CN104871615A - Method for determining powers and locations of radio transmitters - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0205—Details
- G01S5/0242—Determining the position of transmitters to be subsequently used in positioning
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
- H04W64/003—Locating users or terminals or network equipment for network management purposes, e.g. mobility management locating network equipment
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Abstract
The present invention relates to a method for determining powers and locations of j=1,..., K numbers of radio transmitters based on a plurality of received signal strengths measured at i=1,..., N s number of sensors, where K and N s are positive integers and K>= 2 and N s>=1, respectively; the method comprising the step of: using the expectation-maximization (EM) method for determining the powers P j and locations X j of the j=1,..., K numbