38) given the best available position estimate (x, y).
Observations containing blunders will generally have much larger misclosures than observations not containing blunders. When an observation is detected as having a blunder it may be removed from the position estimation process.
It is preferred to reduce the effect of geometry, i.e. reduce the value of HDOP in (40), by allowing a large number of MSs to monitor one CT. In cellular communications, frequency reuse and flat fading are common occurrences.
Therefore, increasing the number of monitoring MSs (which probably reduces HDOP) generally increases std(R~,k). As a result blunder detection is crucial as part of the method of minimizing positional error by maximizing the number of MSs (and hence reducing HDOP) without incurring a large penalty on std(R~,k). In cases where blunders are not detected, poor SNR at some MSs may cause the inclusion of measurements from those MSs to increase the std(range) more than they reduce HDOP. With this trade-off in mind, the invention optimizes the number of MSs used to locate the CT such that std(position) in (39) is minimized.
Blunders may also be detected by a statistical analysis of the observation residuals computed from the Least Squares process as shown by Vanicek, P., Krakiwsky, E., "Geodesy: The Concepts," North-Holland Publishing Company, Amsterdam, 1982. The residual of each TOA observation may be standardized by its own estimated standard deviation such that the entire set of residuals is assumed to belong to the normal distribution with zero mean and unit standard deviation.
If this hypothesis is correct, the standardized residuals should fall within some specified confidence region for the standard normal distribution. An observation whose residual is flagged is suspected of containing a blunder.
5.2 TDOA Positioning (Hyperbolic Multilateration) Instead of estimating the unknown time of transmission, it is possible to eliminate it. This is accomplished by differencing TOAs from two different MSs.
Since the time of transmission is common to both it is eliminated from the resulting TDOA (Time Difference Of Arrival). It can be shown that the locus of points for which a particular TDOA is valid corresponds to a hyperbola. The side of the hyperbola on which the CT must lie is known by the sign of the TDOA. Given TOAs from three MSs, two independent TDOAs may be formed. The intersection of the two corresponding hyperbolas estimates the position of the CT. This method is commonly referred to as hyperbolic multilateration.
The 2-D positioning model for hyperbolic multilateration is 7g ~'Lij,km C \X Xi,k /2 + ly yi,k l2 + C lX X j,m ~ + \y yj,m ~ - 0 (42) where ~ ~~ij,km - ~i,k ~.l,m' 1 ~ ~ Or k ~ 111, arid ~ ~i,k is the Time Of Arrival of signal r;,k(t) at the k'h antenna of the i'h MS.
5.2.1 Effect of Geometry on TDOA Positioning Geometry affects TDOA positioning as well. The HDOP is again calculated from (40) where the design matrix is now X X2,m + X Xl,k - 5' - + y -y2,m yl,k d2,m dl,k d2,m dl,k 1 _X x3n +x xlk -yy3n +y-yl,k C d3,n , d~,k d3 n . dl,k ( ) - X XN,I + X xl,k - y - + y -yN,l yl,k dN,l dl,k dN,l dl,k where N in (43) is the number of MSs. Note that the TOA at the k'h antenna of the first MS is subtracted from all other TOAs.
The unscaled observation covariance matrix is 2 1 ~~~ 1 1 ~ ~ . .1 : (44) 1 . 1 1 ~~~ 1 2 5.2.2 Wei~htin~ of the TDOA Observations Weighting of the TDOA observations is possible. However, because the TDOAs are a function of two TOAs, the method of assigning weights is no longer straightforward.
5.2.3 Blunder Detection in TDOA Positioning Blunder detection may also be performed in TDOA positioning. However, in this context, misclosures and residuals correspond to TDOAs. Therefore, a failing misclosure or residual may be due to a blunder in either of the TOA
observations from which the TDOA is derived. It is not always possible to isolate the offending MS.
5.2.4 Multiple Solutions in TDOA PositioninE
Two hyperbola halves, formed from two independent TDOAs, may intersect twice. This results in two mathematically correct solutions. This is particularly true in the case of positioning CTs where short distances and poor geometry are commonplace.
Solution bifurcation (the existence of two solutions to the positioning equations) is most often a concern in the exactly determined case. For the exactly determined case, the existence of two solutions can be detected with the method given in Chaffee, J. W. et al., "Bifurcation of Pseudorange Equations," Proceedings of the 1993 National Technical Meeting, San Francisco, California, January 20-22, 1993, The Institute of Navigation. Although originally intended for the detection of bifurcation in the GPS (Global Positioning System), this method is equally applicable to the case of CT positioning.
When more than two TDOAs are available in the 2-D positioning case, the probability of exact solution bifurcation is extremely small. It is, however, possible for bifurcation to exist for a subset of two TDOAs. In such a case, the second solution may affect the final solution obtained when using all available TDOAs.
In any case, when solution bifurcation exists, the iterative Least Squares position estimation algorithm may converge to either of the solutions. The solution 5 converged to is a function of the initial starting position used to begin the iterative Least Squares process. To converge to the solution corresponding to the actual position of the CT, the initial position used to begin Least Squares must be relatively accurate. Given no a priori information about the location of the CT, a closed-form position estimation algorithm, using the TOA or TDOA observations, is the only 10 choice.
A number of closed-form positioning algorithms have been developed.
Examples are:
~ spherical interpolation (Smith, J.O., et al., "Closed-Form Least-Squares Source Location Estimation from Range-Difference Measurements," IEEE
15 Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, No.
12, Dec. 1987, pp. 1661-1669), ~ the method of Schau and Robinson (Schau, H.C., et al., "Passive source localization employing intersecting spherical surfaces from time-of arrival differences," IEEE Transactions on Acoustics, Speech, and Signal Processing, 20 Vol. ASSP-35, No. 8, Aug. 1987, pp. 1223-1225), ~ Bancroft's method (Bancroft, S., "An algebraic solution of the GPS
equations,"
IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-21, No. 7, Jan. 1985, pp. 56-59), the method of Chan and Ho (Chan, Y.T., et al., "A
Simple and Efficient Estimator for Hyperbolic Location," IEEE Transactions on 25 Signal Processing, Vol. 42, No. 8, Aug. 1994, pp. 1905-1915), and ~ LOCA (Location On the Conic Axis) by Schmidt, R.O. "A New Approach to Geometry of Range Difference Location," IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-8, No. 6, Nov. 1972, pp. 821-835.

LOCA is used in the preferred embodiment of the invention as it pertains to the precise location of mobile transmitters. LOCA is the mathematical dual of hyperbolic trilateration. The fundamental theorem of LOCA states that TOA differences for three MSs of known location yield a straight line of position. This straight line is the major axis of a conic. The three MSs lie on the conic and the CT, the location of which is being estimated, lies at one of the foci of the conic. In the case of redundancy and 3-D positioning, LOCH is expanded into Plane Intersection as shown by Schmidt, R.O., "A New Approach to Geometry of Range Difference Location,"
IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-8, No. 6, Nov.
1972, pp. 821-835. Plane Intersection is equally applicable to the case of redundancy in 2-D positioning.
In LOCA, three conks are possible: an ellipse, hyperbola, or parabola. The conic of interest depends on the relative positions of the MSs and the CT to be positioned. Each of these conics has two foci (for the parabola one focus is at infinity) and therefore two possible solutions. In the case, of an ellipse, the correct focus is determined from the signs of the TDOAs. In the case of the parabola, the solution is obvious. When the conic is a hyperbola, however, the correct focus cannot be determined from the given TDOAs. Chaffee's method of bifurcation detection in Chaffee, J. W. et al., "Bifurcation of Pseudorange Equations," Proceedings of the 1993 National technical Meeting, San Francisco, California, January 20-22, 1993, The Institute of Navigation, will indicate bifurcation for the case of the hyperbola and no bifurcation for the cases of the ellipse and parabola. With four MSs, a second conic is obtained. The intersection of the major axes of the two conics is the CT
position estimate. Hence, there is no ambiguity and bifurcation is, therefore, not of concern when using Plane Intersection in the presence of redundancy.
If the TOAs contain large errors, LOCA or Plane Intersection may give a very poor solution. When used as the initial position for Least Squares, this poor solution may cause Least Squares to diverge. In that case, the best available course of action may be to average the coordinates of the participating MSs and use that as the initial position for Least Squares. Another alternative is to use the approximate coordinates of the MS with which the CT is communicating, as the initial position.
5.3 Hybrid TDOA Positioning (Circular Multilateration with TDOAs) In some cases it is desirable, or even necessary, to use TDOAs as opposed to TOAs. However, as explained above, it is not always possible to isolate blunders when using TDOAs. It is possible, however, to construct a positioning model that uses TDOAs but gives residuals and misclosures for individual TOAs.
To do this, one MS is chosen as the reference. The assumption is then made that the TOA at the reference site is equal to the time of transmission, ~o .
From this point on, the development follows that of circular multilateration except that the TOA
of the reference MS is subtracted from all TOAs (including that of the reference MS) instead subtracting the time of transmission. The positioning model is then IS ~"Cil,kl+~Ru-~ ~X-X~,k~2+~y-Yi,k~ =0 (45) where ~~il,kl - ~i,k X1,1 ~ 1 = 1, .. . ~ N ~d ~ Ru is the range from the reference (first) antenna of MS1 to the position of the CT.
The model of (45) has the same structure as that of circular multilateration (equation(38)) except that the third unknown is Ru and not the time of transmission.
The model of (45) gives N observations, and therefore N residuals and misclosures, for N MSs. The N observations, however, are a 0 and N-1 TDOAs.
The structure of the equations is that of TOA positioning whereas the observations are that of TDOA positioning. Hence, the name Hybrid TDOA Positioning.

5.3.1 Effect of Geometry on Hybrid TDOA Positioning The design matrix for hybrid TDOA positioning is - Y - Y~,~

d,,l dl,, X2,k Y - Y2,k _ A- k d2 d2 k C , , XN,m - Y - YN,m dN,m dN,m (46) Note that (46) is the same as (41 ) except for the third column which corresponds to the third unknown.
The unweighted and unscaled observation covariance matrix, C ~ , is the same as that for TOA positioning, the identity matrix of dimension N.
_ i DOPs may be calculated, as before, from [ATC~ ~Ar .
5.3.2 Wei~htinE of the Hybrid TDOA Observations Although the observations are, strictly speaking, TDOAs, they may be treated as observations corresponding to the individual MSs. That is, the first observation, which is always zero, may be viewed as the observation of the reference (or first) MS.
The second observation, consisting of the TOA of the reference MS subtracted from the TOA of the second MS, is treated as the observation of the second MS, and so on.
Therefore, the N diagonal elements of C~ may be weighted for the individual MSs.
5.3.3 Blunder Detection in Hybrid TDOA Positioning In like manner, N independent misclosures and residuals, one for each MS, are available for analysis. Blunder detection may then be performed as in the case of TOA positioning and blunders in individual TOA observations may be detected.
5.3.4 Multiple Solutions in Hybrid TDOA PositioninE

Since the observations used are actually TDOAs, this method of positioning is subject to solution bifurcation. The method of dealing with multiple solutions discussed under hyperbolic multilateration is equally applicable here.
5.4 AOA Positioning:
Given unambiguous AOA measurements, only two unknowns exist for position estimation - the 2-D coordinates of the CT to be positioned. Therefore, a minimum of two independent AOA measurements are required. Again let (x, y) be the 2-D
coordinates of the CT and ~x~,k, y~,k ~ the 2-D coordinates of the k'" antenna of the i'n MS. At the k'" antenna ofthe i'" MS, the AOA, A~,k, is measured, where: A~,k is the clockwise angle from Northing to the line joining the CT to the kth antenna of the ith MS (similar to A~,k in equations (35) and (36); not to be confused with y~,k in equations (15), (16), (21), (22) and (23)).
The mathematical positioning model is then ~x - x~,k ~cos A;,k - (y - Yak sin A;,k = 0 (47) When more than two independent AOA observations axe available, Least Squares may be used to obtain a unique solution. We may assume that A~ , i.e. that the CT is far from the i'" MS with respect to the baseline between all antennas at the i'" MS, and that the ranges Ra.~ = R~,2 = ~ = R~ .
5.4.1 Effect of Geometry on AOA Positioning The relative positions of MSs with respect to each other and the CT to be positioned are also important for AOA positioning. DOP may again be used to quantify geometry. From the 2-D positioning model (47), the design matrix is found to be COS n~ - Sln n~
COS n2 - Sln n2 A - : : (48) cos nN - sin nN
The unscaled and unweighted observation covariance matrix, C~, is the identity matrix of dimension N. The DOPs can again be found from [ATC~ ~Ar .
5 5.4.2 Wei~htin~ of the AOA Observations The individual AOA observations may be weighted through the observation covariance matrix C ~ . Those AOA observations deemed more reliable are assigned a smaller variance, or conversely, a heavier weight.
5.4.3 Blunder Detection in AOA Positioning 10 As in the case of TOA or TDOA observations, AOA observations may contain blunders. When redundant observations are available, statistical testing of the observation residuals and misclosures may be used to detect observations which contain blunders.
As mentioned above, the AOA solution in equation (12) has an ambiguity 15 problem which can be resolved either by using TDOA as well as AOA as explained in the next section, or using more than two antennas at the same MS. This is possible in sectorized cells since each sector has usually two diversity antennas. In other words, in a three sector cell a total of six antennas could be available.
When the diversity antennas are separated only vertically, the estimated AOA
is 20 the elevation angle. In this case, it is possible to use both diversity antennas since they are independent from each other, i.e. they offer independent observations. The simplest method to use both observations is by combining them using: selection combining, maximal ratio combining, co-phasing combining, equal gain combining, or other methods of combining.

5.5 AOA/TDOA Positioning:
Least Squares allows for the combination of different types of observations.
In particular, it is possible to estimate 2-D position using both AOA
observations and TDOA observations within a single Least Squares adjustment.
A combination of the two different observation types is particularly useful in situations where only two MSs are available for estimating the 2-D position of a CT.
When two antennas at a particular MS are used to estimate the incoming signal AOA
for that MS, numerous AOA ambiguities are possible as shown in equation (15).
This is due both to the nature of AOA estimation with a 1-D linear array, and to the fact that the spacing between elements can be greater than one wavelength.
Therefore, with two MSs and AOA observations only, many position solutions are possible and there is no way of determining which of the many solutions is correct.
If, however, TOA is also measured at each of the two MSs (maybe using p(t -i;,k + io - Ot;,k) in equation (18)), a TDOA can be calculated. This TDOA
corresponds to a hyperbola side which, in the absence of error, will cross through the intersection point of two of the many bearing lines derived from the ambiguous AOAs.
When the AOA and TDOA observations include error, no two bearing lines and the measured hyperbola side will exactly intersect. For the measured TDOA and any two particular AOAs, Least Squares will give the position solution which minimizes the sum of the squares of the residuals. Observation residuals are available since there are two unknowns, the 2-D coordinates, but three observations (2 AOAs and 1 TDOA).
In order to separate the correct AOA pair from the ambiguities, each AOA
combination is combined with the TDOA observation in Least Squares. That combination of AOAs which results in the smallest sum of squares of residuals is chosen as correct. The corresponding position solution is used as the CT
position estimate.
When combining AOA and TDOA observations in Least Squares, both the model for AOA positioning (47) and the model for TDOA positioning (42) are used.

g7 Without loss of generality, the design matrix A for two AOA observations (one at each of two MSs) and one TDOA observation (for the same two MSs) is cos nl - sin n~
A = cos n2 - sin n2 -x x2 +x xl -y-y2 +y-yi d2 d~ d2 d, (49) where d; is the best derived distance between the CT and the i'h MS assuming that the CT is far from the MS such that d;,~ = d~,2 - - = d; , where d;,k is the best derived distance between the CT and the k'h antenna at the ith MS for i=l, 2. Note that the first two rows correspond to the two AOA measurements whereas the third row corresponds to the TDOA measurement. The two columns correspond to the two unknowns, x and y. Additional AOA and TDOA measurements may be included by adding appropriate rows to (49). Note that the l~c factor seen in (43) is missing in the TDOA measurement row of (49). This is done such that the units throughout A
are dimensionless.
The misclosure vector, necessary for the Least Squares adjustment mechanism, merely consists of the misclosures of all observations. The misclosure vector corresponding to the design matrix of (49) is ~x-x~)cosn~ -(y-y~)sinn~
w = (x - x2 )cos n2 - ~y - y2 )sin n2 C * ~'L~2 - lx x1 /2 + \y - y1 l2 +' 'x x212 + \y - y212 (50) where gg ' 0~~,2 - ~~ - ~2 ~ assuming that the CT is far from the ith MS such that 't;,~ - 'C;,2 - ~ - ~~ for i=l, 2 and that X~,~ = X;,2 = ~ = X~ and y;,~ - yi,2 = ~ _ Since the AOA and TDOA observations are independent, the unscaled observation covariance matrix is the identity matrix of appropriate dimension (number of AOA
observations plus the number of TDOA observations).
5.5.1 Effect of Geometry on AOA/TDOA Positioning DOP may again be used to quantify geometry. The DOPs (HDOP, EDOP, _ t NDOP) can be found from [ATC~ ~Ar where A and C~ are defined immediately above.
5.5.2 Weighting of the AOA/TDOA Observations The individual AOA and TDOA observations may be weighted through the observation covariance matrix C ~ . Those AOA and/or TDOA observations deemed more reliable are assigned a smaller variance, or conversely, a heavier weight.
5.5.3 Blunder Detection in AOA/TDOA Positionin Both the TDOA and AOA observations may contain blunders. Statistical testing of the observation residuals and misclosures may be used to detect observations which contain blunders.
5.6 AOA/Ran~e Positioning:
If the time of transmission or round-trip delay is known, the range, R~ , from the CT to the i'" MS is the observed parameter. In that case, AOA and TOA
positioning may also be combined in order to estimate the position of the CT
with as little as two MSs. (Note that when the two MSs are collocated, such as in a sectorized cellular system, then in fact only one BS is needed). Without loss of generality, the design matrix A for two AOA observations (one at each of two MSs) and two range observations (one for each of the same two MSs) is g9 cos A~ - sin A~

cos A2 - sin X - X1 Y Yl,k A k -= -(51 ) dl,k dl,k X - X2,k _ Y Y2,k d2>k d2>k The misclosure vector corresponding to this design matrix is (x-x~~cosl~~ -(y-y~~sinA~
~, _ (x-x2~cos112 -(y-Yz)sinA2 1Z1 (x xl )2 + (y - Y1 )Z ($2) R2 (x x22 +(Y-YZ)2 Since the AOA and range observations are independent, the unscaled observation covariance matrix is the identity matrix of appropriate dimension (number of AOA
observations plus the number of range observations).
5.6.1 Effect of Geometry on AOA/Range Positioning DOP may again be used to quantify geometry. The DOPs (HDOP, EDOP, _ 1 NDOP) can be found from [ATC~ IAr where A and C~ are defined immediately above.
5.6.2 Weishtin~ of the AOA/Ran~e Observations The individual AOA and range observations may be weighted through the observation covariance matrix C ~ . Those AOA and/or range observations deemed more reliable are assigned a smaller variance, or conversely, a heavier weight.
5.6.3 Blunder Detection in AOA/Ran~e Positioning Both the AOA and range observations may contain blunders. Statistical testing of the observation residuals and misclosures may be used to detect observations which contain blunders.
5.7 Sneed and Direction of Travel Estimation:
5 In a kinematic location system, the 3-D or 2-D location of the moving CT
must be estimated at various epochs of time. In addition, the doppler shift of the signal arriving at each MS may be estimated as discussed earlier. The equations relating the frequency (including Doppler shift) of the arriving signal at the MS to the CT
speed, DOT and frequency offset are given in equations (35).
10 The estimation model for speed and DOT is, therefore, f;,k - v/~, cos(cp - n;,k ) + 0f - Ofo = 0 (53) where Of , the frequency offset, is assumed to be equal for all MSs. Given that at 15 any particular epoch the position of the CT ~x, y) is estimated by one of the above methods, the angle n;,k in (53) may be calculated for each MS. In equation (53) then, the knowns are f;,k , ~, and A;,k , (where f;,k is measured or observed), and v, cp , Of and Ofo are the unknowns. Three MSs are required - the same number required to estimate the 2D CT position using TOA or TDOA positioning.
5.7.1 Effect of Geometry on Sueed and Direction of Travel Estimation' Geometry affects the estimation of speed and DOT as well. For instance, it is intuitively obvious that when the CT is traveling on a line perpendicular to the line connecting it and an MS, no information regarding the speed of the CT is available from observed data at that MS.
The design matrix for the model of (53) is cos(cp - n,,k ) - ~ ~ sin(cp - n,,k ) -1 - cos(cp - n2,m ) ~ sin - n -1 A - a, ~, (tP 2, m ) - cos(cp - nN,, ) v sin .- n (tP N,~) -1 (54) The DOPs can again be found from [ATC, lAr . In this case the DOPs will be speed DOP, direction of travel DOP, and frequency offset DOP. C, is the unscaled and unweighted identity matrix of dimension N.
Inducement and Acguisition of CT Signals A CDMA-CT may be located from observation of one or more MSs of one or more of the following types of transmissions: CT Access channel transmissions;
CT
Reverse Traffic channel transmissions; BS Forward Traffic channel transmissions;
and CT message contents (on the Access or Reverse traffic channels).
Therefore, estimation of CT location requires the CT be involved in forward and/or reverse link transmissions. MSs may continually monitor and wait such call activity, or additional steps may be taken in order to induce call activity, as described 1 S in the following sections.
Locating a Designated CT
In this context, a designated CT is a CT for which the Host knows the phone number before the location procedure begins. This situation might arise in several applications such as in: fleet management; kidnapping/person tracking;
safety/Mayday; pet tracking; and stolen vehicle/CT. There are two overall approaches to locating a designated CT: Using Access channel measurements, and/or Using Reverse Traffic channel measurements.

Procedures IA and IB are used to locate a known CT using Access channel measurements. Procedures IIA and IIB are used to locate a known CT using Reverse Traffic channel measurements.
Procedure IA: Locating a known CT using the Access Channel with stored information 1. The host initiates a call to the designated CT.
2. The host orders a number of MSs to store received reverse link signals in a circular buffer in random access memory. The MSs may also do so automatically by replacing outdated data with recently collected data in a continual fashion independently of the Host.
3. The host orders a number of MSs to process their stored received signals searching for an Access channel transmission from the designated CT.
4. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of their successful detection; the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission; and the message content and encoding.
5. The host informs one or more MSs of the estimated TOA, FOA, SOA and/or POA
of the received Access channel transmission, and the message content and encoding of the Access channel transmission of the designated CT.
6. All MSs informed in the previous step attempt again to detect the CT
transmission, and inform the host of success or failure. The successful MS
informs the host of the estimated TOA, FOA, SOA, and/or POA of the received Access channel transmission.
7. The host uses the information reported by the successful MSs to estimate the location of the designated CT.
Any step or steps of Procedure IA may be repeated as necessary to achieve or improve an estimate of the location information of the designated CT, i.e. an estimate of TOA, FOA, SOA, and/or POA.

The following steps may be used in Procedure IA to assist the host in determining which MSs are likely to detect the Access channel transmission of the designated CT:
3a. The host orders MSs to monitor for a particular (forward link) paging message to the designated CT, such as a Channel Assignment Message. (This message would typically be transmitted only by a BS engaged in communications with the designated CT).
3b. All MSs which successfully detect a forward link paging message to the designated CT inform the host of their successful detection of said message, and the message content.
Procedure IIA: Locating a known CT using the Reverse Traffic Channel with stored information 1. The host initiates a call to the designated CT.
2. The host orders a number of MSs to store received reverse link signals in a circular buffer in random access memory. The MSs may also do so automatically by replacing outdated data with recently collected data in a continual fashion independently of the Host.
3. The host orders a number of MSs to process their stored received signals searching for an Access channel transmission from the designated CT.
4. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of their successful detection, the message content and encoding.
5. The host orders one or more MSs to process their stored received signals searching for a Reverse Traffic Preamble from the designated CT.
6. All MSs ordered in the previous step attempt to detect the Reverse Traffic Preamble, and if successful, inform the host of the estimated TOA, FOA, SOA, and/or POA of the received Reverse Traffic Preamble.

7. All MSs which successfully detected detect the Reverse Traffic Preamble in the previous step:
~ demodulate the Reverse Traffic frames from the designated CT following the preamble; and ~ inform the Host of the estimated TOA, FOA, SOA and/or POA of the received Reverse Traffic Preamble, and the message content and encoding of the preamble and successive frames.
8. The host informs one or more MSs of the estimated TOA, FOA, SOA and/or POA
of the received Reverse Traffic Preamble, and the message content and encoding of the Reverse Traffic Preamble and subsequent Reverse Traffic frames of the designated CT.
9. All MSs informed in the previous step attempt again to detect the CT
transmission, and inform the host of success or failure. The successful MS
informs the host of the estimated TOA, FOA, SOA, and/or POA of the received Reverse Traffic Preamble.
10. The host uses the information reported by the successful MSs to estimate the location of the designated CT.
Procedure IIA may be aided by a MS decoding the Channel Assignment message transmitted by a BS to the CT, in order to obtain the Frame Offset, which controls the timing of the Reverse traffic frames.
Procedures IA and IIA can be combined in order to attempt to locate a designated CT using both the Access and Reverse Traffic channels.
Procedure IB: Locating a known CT using the Access Channel in real time 1. The host initiates a call to the designated CT.
2. Simultaneously, the host orders a number of MSs to process the received reverse link signals in real time searching for an Access channel transmission from the designated CT.
3. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of their successful detection; the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission; and message content and encoding.
4. The host uses the information reported by the successful MSs to estimate the location of the designated CT.
5 Procedure IB may be repeated as necessary to achieve or improve an estimate of the location information of the designated CT, i.e. to improve the estimate of TOA, FOA, SOA, and/or POA of the received Access channel transmission.
The following steps may be used in Procedure IB to assist the host in determining which MSs are likely to detect the Access channel transmission of the designated CT:
10 3a. The host orders a number of MSs to process the forward link searching for a particular paging message to the designated CT, such as a Channel Assignment Message. This message would typically be transmitted only by a BS engaged in communications with the designated CT.
3b. All MSs which detect a forward link paging message to the designated CT
15 inform the host of their successful detection of said message, and the message content.
Procedure IIB: Locating a known CT using the Reverse Traffic Channel in real time 1. The host initiates a call to the designated CT.
20 2. The host orders a number of MSs to process the received reverse link signals in real time searching for an Access channel transmission from the designated CT.
3. One or more MSs successfully detect an Access channel transmission from the designated CT, and attempt to detect the Reverse Traffic Preamble and inform the host of the estimated TOA, FOA, SOA, and/or POA of the received Reverse 25 Traffic Preamble.
4. The host uses the information reported by the successful MSs to estimate the location of the designated CT.

Procedure IIB may be aided by a MS decoding the Channel Assignment message transmitted by a BS to the CT, in order to obtain the Frame Offset, which controls the timing of the Reverse Traffic frames.
Procedures IB and IIB can be combined in order to attempt to locate a designated CT using both the Access and Reverse Traffic channels.
Locating a CT that is Making a Call In this section, procedures are described for estimating the location of a CT
which is making a call. The Host may not know the identity of the CT before the procedure begins. It is assumed that the criterion which triggers the need for the CT to be located is one of the following:
~ the CT has originated a call (useful in RF planning and in traffic monitoring applications);
~ the dialed number in the CT's call origination matches a desired called number (useful in emmergency/911 calls and electronic yellow pages);
~ the Electronic Serial Number (ESN) of the CT originating a call matches a desired ESN (useful in crime prevention and security applications); or ~ the Mobile Identification Number (MIN) of the CT originating a call matches a desired MIN (useful in detecting fraudulent calls).
The main difference between procedures in this section and those for locating a known CT in the previous section is that in this section we assume that the CT
originates the call.
Procedure IIIA and IIIB are used to locate a CT making a call using Access channel measurements. Procedure IVA and IVB are used to locate a CT making a call using Reverse Traffic channel measurements.
Procedure IIIA: Locating a CT that is making a call using the Access channel with stored information 1. A number of MSs continually store the received reverse link signal in a circular buffer in random access memory, and process this stored signal searching for Access channel transmissions.

2. A CT makes a call by transmitting an origination message on the Access channel.
3. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of ~ their successful detection;
~ the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission; and ~ message content and encoding.
4. The host determines from the message content (which identifies the CT and the called number) whether to proceed with locating the CT by executing the remainder of this procedure, or to abort it.
5. If the host has determined to proceed, it informs one or more MSs of the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission, and the message content and encoding of the Access channel transmission of the CT.
6. All MSs informed in the previous step attempt again to detect the CT
transmission, and inform the host of success or failure. The successful MS
informs the host of the estimated TOA, FOA, SOA, and/or POA of the received Access channel transmission.
7. The host uses the information reported by the successful MSs to estimate the location of the designated CT.
This procedure can also be used to locate CTs, which transmit any Access channel message, including Registration messages. In this case, a dialed number will not be available in the message.
Procedure IVA: Locating a CT that is making a call using the Reverse Traffic channel with stored information 1. A number of MSs continually store the received reverse link signal in a circular buffer in random access memory, and search this stored signal for Access channel transmissions.
2. A CT makes a call by transmitting an origination message on the Access channel.

3. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of:
~ their successful detection;
~ the estimated TOA, FOA, SOA, POA of the received Access channel transmission, and ~ message content and encoding.
4. The host determines from the message content (which identifies the CT and the called number) whether to proceed with locating the CT by executing the remainder of this procedure, or to abort the procedure.
5. If the host has determined to proceed, it orders one or more MSs to search for the Reverse Traffic Preamble transmitted by the CT, and provides these MSs with a range of times over which to search, an estimated frequency offset, and the encoding of the Reverse Traffic Preamble.
6. All MSs ordered in the previous step attempt to detect the Reverse Traffic Preamble, and if successful, inform the host of the estimated TOA, FOA, SOA, and/or POA of the received Reverse Traffic Preamble.
7. All MSs, which successfully detected Reverse Traffic Preamble in the previous step:
~ demodulate the received Reverse Traffic frames from the designated CT
following the preamble; and ~ inform the Host of the estimated TOA, FOA, SOA and/or POA of the received Reverse Traffic Preamble, and the message content and encoding of the preamble and successive frames.
8. The host informs one or more MSs of the estimated TOA, FOA, SOA and/or POA
of the received Reverse Traffic Preamble, and the message content and encoding of the Reverse Traffic Preamble and subsequent Reverse Traffic frames of the designated CT.
9. All MSs informed in the previous step attempt again to detect the CT
transmission, and inform the host of success or failure. The successful MS

informs the host of the estimated TOA, FOA, SOA, andlor POA of the received Reverse Traffic Preamble.
10. The host uses the information reported by the successful MSs to estimate the location of the designated CT.
This procedure may be improved by the inclusion of the following steps to monitor forward link transmissions:
3a. A MS detects a Paging Channel message addressed to a particular CT, and notifies the host of the message timing and content.
3b. The host extracts from the Paging message content information useful in predicting or detecting subsequent CT transmissions, such as the ESN of the CT, and the assigned frame offset.
Procedures IIIA and IVA can be combined in order to attempt to locate a designated CT using both the Access and Reverse Traffic channels.
Procedure IIIB: Locating a CT that is making a call, using the Access channel in real time 1. A number of MSs continually process the received reverse link signal searching for Access channel transmissions.
2. A CT makes a call by transmitting an origination message on the Access channel.
3. One or more MSs successfully detect an Access channel transmission from the designated CT, and notify the host of ~ their successful detection;
~ the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission; and ~ message content and encoding.
4. The host determines from the message content (which identifies the CT and the called number) whether to proceed with locating the CT by executing the remainder of this procedure, or to abort it.

5. If the host has determined to proceed, it uses the estimated TOA, FOA, SOA
and/or POA of the received Access channel transmission, and the message content and encoding of the Access channel transmission of the CT to estimate the location of the designated CT.
This procedure can also be used to locate CTs, which transmit any Access channel message, including Registration messages. In this case, a dialed number will not be available in the message.
Procedure IVB: Locatine a CT that is making a call using the Reverse Traffic channel in real time 1. A number of MSs continually process the received reverse link signal searching for Access channel transmissions.
2. A CT makes a call by transmitting an origination message on the Access channel.
3. One or more MSs detect an Access channel transmission from the designated CT, and notify the host of:
~ their successful detection;
~ the estimated TOA, FOA, SOA and/or POA of the received Access channel transmission, and ~ message content and encoding.
4. The host determines from the message content (which identifies the CT and the called number) whether to proceed with locating the CT by executing the remainder of this procedure, or to abort it.
5. If the host has determined to proceed, it orders one or more MSs to process the Reverse Traffic signals transmitted by the designated CT, and provides these MSs with a range of times over which to search, an estimated frequency offset, and the encoding of the Reverse Traffic signals.
6. All MSs ordered in the previous step process the Reverse Traffic signals, and inform the host of the estimated TOA, FOA, SOA, and/or POA of the received Reverse Traffic signals.

7. The host uses the information reported by the MSs to estimate the location of the designated CT.
This procedure may be improved by the inclusion of the following steps to monitor forward link transmissions:
3c. A MS detects a Paging Channel message addressed to a particular CT, and notifies the host of the message timing and content.
3d. The host extracts from the Paging message content information useful in predicting or detecting subsequent CT transmissions, such as the ESN of the CT, and the assigned frame offset.
Procedures IIIB and IVB can be combined in order to attempt to locate a designated CT using both the Access and Reverse Traffic channels.
In order to reduce or avoid: Gain Imbalance; Phase Imbalance; Carrier Feed-through; and DC offset, and be able to use the same RF front end for all standards (analog or digital) over a fixed band; and reject out-of band Interferers (e.g. paging, trunked radio, etc.) using digital filters in the Digital Signal Processor (DSP), it is desirable to use a linear IF-sampling receiver for the Reverse and Forward channels.
The IF-sampling receiver at the i~h MS is designed to have high rejection, low group delay variation and good sensitivity.
Design I:
1. Initial rejection is achieved at RF using an RF Band Pass Filter (BPF) (802), followed by an RF amplifier (803) for good sensitivity. The output of said amplifier is passed through another RF BPF (804).
2. The RF signal is downconverted to the desired IF frequency by a mixer (805). The mixer is driven by a LO signal from the RF Synthesizer (812) which is in turn driven by a Frequency Reference (811). The Frequency Reference is preferably obtained from a stable source, such as a GPS
receiver.

3. The IF signal, output from the Mixer (805), is amplified by a first IF
amplifier (806), filtered by a BPF(807), and is amplified by a second IF
amplifier (808).
4. The IF signal is sampled and converted to a digital signal by the A/D
converter (809), and is then stored and/or further processed by the Digital Signal Processor (810).
5. Selection of a specific CDMA frequency channel is accomplished by programming the RF Synthesizer (812) and/or adjusting the frequency of the Frequency Reference (811 ) to obtain a LO frequency which will downconvert the desired CDMA channel frequency to the desired IF. The LO frequency is the difference of the CDMA channel frequency and the IF
frequency. The RF BPFs (802, 803) are designed to have a passband encompassing all CDMA frequency channels which the hardware is designed to support. The IF BPF (806) is designed to have a passband width encompassing most or all of the CDMA channel bandwidth. The IF
BPF will reject signals outside of the desired CDMA frequency channel.
The CDMA signal at the output of the AID converter (809) may not be at baseband, but the baseband CDMA signal is recovered by subsequent digital operations.
In the preferred embodiment, the IF frequency has a value of (2k + 4~F~hip where k is a positive integer and F~hip is the IS-95 CDMA chip rate of 1.2288 x 106 Hz. The A/D is samples the IF signal at a rate of 8F~hip , or 9.8304 MHz. Let x(n) be the nth output of the A/D converter. The in-phase, or "real"
part of the CDMA baseband signal is given, at a sampling rate of 4F~hip , by the sequence:
Re{r;,k ~n)}= (-1~" x(2n) The quadrature, or "imaginary" part of the CDMA baseband signal, is obtained by the following steps:
1. Let xl (n~= x~2n -1~.
2. Form the sequence x2 (n~ by fractionally delaying xl (n~ by one-half sample (see Timo I. Laakso, Vesa Valimaki, Matti Karjalainen, Unto K. Laine, "Splitting the Unit Delay," in IEEE Signal Processing Magazine, vol. 13, no. 1, pp. 30-60, January 1996). The required passband for the fractional delay filter is approximately 3n~5 radians, based on the bandwidth of the IS-95 CDMA
forward and reverse link signals.
3. The quadrature of "imaginary" part of the CDMA baseband signal is then given by the sequence:
Im{r;,k (n~~= (-1)n+1 xa O
Estimation of CT Location Estimation of AOA
The AOA may be estimated from using SOA and/or POA from two or more antennas as described above. ML-AOA estimation may use training from CT
location estimated by TDOA along with accompanying POA and SOA measurements.
An AOA estimate is an estimate of the angular orientation of a ray (a line with a beginning point that extends indefinitely in one direction) originating at a MS and passing through the location of the CT (Figure 3). The point of intersection of two such AOA estimates forms an estimate of the location of the CT.
Alternatively, the intersection of one such line with another locus on which the CT lies forms an estimate of the location of the CT. Combinations of loci leading to a location estimate include: a hyperbola branch from TDOA and a line from AOA; a circle from RTD range and a line from AOA; and a circle from FGRE and a line from AOA. A measure of confidence in each AOA estimate can be used to weight the contribution of the AOA estimate to the position estimate.
Estimation of Range by FGRE
The relationship between path loss and BS-CT range may be used to estimate the position of the CT. When the forward gain is below a certain threshold, the range of the CT may be estimated by a fixed value, which is fairly close to the BS.
A
preferred value for the threshold is 5% of the maximum forward gain, and a preferred value for the corresponding range is 5% of the cell radius.
A FGRE range estimate will typically be combined with an AOA estimate to produce an estimate of the CT location.
Estimation of CT Location by TOA/TDOA
If TOA of a CT transmission has been measured at three or more MSs, then the location of the CT may be estimated from these measurements. If two such TOA
measurements are available, then a branch of a hyperbola is defined on which the CT
lies. This, combined with an AOA estimate, can yield an estimate for the location of the CT.
Estimation of CT Location by Ranse An estimate of the range between the CT and a BS defines a circle centered at the BS, with radius equal to the estimated range, on which the CT lies. A
range estimate relative to a second BS defines a second circle, which will generally intersect the first circle at two points. Each of these points of intersection is a potential solution for the location of the CT. If no other information (such as an additional range or and AOA estimate) is available, then the midpoint of the two solutions may be used as the estimate for the location of the CT.
Estimation of CT Location from Transmitted Messages Under certain conditions, the CT will transmit messages whose content is useful in determining the location of the CT. In particular, the Pilot Strength Measurement Message defined in IS-95A and J-STD-008 is transmitted by the CT and contains measurements of pilot signal strength or quality, and the TOA of pilot signals measured at the CT. IS-95B allows for similar information on pilot signal TOAs to be included in Access channel messages as well. Pilot TOA information may be used to estimate the location of the CT by the TOA/TDOA
Estimation of Mobile Location with Redundant Measurements If more information is available than the minimum amount necessary to arrive at an estimate of the CT location, then there is redundant information available. Due to measurement error, the solutions for CT location arising from non-redundant subsets of the available information will generally differ. Weighted Least Squares, as described in this patent application, can effectively handle redundant measurements.
An alternative approach for dealing with redundancy across diverse types of measurements is to assign a weighting or confidence factor to each measurement.
This confidence factor is an estimate of the accuracy of each measurement, and might typically be derived from the SOA and the type of measurement. For example, of two TOAs, the one with the higher SOA would be assigned a higher confidence factor than the other. A FGRE range estimate would be assigned a lower confidence estimate than most or all other methods due to the low reliability of FGRE.
Measurements with the lowest confidence factors are removed, until the remaining measurements form a non-redundant set for estimating the CT location.
Alternatively, measurements with the lowest confidence factors are removed until the remaining measurements can be processed together to estimate CT location with each measurement appropriately weighted by its confidence factor.
TOA Calibration A wireless location system has to be calibrated prior to operation (and occasionally during operation) in order to remove the effect of the overall Group Delay, Ot;,k, at each MS. Moreover, temperature and aging can cause the overall Group Delay to change with time. Therefore, it is necessary to calibrate the system on a regular basis. A method to calibrate a wireless location system is as follows:
Procedure V:
1. calling a CT whose location is known to the Host;
2. monitoring the paging of the CT by a BS over the corresponding Paging channel using a MS;
3. monitoring the response of the phone to the page over the corresponding Access channel by the same MS;
4. notifying a plurality of MSs to monitor the signal r;,k(t) of the CT
over the assigned Access channel during an observation time T;,k;
and 5. dropping the call; and 6. estimating the relative group delay between MSs by comparing the estimated location of the CT with the known location of the CT.
The estimated location of the CT is based on the measured TDOAs of the CT signal.
Procedure V can be repeated a number of times in order to average the relative group delay over time.
Host Software Given a number of positioning algorithms and a number of methods for blunder detection, the invention makes use of positioning strategy illustrated in Figures 9a, 9b, 9c and 9d for TOA/TDOA positioning. Figures 9 illustrate the preferred embodiment for adjusting the observed TOAs such that the sum of the squares of the residuals is a minimum. Other methods for adjusting the observed TOAs such that the sum of the squares of the residuals is a minimum are available including: General Minimum Variance Unbiased Estimation, Best Linear Unbiased Estimation, Maximum Likelihood Estimation, Method of Moments, General Bayesian Estimation, Linear Bayesian Estimation, Kalman Filtering, etc.

The TOA/TDOA positioning process begins with a set of TOA observations from a minimum of three MSs. If only three TOAs are available (901), solution bifurcation is tested for (902). In the event of solution bifurcation, the LOCA
algorithm (903) is performed on the TOA observations yielding two solutions.
These two solutions are each used as the initial position for Least Squares (904 and 905) resulting in two Least Squares solutions for the CT. The Least Sauares al~nrirht"
here, and in all other parts of Figure 9, is Hybrid TDOA positioning with received signal strength used to weight the individual MS observations. During every iteration of Least Squares, misclosures for each MS are calculated. If any misclosure exceeds some multiple of the RMS value of the entire set of misclosures, the corresponding MS, and its TOA, is no longer used within that particular execution of Least Squares.
If both Least Squares solutions (904 and 905) converge (906) but are not equal (907), it is assumed that Least Squares has converged to the two possible solutions and both Least Squares solutions are reported as possible positions for the CT
(908).
1 S If the either of the LS solutions diverge (906) or the convergent solutions are equal (907), the two LOCA solutions from (903) are reported as possible positions of the CT (909).
If at (902) bifurcation is found to not exist, LOCA is again executed (910) but yields only one solution. This solution is used as the initial position in Least Squares (911).
When redundancy does exist (901 ), Plane Intersection (912) (or any other closed-form position estimation algorithm) is executed. The resulting solution is used as the initial position for Least Squares (913). At this point a check is made as to whether Least Squares (913 or 911) converged (914). If Least Squares converges, another check for observational redundancy is made (915). If there is no redundancy, the Least Squares solution is reported as the position estimate of the CT
(923). If there is redundancy, the normalized residuals are statistically tested for normality (916). The Least Squares solution is reported (923) should all residuals pass.
If any residuals fail, the redundancy numbers of the failing observations are checked (917).
The redundancy number of the ith observation is defined as (55) g; _ (CrC~ ~a where C ~ is the covariance matrix of the residuals and is defined as Cr = C, - A[ATC,-~Ar~ AT . (56) Should all failing observations have redundancy numbers less than some threshold (in the preferred embodiment of the invention, this threshold is 0.5), the Least Squares solution is reported as the CT position estimate (923).
If observations with failing residuals have redundancy numbers larger than the threshold (917), that observation with redundancy number greater than the threshold and with the largest standardized residual is permanently removed from the observation set (928). The initial position used for the previous execution of Least Squares is remembered (929) and used again in Least Squares with the truncated observation data set (930 or 931).
Should Least Squares now diverge (932), the previous Least Squares solution which did converge is reported as the position estimate of the CT (936). If Least Squares does converge (932), and there is no redundancy (933), the newly convergent Least Squares solution is reported (936). If there is redundancy (933), the standardized residuals are tested for normality (934). Should all the residuals pass, the newly convergent Least Squares solution is reported (936). Otherwise, if all failing observations have redundancy numbers less than some threshold (in the preferred embodiment of the invention, this threshold is 0.5), the newly convergent Least Squares solution is reported (936).
If observations with failing residuals have redundancy numbers larger than the threshold (935), that observation with redundancy number greater than the threshold and with the largest standardized residual is permanently removed from the observation set (928). The process then continues as described immediately above.

If at (914) Least Squares diverges, Least Squares is executed again but with the average of participating MSs coordinates used as the initial position (918).
If Least Squares now converges (919) but there is no observation redundancy (920), the newly convergent Least Squares solution is reported as the position estimate of the CT
(923). If there is redundancy (920), the standardized residuals are tested for normality (921). Should all residuals pass, the newly convergent Least Squares solution is reported (923). If some of the residuals fail but none of the corresponding observations have redundancy numbers greater than some threshold (922), the newly convergent Least Squares solution is reported (923).
If observations with failing residuals have redundancy numbers larger than the threshold (922), that observation with redundancy number greater than the threshold and with the largest standardized residual is permanently removed from the observation set (928). The process then continues from (928) as described above.
When Least Squares does not converge at (919), and there is no redundancy (924), either no solution is reported for this particular set of observation data or the solution from the last iteration before divergence is reported (927). If there is redundancy, but all of the standardized residuals pass the normality test (925), no solution is reported for this particular set of observation data or the solution from the last iteration before divergence is reported (927). Should some of the residuals fail, the observation with the largest standardized residual is permanently removed from the data set regardless of its redundancy number. The process then begins at point (912) as described above. Figures 9A-9D are also applicable for AOA
positioning, AOA/TDOA positioning, and AOA/Range positioning.
Transferring Location Information of the CT over the Internet 2$ Given that the Internet is global and inexpensive, the communication between the Host and the customer can be achieved over it. For example when a CT calls for emergency, it is possible to relay the positional information of the CT
from the Host to the PSAP over the Internet. Similarly, in the case when a powered-on CT is to be located by a customer, its positional information can be relayed from the Host to the customer through the Internet.
The utility of the Internet in its capacity of transferring CT location information on a global scale, extends the application of the wireless location system beyond the cellular network for which the MS's have been deployed. Through the latest Internet technology such as Java, JavaBeans, as well as CORBA (Common Object Request Broker Architecture), CT location information residing at the Host can be integrated with third-party information (i.e. a map database, or a database consisting of geo-coded business addresses such as restaurants, towing companies, etc.) residing in some other geographical location, perhaps even in another country. The combination of this CT location information with the third party information can be transferred over the Internet to allow customers to locate a particular CT wrt to either a map location (i.e. street address) and/or a business location, provided that the CT is within network coverage for the wireless location system. Through this process the CT
location information and the third party database information can be accessed or "served up" to the customer through efficient Java Internet technology processes. The service provider will integrate together the various components including the CT
location information derived from the wireless location system and the third-party information database. The integration process of the different databases is transparent to the customer. The customer will only know that the location-based service exists as such to bring all of the different components together to provide for a complete service which can be offered either on a regional, national or perhaps global basis.
Through the Internet these location-based services can now be offered on an economical basis to the customer. Examples of such services are fleet management, concierge services, roadside assistance, child find services, etc. Legality and security aspects are a concern on the Internet and a dedicated link might be sometimes necessary.

There will now be described an embodiment of the invention, incorporating maximum likelihood estimation, that uses downlink signals, and which may use signals from a single transmitter received by several antennas at the mobile transmitter. The same principles may be applied to maximum likelihood estimation using uplink signals.
The method of maximum likelihood estimation described herein in the case of AOA estimation takes advantage of the variation of signal strength with angle of arrival as shown in Fig. 20a and 20b for exemplary antennas A and B of Fig.
19. An idealized relationship between strength difference of arrival and angle of arrival is shown in Fig. 21. The effect of an obstruction is shown in Fig. 22, where a transmitter 2201 transmits to a multiple antenna receiver 2202. Ray 202 is the direct path, while the rays 201 and 203 constitute an indirect path reflecting off obstruction 2203. The detected signal in the case of the multipath situation of Fig. 5 may look like Fig. 23, where 501 is the direct path, while 502 is the reflected path.
The hardware of the preferred embodiment of the invention consists of one or more IS-95 CDMA mobile phones 1803 operating within a network of IS-95 CDMA
base stations 1801, modified in accordance with the description of the invention.
Each base station 1801 typically transmits three separate pilot signals, differentiated by code phase, on three separate directional antennas 1802, as shown in Fig.
19, which are received by the receiver 1803. Fig. 20 shows directional antenna gain patterns that are typical of sectorized antennas for exemplary antennas 1802 shown in Fig. 19.
In addition, there is an FML-AOA computational unit that is connected to the IS-95 base station network by suitable communications links. An exemplary structure is shown in Fig. 14, with the communications links shown in bold lines. In the case of the FML-AOA embodiment, the host 1411 embodies the FML-AOA computational unit, which may be any of various hardware platforms programmed according to the description in this patent document. In the IS-95 network, mobile phones regularly measure and report on pilot signal strengths. These reports are made available to the FML-AOA computational unit through its communications link.
The overall procedure for configuring, training, and estimating using FML-AOA is shown in Fig. 28. Overall, the procedure includes the steps of creating the distributions and setting all elements to zero (2801 ). Optionally, as described in more detail below, the distributions are initialized (2802). Next, the host waits until a signal strength measurement is reported (2803). If the angle of arrival is known, as for example determined by one of the precision location methods described in this patent document, then the angle of arrival and strength measurement pair is used to train the distribution (2804) and the system returns to the wait mode (2803). If the angle of arrival is not known, the system estimates the angle of arrival (2805) according to the method of maximum likelihood and returns to the wait mode (2803).
In the preferred embodiment, a two-dimensional SDOA-AOA likelihood distribution is defined for all possible pairs of transmitter antennas at a cellsite. For example, if a cellsite has three sectors (sector A, sector B, and sector G) with one transmit antenna each, then distributions would be defined for the following pairs:
D AB for sector A and sector B, D BG for sector B and sector G, and D AG for sector A and sector G.
If a cellsite had six sectors, A, B, G, X, Y, and Z arranged in the order listed, then the distributions defined would be D AB for sector A and sector B, D BG for sector B and sector G, D GX for sector G and sector X, D XY for sector X and sector Y, D YZ for sector Y and sector Z, and D AZ for sector A and sector Z.

Depending on the sector orientations, sector widths, propagation environment, and sensitivity of signal measurements, the performance of FML-AOA may be enhanced by creating distributions for other sector pairs in addition to the adjacent pairs. Definition of distributions for excessive sector pairings should not significantly degrade estimation performance.
Each distribution is a two dimensional numeric array with dimensions (1V_sdoa bins, N aoa bins) as illustrated in Fig. 25. The elements are indexed from 0 to N-SDOA bins-1 along the first (SDOA) dimension and from 0 to N aoa bins-1 along the second (AOA) dimension. These distributions may be implemented as a full array or as a sparse matrix structure, in which the indices and values of only nonzero values are stored. All elements of all distributions are initially set to zero.
Note that whenever an SDOA is computed as the difference of SOA for two particular sectors, one sector must always provide the minuend and the other must always provide the subtrahend. As the sign of the SDOA affects the estimation, the roles of subtrahend and minuend must not be exchanged in nor between training and estimation. The preferred means of maintaining this order is to assign a unique number to each sector in a cellsite, and to ensure that the sector with the lower number is always the minuend and the sector with the higher number is always the subtrahend. SDOA low bin should be assigned as a consequence of non-detection by the minuend antenna, and SDOA_high bin should be assigned as a consequence of non-detection by the subtrahend antenna. Note that if detection is unsuccessful at both of a pair of antennas, then the distribution for that antenna pair is not included in training or estimation. Note that in the expression A - B = C, A is the minuend, B is the subtrahend, and C is the difference.
Each element of each distribution has an associated SDOA and AOA bin value, and an associated SDOA and AOA region which encompasses SDOA,AOA
values within a certain neighbourhood of the bin value, as illustrated in Fig.
26. The value of the element serves as a measure of the likelihood of the associated region.
The region associated with an element is defined as all (SDOA,AOA) points which are closer to the associated (SDOA, AOA) value than to the (SDOA,AOA) values of all other elements.
The preferred measure of distance is (SDOA-SDOA(i)~ + ~AOA-AOA(i)~, where ~x~ refers to the absolute value of x. Many other useful definitions of distance may be used. Other implementations using regions of different sizes, possibly overlapping, and adapted to the nature of the observed data, may be used.
In the preferred embodiment, the associated SDOA values are linearly spaced (in dB) between low sdoa bin and high sdoa bin and the AOA values are linearly spaced between 0° and 360°.
The preferred values defining the SDOA-AOA distributions are N SDOA bins = 41, low SDOA BIN = -20 dB, high_SDOA bin = +20 dB, and N AOA bins = 361.
Thus, the associated SDOA bin value for the SDOA-AOA distribution D(i,j) is i.(high_sdoa_bin-low sdoa bin+low sdoa bin N sdoa bins-1 - -and the associated AOA bin value for D AB(i,j) is (360°-0°) +0°= J~360°
~~ N aoa bins-1 N aoa bins-1 In the preferred embodiment, an observation (SDOA,AOA) consisting of a strength difference of arrival SDOA and an angle of arrival AOA is within the region associated with D(i,j) if all of the following four conditions are true, expect as stated in the accompanying exceptions.

condition 1: SDOA >- SDOA - - -low bin +(i-? )(sdoa high bin -sdoa_low bin N sdoa bins-1 exception 1: If i=0 then condition 1 is removed.
condition 2: SDOA - - -< SDOA low bin+~i+ 2)(sdoa high_bin-sdoa_low bin N sdoa bins-1 exception 2: If i=N sdoa_bins-1 then condition 2 is removed.
condition 3: AOA >- 0° + ~ -? ~ (360° - 0°~
2 N aoa bins-1 exception 3: If j=0 then condition 3 is removed.
condition 4: AOA < 0° + (i + ? ) (360° - 0°) 2 N aoa bins-1 exception 4: If j=N aoa bins-1 then condition 4 is removed.
Given an observation of strength difference of arrival SDOA and angle of arrival AOA, the indices of the associated distribution element D AB(i,j) may be determined by Procedure A 1.
Procedure Al: Calculation of Distribution Indicies (i,j) for an Observed (SDOA, AOA) step 1. Let i = the integer 0,1,2,...,(N sdoa_bins-1) which is closest to (SDOA - SDOA_low bin) N sdoa_bins -1 SDOA_high bin-SDOA low bin step 2. Let j = the integer 0,1,2,...,(N-aoa bins-1) which is closest to (AOA)(N _ aoa_bins -1) 360°
Procedure A2: Overall ML-AOA Training and Estimation step 1. Select values for N-SDOA bins, low SDOA bin, high_SDOA bin, N AOA bins. The preferred values are 41, -20, 20, and 361, respectively.
step 2. Let N sites be the number of cellsites in the region or network over which FML-AOA is implemented.
step 3. Let Site(i) represent the i'" cellsite in the region or network over which FML-AOA is implemented, 1 <_ i <_ N sites.
step 4. For i = 1,2,...,N sites execute step 5 and step 6.
step 5. For Site(i), select which pairs of transmitters will have SDOA-AOA distributions. The preferred embodiment selects all adjacent pairs of sectors.
step 6. Create SDOA-AOA distributions for all selected pairs of transmitters.
step 7. Optionally, initialize some or all the SDOA-AOA distributions which have been created. In the preferred embodiment, azimuth initialization is applied to all distributions (Procedure A3).
step 8. Each time a receiver reports a signal strength measurement from one or more transmitters, execute step 9 and step 10.
step 9. Attempt to determine the actual angle of arrival by means other than FML-AOA. Preferred means for doing so include network-based TDOA, GPS, and network-assisted GPS.
step 10. If the angle of arrival was determined in the previous step then train the SDOA-AOA distributions using Procedure A4, otherwise, estimate the AOA from one or more cellsites using Procedure A7. Return to step 8.
The receiver should try to detect and measure as many as possible signals in order to obtain as much training and estimation information as possible. These detection and measurement attempts may be entirely autonomous and/or as ordered to do so by a central network control element. Said network control element may assign specific search parameters, such as which frequency or code channels, or code phase offsets to search in order to simplify or enhance the detection and measurement attempts of the receiver.
If a high-confidence position estimate can be obtained by use of FML-AOA
alone or in conjunction with other means, the AOA can be computed for one or more receiver sites and said AOA along with SOA measurements can be used for FML-AOA training of receiver pairs not directly involved in obtaining the high-confidence position estimate.
Similarly, if a high-confidence AOA estimate can be obtained by use of FML-AOA alone or in conjunction with other means, the AOA can be computed for one or more receiver sites and said high-confidence AOA along with SOA measurements can be used for FML-AOA training of receiver pairs not directly involved in obtaining the high-confidence AOA estimate.
An optional step following the creation and zeroing of the distributions is an initialization of the distributions using the azimuths of the cellsite antennas, along with some fixed parameters. This initialization may be applied to some or all distributions of some or all cellsites. In the preferred embodiment, the azimuth initialization is applied to all distributions for which the azimuths of both antennas are known or can be estimated.
In the preferred embodiment, azimuth initialization models the SDOA-AOA
distribution as a piecewise-linear relationship between two points determined by a fixed estimate of the peak SDOA and the azimuths of the two sector antennas.
This results in two line segments, as shown in Fig. 27. The shorter of the two line segments is assumed to be on the front side of both antennas, and receives a heavier weighting than the other line segment. Other initializations based on the same concepts, such as various curves and distribution weightings, will be apparent to one of ordinary skill in the art.

The algorithm presented in Procedure A3 initializes the distribution D AB, associated with the sector A antenna and the sector B antenna. In the preferred embodiment, this initialization is repeated for every distribution.
Procedure A3: Azimuth Initialization of a Distribution for Sectors A and B
step I . Let D AB represent the SDOA-AOA distribution for sectors A
and B.
step 2. Select a value for the peak SDOA, So. The preferred value is 20 dB.
step 3. Select a value for the front side weighting, WF . The preferred value is 10.
step 4. Select a value for the back side weight, WB . The preferred value is 2.
step 5. Assign to 0A the azimuth of the sector A antenna, and to eB
the azimuth of the sector B antenna.
step 6. Compute i low and j_low such that D AB(i low, j low) is the element of D AB whose region contains the SDOA, AOA pair -So , eB
(see Procedure A 1 ).
step 7. Compute i high and j high such that D AB(i_high, j high) is the element of D AB whose region contains the SDOA, AOA pair So , 6A (see Procedure A 1 ).
step 8. Compute k=sgn(j low j high), where sgn is the signum function.
step 9. If I6A - 6B I > 180° then let D 1 = WB and D2 = WF .
step 10. If ~6A - 9B ~ -< 180° then let D 1 = WF , D2 = WB .
step 11. Repeat steps 11 through 14 for i = i low, i low+1, i low+2, ..., i high step 12. Let j = the int eger closest to Llow + (i - i low) ~--high - Llow i high - i low step 13. Let D_SDOA(i,j)=Dl step 14. Let j = the int eger closest to flow + (i -i low) ~-high - j_low + k(360°), mod 360°
- i high-i low step 15. Let D_SDOA(i,j)=D2.
In the preferred embodiment, each SOA-AOA distribution is trained when a receiver at a known azimuth with respect to a transmitter site attempts to detect a transmission from the two transmitters associated with said distribution, and is successful in detecting and measuring the strength of arrival of the signal from at least one of the two transmitters.
There are various well-known means for determining the azimuth, including satellite location systems such as GPS, network-assisted GPS, trilateration using the time of arrival of transmissions from the mobile at cellsites, trilateration using the times of arrival of pilot signals at the mobile, and measurement of the AOA of transmissions from the mobile by RML-AOA, doppler, pseudo-doppler, or phased arrays.
There are various means for detecting the transmissions and measuring strength of arrival, including correlation and grouped coherent correlation as described in this patent document. Grouped coherent correlation is preferred.
Factors which will affect the measurement of strength of arrival which are or can be known should be corrected, including receiver AGC and transmitted pilot signal strength.
B can be computed from the known location of the cellsite, and from a mobile position estimate obtained by any suitable means, including network-based TDOA, TDOA of forward pilot signals, and mobile-based GPS.
Procedure A4: FML-AOA Training for Multiple Cellsites step 1. Let N sites be the number of cellsites in the region or network over which FML-AOA is implemented.

step 2. Let Site(i) represent the ith cellsite in the region or network over which FML-AOA is implemented, 1 <_ i <_ N sites.
step 3. For i = 1,2,...,N_sites execute step 4, step 5, and step 6.
step 4. Let N-sectors be the number of sectors at Site(i).
step 5. Let Sector(j) -represent the jth sector of Site(i), 1 <_ j <
N sectors.
step 6. For j = 1,2,...,N_sectors-1 execute step 7.
step 7. For k = j+l,j+2,...,N sectors-1 execute step 8.
step 8. If a FML-AOA distribution exists for the pair of sectors Sector(j) and Sector(k) then execute Procedure AS to train the distribution for Sector(i) and Sector(j) using the known AOA, the detection of the transmission at Sector(i), if available, and the detection of the transmission at Sector(j), if available.
Procedure A5: Training of the FML-AOA distribution for a given pair of sectors step 1. Let A be the first, and B the second of the two sectors corresponding to the distribution.
step 2. Let SA be the strength of arrival, in dB, reported for sector A, and SB the strength of arrival, in dB, reported for sector B.
step 3. Let AOA be the angle of arrival, expressed as an azimuth, of the receiver with respect to the transmitter site (cellsite).
step 4. If the signal from sector A was detected and the signal from sector B was detected, then compute SDOA = SA - SB.
step 5. If the signal from sector A was detected and the signal from sector B was not detected, then let SDOA = high SDOA bin.

step 6. If the signal from sector A was not detected and the signal from sector B was detected, then let SDOA = low SDOA bin.
step 7. If the signal from sector A was not detected and the signal from sector B was not detected, then omit step 8 and step 9.
step 8. Compute the distribution indicies i_SDOA and i_AOA such that the observation SDOA, AOA is within the region associated with the distribution element D AB(i_SDOA, i AOA). This may be done using Procedure Al.
step 9. Let D AB(i_SDOA,i AOA) = D AB(i SDOA,i AOA)+1.
After many training iterations at varied AOAs, D SDOA will form an empirical likelihood distribution of SDOA and AOA, which can be used to predict AOA from an observed SDOA.
In an alternative embodiment of the invention, distributions associated with antenna pairs are dynamically created in response to detection of transmissions for which the angle of arrival is known or determinable. In this case, steps 5 and 6 of Procedure A2 may be partially or completely omitted. Procedure A6 describes the preferred embodiment for training including dynamic creation of distributions.
This procedure will create distributions as required in order to make full use of available signal information in order to estimate angle of arrival.
Procedure A6: Training of the FML-AOA distribution for a given pair of sectors with dynamic creation of distributions step 1. Let N sectors be the number of sectors at the cellsite.
step 2. Let Sector(i) represent the ith sector of the cellsite, 1<_i<_N sectors.
step 3. For i = 1, 2, 3,...,N sectors-1 execute step 4.
step 4. For j = i+l, i+2,...,N sectors execute step S and step 6.

step 5. If the transmission was detected on Sector(i) and Sector(j) and a distribution for that sector pair does not yet exist, then create a distribution for that pair, and optionally initialize it using Azimuth initialization (Procedure A3).
step 6. If the transmission was detected on one or both of Sector(i) and Sector(j) and a distribution for that sector pair exists, then execute Procedure AS to train the distribution for Sector(i) and Sector(j), using the known AOA.
Procedure A7: Estimation of AOA by FML-AOA
step 1. Let N sites be the number of cellsites in the region or network over which FML-AOA is implemented.
step 2. Let Site(i) represent the ith cellsite in the region or network over which FML-AOA is implemented, 1 <_ i <_ N sites.
step 3. For i = 1,2,...,N sites execute the following steps.
step 4. Let SP be the set of AOA likelihood distributions selected for Site(i). Initialize SP to be the empty set.
step 5. Let N sectors be the number of sectors at Site(i).
step 6. Let Sector(j) _represent the jth sector of Site(i), 1 <_ j <
N sectors.
step 7. For j = 1,2,...,N sectors-1 execute step 8.
step 8. For k = j+l,j+2,...,N sectors execute step 9.
step 9. Execute step 10 through step 16 if and only if a FML-AOA distribution exists for the pair of sectors Sector(j) and Sector(k), and the signal from Sector(j) and/or Sector(k) was detected.

step 10. Let SA be the strength of arrival, in dB, reported for Sector(j), and SB the strength of arrival, in dB, reported for Sector(k).
step 11. If the signal from Sector(j) was detected and the signal from Sector(k) was detected, then compute SDOA = SA -SB.
step 12. If the signal from Sector(j) was detected and the signal from Sector(k) was not detected, then let SDOA =
high SDOA bin.
step 13. If the signal from Sector(j) was not detected and the signal from Sector(k) was detected, then let SDOA =
low SDOA bin.
step 14. Compute the distribution index i-SDOA
corresponding to SDOA (using step 1 of Procedure A1).
step 15. Let P(n) = D(i-SDOA, n) for n=1,2,3,...,N_AOA bins, where D is the currently selected SDOA-AOA distribution.
step 16. Add P(n) to SP (the set of AOA likelihood distributions for Site(i)).
step 17. Denote the members of SP,in any order, as P,, P2, P3,..., PNP
where NP is the number of AOA distributions in the set Sp.
step 18. Select a value for po. The preferred value is 2.
step 19. For n=0,1,2,...,N AOA bins-1 compute PNP
Pcombined~n~= n ~Pm~n)+pa~
m=1 =~P1O+Po~vP2~n~+Po~~..(PNPU+Po~

step 20. Select a value for a, the weighting exponent. The preferred value is 1.5.
N AOA bins-1 ste 21. Com ute x = ~ P (n~a cosC n ~ 360°
p p combined [~ AOA bins 1 ' n=0 where the cosine function takes its argument in degrees.
N AOA bins-1 n ~ 360°
step 22. Compute y = ~ PcombinedOa sinC -n-- -o N AOA bins 1 ' where the sine function takes its argument in degrees.
step 23. Compute a , the angle measured clockwise from the line segment from (0,0) to ( x, y ) and the x-axis. The estimated AOA for Site(i) is a .
The parameter a varies the weighting of distribution values P(n) according to their magnitude. A value of a=1 yields the mean or first-order moment in the following equations. A higher value of a will increase the weighting of higher values of P(n) versus lower values. The preferred value is a=1.5.
The parameter po serves to diminish the contribution of small amounts of training data (which are considered to be less reliable). po also prevents empty bins in one distribution from completely nullifying the corresponding bin values in other selected distributions.
The step 19 is illustrated graphically in Figs. 24a, 24b and 24c for first and second SDOAs, where the probability distributions for the first SDOA (Fig.
24a) is multiplied by the probability distribution for the second SDOA (Fig. 24b) to yield a combined AOA likelihood distribution (Fig. 24c).
In an alternative preferred embodiment of Procedure A7, step 15 is augmented by applying smoothing to the SDOA-AOA distribution. Smoothing consists of summing weighted contributions of nearby elements of the SDOA-AOA distribution in order to obtain an AOA distribution for the observed SDOA. This smoothing operation may be understood as a two-dimensional discrete convolution. The preferred smoothing filter is defined as follows:
h(-2,-2) h(-2,-1 ) h(-2,0) = h(-2,1 ) = h(-2,2,) = 1 = 2 4 2 = 1 h(-1,-2) h(-1,-1) = h(-1,0) = h(-l,l) = h(-1,2) = 2 4 8 4 = 2 h(0,-2) h(-1,0) = h(0,0) = h(0,1) = 8 h(0,2) = 4 8 16 = 4 h(1,-2) h(-1,1) = h(1,0) = h(1,1) = 4 h(1,2) = 2 4 8 = 2 h(2,-2) h(-1,2) = h(2,0) = h(2,1) = 2 h(2,2) = 1 2 4 = 1 Step 15 of Procedure A7 is then revised to the following:
2 z Let P(n)= ~ ~D(i_SDOA-k, (n-m~mod N AOA bins~~h(k,m) for k=-2 m=-2 n=1,2,3,...,N AOA_bins, where D is the currently selected SDOA-AOA
distribution, and any nonexistent values referenced in the double summation are interpreted as zero.
Many other suitable smoothing filters (typically lowpass filters) will be apparent to those skilled in the art. The limits of the double summation are adjusted to encompass the region over which the smoothing filter h(k,m) is defined.
FML-AOA may be implemented as previously described, but with the strength of arrival measurements (in dB) replaced with phase of arrival measurements.
As well, FML-AOA may be implemented using both phase and SOA measurements, and combining all one-dimensional distributions P1(n), P2(n), P3(n),... as follows:
P(n) _ (P~(n)+pp~~(P2(n)+pp~~(P3(n~+pp)... DOA bins should range from 0 to 360 degrees.

There will now be described embodiments of the invention in which reverse link signals are used to locate a mobile transmitter, the emphasis being on use of maximum likelihood estimation to improve the accuracy of location estimates, and improved detection of mobile transmitter signals, particularly in reference to a CDMA system.
An exemplary MLR System is shown in Fig. 30. The main physical elements of the MLR system are ~ the transmitter 3001, ~ receivers 3002, ~ the backhaul communications network 3003, and ~ the MLR Host 3004.
The MLR system is used to determine or estimate the location of a transmitter.
The system can determine the location of many transmitters in succession or in parallel.
The transmitter 3001 transmits a wireless signal having certain properties which allow this signal to be received, detected, and measured. In the preferred embodiment, the transmitter 3001 is a mobile station as defined by the IS-95 standard, and the transmission consists of an IS-95 Access Probe. Many other embodiments are possible, such as other types of wireless communications devices, including transmit-only devices.
Each receiver 3002 includes means for detecting and measuring a transmission from the transmitter. In the preferred embodiment, a receiver 3002 comprises a radio frequency antenna, a bandpass filter, a low-noise amplifier, a iiequency downconverter, an analog to digital sampler, and a digital processor. A number of suitable receiver basic hardware implementations are well known by those or ordinary skill in the art.
There are two techniques which are particularly applicable to the receiver which bear mention as they are not known in the art: ( 1 ) grouped coherent combining, and (2) the secondary search method, both of which are described in this patent document and may be incorporated in the digital processor of the receiver 3002, as for example with software prepared according to the description in this patent document. These two techniques, applied either jointly or independently, are useful for increasing the effectiveness of signal detection with limited signal processing resources.
Note that groups of receivers may be located closely together, as in sectors of a cellsite. In this case, each sector would correspond to a receiver. If a sector has more than one antenna for diversity reception, then each antenna can correspond to a receiver.
The preferred method by which receivers attempt to detect and measure a potential received transmission is to correlate the actual received signal with a reconstruction of part or all of the expected signal. The expected signal may be a preamble in IS-95 access channel, a replica of which may be stored at the receiver 3002. Frequency offset in the received signal may arise due to doppler effects and frequency errors. In order to avoid a significant degradation when correlating signals longer than about one quarter of the reciprocal of the possible frequency error, the correlation can be computed at a variety of frequency offsets. Grouped coherent combining, as described in the description of the invention at section 2.4.3, is a computationally efficient means of correlating the signals at a variety of frequency offsets. The preferred spacing of these frequency offsets is one half of the reciprocal of the duration over which signals are correlated. The two signals are correlated in small segments, and the results of these small correlations are superimposed with the various frequency offsets. The preferred duration of the small segments is at most one quarter of the reciprocal of the largest frequency offset anticipated.
A summary of the procedure is shown in Fig. 13A, and includes the following steps:
1303 - sample received signal to obtain r,k (m - T/TS ) 1304 - reconstruct the transmitted baseband signal p(mTs) 1305 - compute subcorrelations c(n, z) 1306 - compute correlation values z3(T,F) using grouped coherent combining, over trial values z; and F~ (using the equation set out in section s. 2.4.3).
1307 - Find maximum of z(z;, F~ ~, denote corresponding ordinates as (T, F).
The secondary search method involves the following elements:
~ a set of receivers called the primary search set, for example receivers 2, 3 in Fig. 30 a set of receivers called the secondary search set, for example receivers 4, 5 in Fig. 30 a transmitter, for example transmitter 3001 ~ the Host, a central processing and decision making entity, for example Host 3004 and ~ means of communications between the Host and each of the receivers in the primary and secondary sets (for example the backhaul network 3003).
The primary set of receivers, with limited or no prior knowledge of the transmission, monitor their respective received signals so as to reliably detect a transmission if one occurs, with small probability of deciding in error that a transmission has occurred. The overall process is illustrated in Fig. 31.
A transmitter transmits a transmission at 3101, 3102, which is called the target transmission, which may include for example a preamble in an access channel.
One or more receivers in the primary search set detect said transmission.
Each receiver which detects the target transmission extracts relevant information from the transmission by measuring the TOA, FOA, SOA, and POA of the transmission, and possibly decoding a message in the transmission.
Each receiver in the primary search set which detected the target transmission composes a message containing the information extracted from the target transmission (3103). This message is called the primary search response. Each receiver which composes the primary search response sends the primary search response to the Host.

The Host aggregates the primary search responses and makes a decision to estimate the location of the transmitter, or to not do so. This decision is based on the content of the message in the target transmission, the identity of the transmitter, the availability of resources required to estimate the location of the transmitter, and other opportunities or requirements for the use of said resources.
If the Host decides to estimate the location of the transmitter and the Host determines that the primary search responses are sufficient for this purpose, the Host proceeds to estimate the location of the transmitter using the primary search responses. The Host is looking for three good responses from three different sites. In practice, the secondary search may always be required.
If the Host decides to estimate the location of the transmitter and the Host determines that the primary search responses may not be sufficient for this purpose, the Host proceeds to send message called the secondary search order to each receiver in the secondary search set (3104). The secondary search order sent to a receiver contains some or all of the following information:
~ the approximate time or a range of times (a window) at which the receiver shall attempt to detect the target transmission, ~ the approximate frequency or a range of frequency offsets at which the receiver shall attempt to detect the target transmission, ~ some or all of the signal and message content of the target transmission, ~ the amount of processing gain or observation time which the receiver shall use to search for the target transmission, ~ the expected direction of arrival of the target transmission, and ~ the priority of this search.
Upon receiving the secondary search order, a receiver executes the search for the target transmission in accordance with the content of said order.

After execution of the specified secondary search, a receiver composes a message called the secondary search response, which is sent to the Host (3105). The secondary search response contains the following information:
~ an indication of whether or not the receiver succeeded in detecting the target transmission (3106), ~ the time of arrival of the detected target transmission, if applicable, ~ the frequency offset of the detected target transmission, if applicable, ~ the carrier phase of the detected transmission, if applicable, ~ the strength of arrival of the detected target transmission, if applicable, ~ the ratio of the energy of the detected target transmission to the noise and interference power in the received signal, if applicable, and ~ the ratio of bit energy of the detected target transmission to the noise power in the received signal, if applicable.
The Host collects the primary and secondary search responses associated with the target transmission and uses them to estimate the location of the transmitter.
In the preferred embodiment of the invention, receivers in the secondary search set store a representation of their respective received signals in memory, to enable the receivers to search for a prior target transmission, as directed by a secondary search order. Said representation is stored in a circular buffer, such that at any instant in time, the received signal over a period of time extending from the present to TB seconds prior is stored. TB is known as the depth of signal storage.
The preferred value of TB is three seconds. TB should be selected so as to be greater than the maximum expected delay between reception of the target transmission by a receiver in the secondary search set, and reception of a secondary search order for that target transmission by said receiver. If the target transmissions are known to be slotted (only transmitted at certain times), then the signal storage can be implemented only for the times over which reception of the target transmission is expected.

Note that a receiver may be a member of both the primary and secondary search sets. In general, the secondary search set will include any receivers with reasonable probability of detecting the target transmission in a secondary search.
The preferred method of determining the secondary search sets is to assign a secondary search set to each receiver, and when said receiver reports a primary detection, the members of its secondary search set are included in the secondary search set for the target transmission. A receiver's secondary search set is initially set to the 5 receivers closest to said receiver. Over time, additional receivers are temporarily added to the secondary search set when doing so utilizes idle system resources, and if they demonstrate reasonable probability of detecting the target transmission, they are added on a permanent basis. A member of the secondary search set which demonstrates less than reasonable probability of such detection is removed from the secondary search set.
In this context, the preferred interpretation of "reasonable probability of detection" is a probability of 0.01 (1 percent) or more.
A receiver 3002 performs some or all of the following measurements on received transmissions:
~ SNR, ~ SOA, ~ POA, ~ FOA, ~ TOA, and ~ message decoding.
SNR, signal to noise ratio, is the ratio of the detected signal energy to the power of the non-signal components in the received signal. This serves as a measure of the confidence in the detection.
SOA, strength of arrival, is the strength of the received signal. The preferred units for this measurement are dBm.

POA, phase of arrival, is the carrier phase of arrival of the detected signal transmission.
FOA, frequency of arrival, is the frequency offset of the detected signal transmission.
TOA, time of arrival, is the time of arrival of the detected signal transmission.
In the MLR system, receivers are numbered 1,2,3,..., NR where NR is the number of receivers. When measurements of a particular transmission are reported and collected by the MLR Host, they are designated as follows. For a particular transmission, some receivers may not report detection nor measurements, and hence some of the following quantities may be undefined.
~ SOAR) is the SOA measured and reported by receiver R, 1 <_ R <_ NR .
~ FOA(R) is the FOA measured and reported by receiver R, 1 <_ R <_ NR .
TOA(R) is the TOA measured by receiver R, 1 s R <_ NR .
~ POA(R) is the POA measured by receiver R, 1 <_ R s NR .
~ SNR(R) is the SNR measured and reported by receiver R, 1 <_ R <_ NR .
The backhaul communications network 3003 provides a bi-directional communications link between the MLR Host 3004 and all receivers 3002. This network will carry primary notifications, orders to execute secondary searches, primary and secondary search responses, and other messages for configuration, control, and operation.
The MLR host 3004 will generate and receive messages related to primary and secondary detections, and will configure and monitor the receivers 3002, as described in previous sections. This section will focus on the two main tasks of the MLR
Host 3 004, which are ( 1 ) to use measurements reported by receivers to train the MLR
distribution, and (2) to use the MLR distribution and measurements reported by receivers to estimate the location of a transmitter.
When the MLR Host 3004 receives measurements from one or more receivers, the MLR Host 3004 assigns a detection value li(R) to each receiver. If receiver R

detected the target transmission, then the Host 3004 assigns p(R) =1. If receiver R did not detect the target transmission, then the Host 3004 assigns ~i(R) = 0 .
The preferred means of determining whether or not detection was successful is by comparing the observed SNR with a fixed threshold. Hence, if SNR(R) >_ SNRm~" then receiver R is deemed to have detected the target transmission and p(R) =1. If SNR(R) < SNRm", then receiver R is deemed to have not detected the target transmission and ~3(R)= 0 .
The Host 3004 also attempts to determine the position co-ordinates of the transmitter by means other than MLR. If this position is thus obtained, then x represents the x co-ordinate, and y the y co-ordinate of the transmitter. The preferred co-ordinate system measures the distance in metres East (x) and North (y) from an origin point.
When the Host 3004 computes an SDOA as the difference of two SOAs, the SDOA may be represented by the variable "s".
The purpose of quantization is to transform a range of closely associated values to a single value which adequately represents said range of values.
Said single value is used as a discretely-valued index along a dimension of the MLR
distribution, D. This process may be referred to as "binning".
The quantization function Q(a; b, c, d) is used to transform an observed parameter (x, y, or s) into a quantized index.
0 if A <_ B, Q(A;B,C,D)= roundCApBI if B < A < C, roundCCpB1 if A >_ C.
An x-position is quantized as follows:

0 If x <_ x,rin, Q(X, Xmin~ Xmax ~ OX~ = round X ~X ~n ~ If Xmin < X < Xmax round xmax -Xmin jf X ? Xmax ~x A y-position is quantized as follows:
0 if y _< ymin~
Q(Y~Ymin~Ymax~DY~= roundCy Qy in J If Ymin < Y < Ymax round ymax - Ymin ~ If y > ymax A SDOA (s) is quantized as follows:
0 if S <_ Smin, Q(S, Smin ~ Smax ~ ~S~ = round S OS'n ) If Smin < S < Smax round Smax - Smin if s >_ smax os The rounding function round() returns the closest integer to its argument, or the next larger integer if the argument is equally close to two integers.
An "un-quantizing" function U(I;B,C,D) is defined in order to transform a quantized index I to a value which is close to observed values which have a quantized value of I.
U(I;B,D~=I~AD+B
Note that with respect to the first argument of both functions, U(I;B,D) inverts the function Q(A;B,C,D) to within a tolerance of D, provided that A is within the range B__<A<_C.
An x-position index IX is unquantized by U(Ix; xm;n, ox) = Ixox + xmin A y-position index iY is unquantized by U~ly; ymin~ ~Y~= Iy~Y + Ymin The MLR Host 3004 maintains a data structure D, called the MLR distribution. D
is a 5-dimensional numeric array.
An element of D is denoted D(R~,RZ,Ix,lY,lg), where R~ is a number which identifies a receiver, 1 <_ R~ <_ NR , R2 is a number which identifies another receiver, 1 <_ R2 <_ NR , IX is a quantized x-position, 0 <_ Ix < roundC xmax - xmin 4x ly is a quantized y-position, 0 <_ ly < roundC ymax - Ymin ~ ~ ~d °Y
IS is a quantized SDOA observation, 0 <_ IS < roundC smax - smin ~ .
Os Thus, the dimensions of D are NR x NR x round xmax - xmin ~ x round( ymax - Ymin ~ x rOUndC Smax - Smin ~ .
~x Dy os This section defines procedures executed by the MLR Host 3004.
Procedure 1: Overall Operation of MLR
step 1: Initialize the MLR data structure D by setting all of its elements to zero.
step 2: Wait until a single transmission is detected by one or more receivers, then proceed with step 3.
step 3: Attempt to determine or obtain the position of the transmitter by means other than MLR. If the position is thusly obtained, then execute Procedure 2, otherwise execute Procedure 3.
step 4: Return to step 2.

Procedure 1 defines the overall operation of MLR. The secondary search method is included in step 2. When the transmitter position is provided along with a set of SOA
observations, the Host 3004 can train the MLR distribution using Procedure 2.
If a set of SOA observations is provided without the transmitter position, the Host can estimate the transmitter position using Procedure 3. In general, it is beneficial to train the MLR distribution as much as possible.
Procedure 2: MLR Training step 1: Let x, y be the known x and y co-ordinates, respectively, of the transmitter.
step 2: Compute IX = Q(x; xm;n , xmax ~ fix) Step 3: Compute IY =Q(y;ymin~Ymax~DY)~
step 4: For R~ =1, 2, 3,..., NR -1 execute step 5.
step 5: For R2 = R~ + 1, R~ + 2,..., NR execute steps 6 to 8.
step 6: If p(R~ ) =1 and li(R2 ) =1 then compute Ig =Q(SOA(R~)-SOA(Rz~Smin~Smax~OS) and increase D(R~,R2,Ix,lY,ls) by 1.
step 7: If p(R~ ) =1 and p(Rz ) = 0 and D(R~, R2, i, j, k) is nonzero for any values of i, j, and k then let Ig =Q~smax~smin,smax,~s) and increase D(R~,R2,IX,IY,Is) by 1.
step 8: If p(Ri ) = 0 and 13(RZ ) =1 and D(R~, R2, i, j, k) is nonzero for any values of i, j, and k then let IS =Q(Smin~Smin,Smax~~S~ and increase D(R~,R2,IX,ly,ls) by I.
Note that for each pass through the inner loop (steps 6-8), no change is made to D if ~i(R1)=0 and p(R2)=0.

Steps 7 and 8 incorporate a rule by which training for a pair of receivers R1, R2 is suppressed if those two receivers are unlikely to contribute to estimation. It is deemed unlikely that a pair of receivers will contribute to estimation if they have no coverage overlap, i.e. there are no previously recorded cases in which they have both detected the transmission. This rule is especially effective in limiting the size of the sparse matrix representation of the MLR distribution, D.
Procedure 3: MLR Estimation step 1: Let SP be the set of 2 dimensional likelihood distributions for position estimation of this transmission. Initialize SP to be the empty set.
step 2: Compute Nx = Q(xmax ~ xmin, xmax ~ ~x)+ 1, the number of x bins.
step 3: Compute NY = Q(ymax ~ Ymin ~ Ymax ~ DY)+ 1 , the number of y bins.
step 4: For R~ =1,2,3,..., NR -1 execute step 5.
step 5: For RZ = R~ + 1, R~ + 2,..., NR execute steps 6 through 10 inclusive.
step 6: If p(R~ ) =1 and p(R 2 ) =1 then compute IS =Q(SOA(R~)-SOA(R2~sr,~in~Smax~Os) step 7: If li(R~ ) =1 and li(R2 ) = 0 then let IS = Q(Smax ~ Smin,smax ~ OS).
step 8: If p(R~ ) = 0 and (3(R2 ) =1 then let IS = Q(Smin ~ Smin,smax ~ ~S~
step 9: If li(R1 ) =1 or li(R2 ) =1 then create the two-dimensional likelihood distribution P with elements P(Ix~IY)= ~(R1~R2~Ix~lY~ls) for 0 <_ IX < Nx , 0 <_ IY < NY .

step 10: If p(R1 ) =1 or p(R2 ) =1 then add (include, not sum) P in the set SP .
step 11: Denote the members of set SP , in any order, as P1,P2,Pg,...,PNP where NP is the number of two-dimensional likelihood distributions in Sp .
step 12: For 0 <_ IX < NX , 0 <_ IY < NY compute Pcombined(IX'IY)= ~ Pn~IX'ly~+ po = ~PI~Ix'ly~+p0~' ~P2~Ix'ly~+p0)~..(pNP
(IX,Iy)+ Po n=1 Nx_1 Nv_1 a U(IX,xmin~~x)~~Pcombined(IX'IY)~
step 13: Compute x = IX-o I N o_1 NY-1 ~Pcombined(IX'IY)~a IX=O IY=O
Nx_1 Nv_1 a U(lY, ymin' DY)' ~Pcombined(IX' IY )~
step 14: Compute y = Ix=° iY=o .
NX-1 Ny-1 ~Pcombined(IX'IY)~a IX=0 IY=0 For a given pair of receivers, steps 6 - 8 attempt to select a spatial likelihood distribution for the transmitter location, based on the observed or assumed SDOA for that receiver pair.
Step 12 combines all selected spatial likelihood distributions into a single likelihood distribution. The constant po is added to all samples to prevent a bin value of zero from completely nullifying other potentially high bin values for the same spatial region.
Steps 13 and 14 compute a moment of variable order ( a ) of the combined spatial likelihood distribution. If a =1, the first-order moment, or mean, is computed.
The preferred value of a =1.5 will yield a result which is similar to the mean, but which places increased emphasis on higher likelihood values. The MLR estimated location of the source of the transmission is given by the co-ordinates (x, jr).

Adding a new receiver to an existing MLR network can be accomplished by increasing NR by one to reflect the new number of receivers. Also, the first two dimensions of the MLR distribution D by one, and the new elements created thereby should be initialized to zero.
Deleting a receiver is accomplished by removing the elements of D
corresponding to the receiver to be deleted, and re-ordering the remaining elements so that the first two dimensions have indices from 1 to the number of receivers after deletion. NR
should be updated accordingly.
If it is known or can be determined that a receiver is currently non-operational, then it should be temporarily excluded from training and estimation so that failure to detect by the non-operational receiver under circumstances in which said receiver would normally have detected does not distort training or estimation.
If it is known or can be determined that the gain of receiver R has changed, such that all subsequent SOA measurements will be offset by a fixed amount compared to previous measurements, then the MLR distribution D should be updated by shifting all elements corresponding to receiver R to new indicies, offset along the SDOA dimension by an amount and direction corresponding to the change in gain, such that the MLR distribution may be expected to reflect the new receiver characteristics.
If it is known or can be determined that receiver R has changed in a manner which is not easily compensated for by an adjustment to the MLR distribution, then receiver R should be deleted and added to the MLR distribution in order to clear out previous training data for R, which may no longer be valid. Examples of such changes include adjustment of receiver antenna orientation or position.
In order to allow the MLR distribution to adapt to changing propagation conditions, it is desirable to implement some means by which more recent training data is more strongly weighted than other training data. The preferred means of accomplishing this is to replace each element in the MLR distribution with a fraction ~, of its previous value:

D(R~,R2,IX,IY,Ig~ ~ ~,~D(R~,RZ,Ix,IY,IS), for all elements of D.
In order to achieve a desirable balance between accumulation and diminution of training data, the preferred rule for applying the forgetting factor is to do so when the average value of nonzero elements of D exceeds a threshold Do . Do is called the Targeted Mean Distribution Value, since with continual training, the mean value of nonzero elements of D will be close to Do . When this value exceeds Dp , it will be decreased by application of the forgetting factor. When this value is less than Do , it will increase due to training.
Table 1 lists the configuration parameters for MLR, and their preferred values under anticipated or typical conditions.
parameter preferred value description sm;n -30 dB lowest SDOA bin smax +30 dB highest SDOA bin os 1 dB SDOA bin separation Xrp;~ -20,000 m lowest x co-ordinate Ymin -20,000 m lowest y co-ordinate XmaX 20,000 m highest x co-ordinate Ymax 20,000 m highest y co-ordinate ax 50 m x dimension bin size oY 50 m y dimension bin size SNRm~n 12 dB minimum SNR for successful detection origin center of the RML origin point from network which the area x co-ordinates are measured East, and y co-ordinates are measured North po 2 offset for MLR combining 0.9 MLR distribution forgetting factor Do 20 Targeted mean distribution value Table 1: Preferred Values for MLR Parameters Smax should be set to the difference, in dB, between the largest SOA observed or expected and the smallest SOA observed or expected which can be detected with reasonable confidence. This is a positive number.
sm;~ should be set the negative of smaX
os should be set to the precision with which SOA can be measured.
xmin should be set to the lowest x co-ordinate for which the ML-R system will be capable of estimating positions.
Ymin should be set to the lowest x co-ordinate for which the ML-R system will be capable of estimating positions.
Xmax should be set to the highest y co-ordinate for which the ML-R system will be capable of estimating positions.
YmaX should be set to the highest y co-ordinate for which the ML-R system will be capable of estimating positions.
An origin point is selected for the MLR network. This selection is fairly arbitrary, it merely serves as a reference for x and y position measurements.
A
preferred location of the origin is the origin of a UTM co-ordinate system. An alternative preferred location for the origin is the center of the region over which MLR is to be implemented.
For example, suppose that MLR is to be implemented over the region of the city of Calgary, Alberta, Canada, and the origin (the point with co-ordinates x=0, y=0) is selected to be a landmark in the center of the city. The MLR network area is chosen to encompass a square with sides 20 km from the origin. The spatial units selected are metres, so xmin=ymin=20000 m while xmax=ymax=20000m.
ox and oy should be set to the smallest distance along their respective dimensions over which the average SDOA is expected to vary by os . ox and oy should not be smaller than the precision of (x,y) positions used for training.
Maximum-Likelihood Region estimation as described in the preceding sections, makes use of measurements collected by multiple receivers of a transmission from a single transmitter in order to estimate the location the transmitter.
This may be more specifically identified as Reverse-Link MLR. The underlying concepts can be applied to a reciprocal situation in which a single receiver measures the SOAs of multiple signals, transmitted from multiple transmitters. This embodiment is particularly applicable to cellular standards in which the mobile units measure and report signal strengths of pilot or beacon signals from multiple cell sties or sectors. Such is the case with IS-136 TDMA and GSM, in which the mobile searches for control signals from potential handoff candidates in idle timeslots.
Forward-Link MLR should include a correction factor for variations in the transmit power of signals for which SOA measurements are made. This affords an opportunity to utilize absolute SOA, rather than SDOA measurements.
In Forward Link MLR, the role of the transmitter (from Reverse Link MLR) is replaced by a single receiver, also called the mobile unit, and the SOA
reported by each receiver (in Reverse Link MLR) is replaced by the SOA from one of the many transmitters, potentially measured and reported by the single receiver.
Another alternative embodiment of MLR incorporates both forward link and reverse link measurements. The object of such a system is to determine the location of a mobile unit which both transmits and receives. This can be done by implementing Reverse Link MLR, and treating each forward link SOA (measured at the mobile unit) as an additional receiver represented in the MLR likelihood distribution.
MLR can be readily extended to additional dimensions - spatial, temporal, or otherwise, beyond the two (x,y) described previously TDOA measurements can be used in place of or in addition to SDOA
measurements, in MLR.
In the preferred embodiment of this invention, the observations SOAR) are used, while the other observations, TOA(R), FOA(R), SNR(R), and POA(R) are not used. However, they may be incorporated in alternative embodiments after the fashion of SOAR) as described in the preferred embodiment.
In an embodiment in which the transmit power of the transmitter is known or can be determined, the use of SOA measurements directly rather than SDOA
measurements may enhance the performance of the system. The system may be further enhanced by using a combination of both SOA and SDOA.
In yet another embodiment of the invention, diverse signal measurements associated with both forward and reverse link signals can be incorporated training and estimation with a MLR distribution.
The preferred embodiment for the invention incorporates a cellular 2o communications network, consisting of multiple base stations and mobile transceivers. However, the invention can be generalized to one or more transmitting devices and a collection of receivers that are capable of receiving signals from the transmitting devices. One alternative embodiment of the invention would be a collection of transmitting devices each capable of transmitting a signal with specified characteristics on demand or at regular intervals, and a collection of receivers, each located near a cellular base station, each receiver being capable of receiving transmissions from said transmitters.
In the preferred embodiment of the invention, D is implemented as a sparse array ( DS ) in order to achieve efficient storage. DS is organized as a two-dimensional array having 6 columns, and a number of rows equal to the number of nonzero elements in D. The six elements of each row if DS represent the 5 indices and the (nonzero) value of one element of D. Any element of D not represented by a row of DS has a value of zero. This storage method is efficient for storing a dimensional array for which most of the elements have a value of zero, as is the expected case for the MLR Distribution. Nonetheless, the implementation of the this invention is fairly independent of whether D is stored as a full 5-dimensional array or as a sparse array.
The quantization of observations is a rule by which an unquantized observation is associated with a quantized observation. In the preferred embodiment, a quantization scheme consisting of uniform intervals defined by a few configuration parameters is used. Alternative embodiments may incorporate other means of quantization, including non-uniform levels and levels which are adapted to the nature of the observed data.
In yet another embodiment of the invention, the transmitter emits transmissions at semi-regular or predictable intervals. Receivers in the secondary search set are not required to store or buffer the received signal. A primary detection report triggers a secondary search of a subsequent transmission, the time of which is either a fixed offset from the first transmission, or can be predicted from the first transmission.
Instructions for a computer to carry out each of the algorithms described here, including the secondary search, grouped coherent detection, and the procedures A 10 for FML-AOA, and procedures 1-3 for MLR, as well as the procedures for precise positioning of a transmitter, may be stored on computer readable media, loaded into a general purpose computer or hardwired into a special purpose digital processor.

Claims (114)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A method of locating a transmitter with respect to a receiver, where the transmitter is in communication with the receiver, the method comprising the steps of:
a) storing, in a database, a first set of likelihood functions, each likelihood function comprising a series of values representing the probability that a measure of location corresponds to a value of a first signal parameter, the first signal parameter being a function of a measured characteristic of signals received at the receiver;
b) receiving signals at the receiver from the transmitter;
c) estimating a value of the first signal parameter from the received signals;
and d) locating the transmitter with respect to the receiver by determining a measure of location which, by reference to the likelihood functions for the first signal parameter, corresponds to the estimated value of the first signal parameter.

2. The method of claim 1 further including the step of:
storing, in a database, a second set of likelihood functions, each of the second set of likelihood functions comprising a series of values representing the probability that a measure of location corresponds to a value of a second signal parameter, the second signal parameter being a function of a measured characteristic of signals received at the receiver;
estimating a value of the second signal parameter from the received signals;
and resolving ambiguities in the location of the mobile transmitter by reference to the likelihood function corresponding to the estimated value of the second signal parameter.

3. The method of claim 2 in which resolving ambiguities in the location of the transmitter with respect to the receiver comprises combining the likelihood function corresponding to the estimated value of the first signal parameter and the likelihood function corresponding to the estimated value of the second signal parameter.

4. The method of claim 3 in which combining the likelihood functions comprises multiplying the likelihood functions.

5. The method of claim 1 in which ambiguities in the location of the transmitter with respect to the receiver are resolved by reference to measures of location based on signals received at additional receivers.

6. The method of claim 5 in which the measure of location is the angle of arrival of the received signals.

7. The method of claim 5 in which the first signal parameter is a function of the phase of the received signals.

8. The method of claim 5 in which the first signal parameter is the difference of the phase of received signals.

9. The method of claim 5 in which the first signal parameter is a function of the strength of the received signals.

10. The method of claim 5 in which the first signal parameter is the ratio of the strength of received signals.

11. The method of claim 2 in which:
the measure of location is the angle of arrival of the received signals;
the first signal parameter is a function of the phase of the received signals;
and the second signal parameter is a function of the strength of the received signals.

12. The method of claim 1 in which the likelihood functions are constructed by an adaptive procedure.

13. The method of claim 12 in which:
the likelihood functions are constructed by defining distinct bins, each bin being bound by corresponding upper and lower bounds of the measure of location and the first signal parameter; and a bin is incremented in value when, for a transmitter with a known measure of location with respect to the receiver and a measured first signal parameter, the known measure of location and measured first signal parameter fall within the upper and lower bounds of the bin.

14. The method of claim 1 in which the likelihood functions are trained using a different signal parameter from the first signal parameter.

15. The method of claim 14 in which the likelihood functions are stored at monitoring sites and the likelihood functions are trained when the monitoring sites are otherwise idle.

16. The method of claim 1 in which the likelihood functions are initialized by estimates.

17. The method of claim 1 further comprising repeating steps b, c and d of claim 1 several times to obtain several estimates of the measure of location and obtaining a value for the measure of location from the several estimates.

18. The method of claim 17 in which obtaining a value for the measure of location comprises obtaining the mean of the several estimates.

19. The method of claim 1 in which the receiver is mobile, the transmitter has known location and signals are received at plural antennas at the receiver.

20. The method of claim 1 in which the transmitter is mobile, the receiver has known location and the signals are received at plural antennas.

21. The method of claim 1 in which the antennas are located at plural monitoring sites, and the receiver is at one of the monitoring sites.

22. The method of claim 1 in which the transmitter is a mobile transceiver.

23. The method of claim 1 in which the transmitter transmits in response to a page from a monitoring site.

24. The method of claim 1 in which, after the receiver has received a signal from the transmitter, at least another receiver is instructed to detect transmissions from the transmitter.

25. The method of claim 1 in which signals from the transmitter are received at an initial set of receivers, and upon detection at the initial set of receivers, a second set of receivers is instructed to detect the transmission.

26. A method of locating a mobile transmitter in relation to a monitoring site having at least first and second antennas, the method comprising the steps of:
a) storing, in a database, a first set of likelihood functions, each likelihood function comprising a series of values representing the probability that a measure of location corresponds to a value of a first signal parameter, the first signal parameter being a function of signals received at the first and second antennas;
b) receiving received signals at the first and second antennas;
c) estimating an estimated value of the first signal parameter from the received signals; and d) locating the mobile transmitter by determining a measure of location which, by reference to the likelihood functions for the first signal parameter, corresponds to the estimated value of the first signal parameter.

27. The method of claim 26 further including the step of:
storing, in a database, a second set of likelihood functions, each of the second set of likelihood functions comprising a series of values representing the probability that a measure of location corresponds to a value of a second signal parameter, the second signal parameter being a function of signals received at at least one of the first and second antennas;
estimating an estimated value of a second signal parameter from the received signals; and resolving ambiguities in the location of the mobile transmitter by reference to the likelihood function corresponding to the estimated value of the second signal parameter.

28. The method of claim 27 in which resolving ambiguities in the location of the mobile transmitter comprises combining the likelihood function corresponding to the estimated value of the first signal parameter and the likelihood function corresponding to the estimated value of the second signal parameter.

29. The method of claim 28 in which combining the likelihood functions comprises multiplying the likelihood functions.

30. The method of claim 29 in which resolving ambiguities in the location of the mobile transmitter is resolved by reference to measures of location based on signals received at additional monitoring sites.

31. The method of claim 26 in which the measure of location is the angle of arrival of the received signals.

32. The method of claim 26 in which the first signal parameter is a function of the phase of the received signals.

33. The method of claim 26 in which the first signal parameter is the difference of the phase of the received signals at the first and second antennas.

34. The method of claim 26 in which the first signal parameter is a function of the strength of the received signals.

35. The method of claim 26 in which the first signal parameter is the ratio of the strength of the received signals at the first and second antennas.

36. The method of claim 27 in which:
the measure of location is the angle of arrival of the received signals;
the first signal parameter is a function of the phase of the received signals;
and the second signal parameter is a function of the strength of the received signals.

37. The method of claim 26 in which the likelihood functions are constructed by an adaptive procedure.

38. The method of claim 37 in which:

the likelihood functions are constructed by defining distinct bins, each bin being bound by corresponding upper and lower bounds of the measure of location and the first signal parameter; and a bin is incremented when, for a mobile transmitter with a known measure of location and a measured first signal parameter, the known measure of location and measured first signal parameter fall within the upper and lower bounds of the bin.

39. The method of claim 26 in which the likelihood functions are trained using a different signal parameter from the first signal parameter.

40. The method of claim 26 in which the likelihood functions are trained when the monitoring site is otherwise idle.

41. The method of claim 26 in which the likelihood functions are initialized by estimates.

42. The method of claim 26 further comprising repeating steps b, c and d of claim 26 several times to obtain several estimates of the measure of location and obtaining a value for the measure of location from the several estimates.

43. The method of claim 42 in which obtaining a value for the measure of location comprises obtaining the mean of the several estimates.

44. A method of locating a mobile transmitter, the method comprising the steps of:
detecting a transmission from a mobile transmitter at several receivers;
grouped-coherent detecting the transmissions to yield a derived signal; and processing the derived signal to find the location of the mobile transmitter.

45. The method of claim 44 in which grouped-coherent detecting the transmissions comprises:
selecting trial values of the time of arrival of the transmission at a monitoring site over a time interval;
correlating the transmission with the trial values over plural subintervals of the time interval to yield subinterval correlations;
coherently combining the subinterval correlations at trial frequencies to yield a set of values of a function z(~, F) where ~ is a time estimate and F is a frequency estimate; and selecting one of the time estimates and one of the frequency estimates as the time and frequency of arrival of the transmission.

46. The method of claim 45 in which the selected one of the time estimates is the time estimate yielding a maximum value of z(~, F) and the selected one of the frequency estimates is the frequency estimate yielding a maximum value of z(~, F).

47. The method of claim 45 in which coherently combining the subinterval correlations comprises computing a Fast Fourier Transform over the subinterval correlations.

48. The method of claim 45 further comprising refining the time of arrival estimate by computing subinterval correlations with a finer spacing of trial values.

49. The method of claim 44 further comprising finding the rising edge of the transmitted signal as it is received by the receivers.

50. The method of claim 45 in which the phase of arrival of the transmitted signal is detected by coherently combining the subinterval correlations without magnitude squaring.

51. The method of claim 45 in which the strength of arrival of the transmitted signal at the receivers is defined as a function of the maximum value of z(~, F).

52. A method for estimating the angle at which a group of two or more transmitters of wireless signals lies with respect to a receiver of wireless signals, in which the difference in strengths of the two received signals is used to compute or select the most likely angle.

53. The method of claim 52 in which a set of numbers representing the likelihood for various angles is selected, from a number of such sets, which has an associated difference in signal strengths which is closest to the observed difference of signal strengths.

54. The method of claim 53 in which failure to detect one of the two signals is interpreted as a fixed difference in signal strength.

55. The method of claim 54 in which multiple pairings of transmitting antennas are used to select multiple sets of numbers representing likelihood of angles of arrival, and the selected sets are combined into one set from which the Angle of arrival is estimated.

56. A method for generating a set of numbers representing the two-dimensional likelihood distribution with respect to difference in strength of arrival and angle of arrival, for a receiver which receives signals from multiple transmitters, in which the observations of pairings of difference in strength of arrival and angle of arrival are made, and for each observation, the element within the distribution most closely associated with the observed difference in strength of arrival and angle of arrival is increased.

57. The method of claim 56 in which said element is increased by a fixed quantity.

58 The method of claim 57 in which said element is increased by a quantity which is the result of a monotonic function of the confidence in the observed angle of arrival and difference in strength of arrival.

59. The method of claim 53 in which the sets of numbers are initialized according to typical antenna gain patterns based on the azimuths and possibly including the sector widths of the transmitting antennas.

60. The method of claim 53 in which the two-dimensional distribution is initialized with piecewise linear segments having endpoints at the azimuths of the transmitting antennas.

61. The method of claim 56 in which the angle of arrival is computed from the known coordinates of the transmitter station, and the coordinates of the receiver as determined by the Global Positioning System.

62. The method of claim 56 in which the angle of arrival is computed from the known coordinates of the transmitter station, and the coordinates of the receiver as determined by time difference of arrival of signals transmitted from a transmitter situated with said receiver, and said signals are received at various other locations, possibly including that of the first group of transmitters.

63. The method of claim 53 in which said set of numbers is selected from a likelihood distribution generated by:
making observations of pairs of difference in strength of arrival and angle of arrival, and for each observation, an element within a probability distribution most closely associated with the observed difference in strength of arrival and angle of arrival is increased.

64. The method of claim 63 further comprising smoothing the probability distribution.

65. A method for estimating the angle, relative to some reference angle, between the location of an antenna receiving wireless signals and a group of two antennas transmitting wireless signals, in which the difference in phases of the two received signals is used to compute or select the most likely angle.

66. The method of claim 65 in which a set of numbers representing the likelihood for various angles is selected, from a number of such sets, which has an associated difference in signal phases which is closest to the observed difference of signal phases.

67. The method of claim 66 in which multiple pairings of transmitting antennas are used to select multiple sets of numbers representing likelihood of angles of arrival, and the selected sets are combined, in a suitable manner, into one set from which the Angle of arrival is estimated.

68. The methods of any one of claims 53 and 66 in which multiple pairings of transmitting antennas are used to select multiple sets of numbers representing likelihood of angles of arrival, some sets with respect to difference in observed signal strength, some sets with respect to difference in observed phases, and the selected sets are combined, in a suitable manner, into one set from which the angle of arrival is estimated.

69. A method for generating a set of numbers representing the two-dimensional likelihood distribution with respect to difference in phase of arrival and angle of arrival, for a receiver which receives signals from multiple transmitters, in which the observations of pairings of difference in phase of arrival and angle of arrival are made, and for each observation, the element within the distribution most closely associated with the observed difference in phase of arrival and angle of arrival is increased.

70. The method of 69 in which said element is increased by a fixed quantity.

71. The method of claim 69 in which said element is increased by a quantity which is the result of a monotonic function of the confidence in the observed angle of arrival and the difference in strength of arrival.

72. The method of claim 69 in which the angle of arrival is computed from the known coordinates of the transmitter station, and the coordinates of the receiver as determined by the Global Positioning System.

73. The method of claim claim 69 in which the angle of arrival is computed from the known coordinates of the transmitter station, and the coordinates of the receiver as determined by the time difference of arrival of signals transmitted from a transmitter situated with said receiver, and said signals are received at various other locations, possibly including that of the first group of transmitters.

74. The method of claim 66 in which said set of number is selected from the likelihood distribution of claim 69.

75. The method of claim 52 applied to transmitting antennas having different polarizations.

76. The method of claim 56 applied to training using forward-link trilateration.

77. A method for estimating the position of a wireless transmitter in which the difference in strengths of arrival of the signal transmitted by said transmitter at one or more pairs of receivers is used to select the a position.

78. The method of claim 77 in which a set of numbers P(ix,iy) representing the likelihood of various positions is selected from among a number of such sets, and the means of selection is to choose the set which has an associated SDOA closest to the observed SDOA.

79. The method of claim 78 in which failure to detect at one of a pair of receivers is optionally interpreted as a fixed difference in signal strength.

80. The method of claim 79 in which all possible pairings of receivers for which at least one receiver detected the transmission are used to select a set of numbers P(ix,iy), and the sets of numbers are combined in a suitable manner into one set from which the position of the wireless transmitter is estimated.

81. The method of claim 80 in which the sets of numbers P1(ix,iy), P2(ix,iy),...(etc.) are combined by adding a fixed number p0 to each number of each set, and the product is taken all sums having the same indicies (ix,iy) in order to yield a single set of numbers P combined(i x,i y).

82. The method of claim 81 in which the (x,y) position estimate is first-order moment of the single resultant set of numbers P combined(i x,i y), transformed by scaling and offseting into the co-ordinate system represented by the quantized co-ordinates (ix,iy)

83. A method for generating a set of numbers D(ir1,ir2,is,ix,iy) representing the likelihood of association of an observed SDOA (is) for the pair of receivers (ir1,ir2) with a known or likely transmitter position (ix,iy) in which the number D(ir1,ir2,is,ix,iy) is increased in response to an observation (ir1,ir2,is,ix,iy).

84. The method of claim 83 in which D(ir1,ir2,is,ix,iy) is increased by a fixed amount in response to an observation (ir1,ir2,is,ix,iy).

85. The method of claim 83 in which D(ir1,ir2,is,ix,iy) is increased by a quantity which is the result of a monotonic function of a measure of confidence, such as SNR, of the observation (ir1,ir2,is,ix,iy).

86. A method of locating a mobile transmitter, the method comprising the steps of:
detecting signals transmitted from the mobile transmitter and received at a first receiver;
upon detecting signals from the mobile transmitter at the first receiver, instructing at least a second receiver to search for and detect signals transmitted by the mobile transmitter; and locating the mobile transmitter by processing signals received at the first and second receivers.

87. The method of claim 86 in which signals from the mobile transmitter are received at an initial set of receivers, and upon detection at the initial set of receivers, a second set of receivers is instructed to search for and detect the signals from the mobile transmitter.

88. The method of claim 86 in which the second receiver is instructed to search for the mobile transmitter using characteristics of the signal received at the first receiver.

89. A method of detecting a transmission from a mobile transmitter, the method comprising the steps of:
detecting a transmission from a mobile transmitter at several monitoring sites to produce a received signal having an observation period;

correlating the received signal with a sought signal over subintervals of the observation period to produce subcorrelation results;
filtering the subcorrelation results to remove signal components outside of a range of preselected frequency offsets to produce filtered subcorrelation results; and noncoherently combining the filtered subcorrelation results to produce a time of arrival estimate.

90. Computer readable media comprising instructions for a computer to carry out a wireless location procedure selected from the group consisting of the MLR
procedures A1-A10 and 1-3.

91. A host computer programmed to carry out a wireless location procedure selected from the group consisting of the MLR procedures A1-A10 and 1-3.

92. Apparatus programmed to carry out any of the methods of any one of the preceding claims.

93. Computer readable media containing instructions for a computer to carry out any of the methods of any one of the claims 1-89.

94. A method of locating a transmitter, the method comprising the steps of:
receiving at multiple sites a signal from the transmitter;
processing the signal to yield observations of a first signal parameter corresponding to the received signal at each of the sites; and applying a wireless location algorithm to the observations to yield an estimate of the location of the transmitter, in which wireless location algorithm the observations are weighted according to reliability of the corresponding received signal.

95. The method of claim 1 in which the wireless location algorithm is an iterative minimizing algorithm.

96. The method of claim 2 in which the iterative minimizing algorithm minimizes the sum of the squares of residual adjustments to the observations that are required to produce a solution.

97. The method of claim 3 further comprising the step of:
finding the received signal strength for each of the received signals to yield a received signal strength corresponding to each observation; and the observations are weighted according to the received signal strength of the corresponding received signal.

98. The method of claim 4 in which an observation is excluded from processing when the observation is a blunder.

99. The method of claim 5 in which a selected one of misclosures and standardized residuals is used to flag observations that may be a blunder.

100. The method of claim 4 further comprising the step of:
excluding observations from application of the iterative minimizing algorithm when inclusion of an observation increases the standard deviation of the estimate of the location of the transmitter more than the dilution of precision of the estimate of the location of the transmitter.

101. The method of claim 2 in which a selected one of Chaffee's method, location on the conic axis and both Chaffee's method and location on the conic axis are used to detect solution bifurcation.

102. The method of claim 2 in which a selected one of location on the conic axis, plane intersection and both location on the conic axis and plane intersection are used to provide an initial position for an iterative algorithm.

103. The method of claim 1 in which each observation is the time difference between arrivals of the received signal at pairs of sites.

104. The method of claim 2 in which the iterative minimizing algorithm begins with an initial position based on the known locations of the sites.

105. A method of locating a mobile transmitter, wherein the mobile transmitter consists of a transmitter without audio section, the method comprising the steps of:
receiving signals from the mobile transmitter that are transmitted on cellular frequencies; and processing the signals to estimate the location of the mobile transmitter.

106. A method of locating a mobile transmitter, the method comprising the steps of:

receiving signals from the mobile transmitter at plural receiving locations and processing the received signals to obtain a set of observations of first signal parameters; and identifying observations that are blunders;
removing blunders from the set of observations; and estimating the location of the mobile transmitter from the set of observations from which blunders have been removed.

107. The method of claim 13 in which observations are removed when inclusion of an observation increases the standard deviation of the estimate of the location of the mobile transmitter more than the dilution of precision of the estimate of the location of the mobile transmitter.

108. A method of locating a mobile transceiver having a ringer, the method comprising the steps of:
turning the ringer off;
paging the mobile transceiver;
instructing the mobile transceiver to transmit a signal;
receiving the signal from the mobile transceiver at a monitoring site; and processing the signal received at the monitoring site.

109. A method of locating a mobile transmitter making a 911 call to a PSAP, the method comprising the steps of:
receiving at a PSAP a 911 call made by a mobile transmitter; and locating the mobile transmitter while the PSAP is in unanswered conversation mode.

110. Computer readable media comprising instructions for a computer to carry out a wireless location algorithm in which processing of observations of a received signal are weighted according to the received signal strength of the received signal.

111. A host computer programmed to carry out a wireless location algorithm in which processing of observations of a received signal are weighted according to the received signal strength of the received signal.

112. Computer readable media comprising instructions for a computer to carry out a wireless location procedure selected from the group consisting of the procedures I, IA, IB, II, IIA, IIB, III, IIA, IIB, IV, IVA, IVB and V.

113. A host computer programmed to carry out a wireless location procedure selected from the group consisting of the procedures I, IA, IB, II, IIA, IIB, III, IIA, IIB, IV, IVA, IVB and V.

114. A method of locating a wireless transmitter selected from the group consisting of the procedures I, IA, IB, II, IIA, IIB, III, IIA, IIB, IV, IVA, IVB and V.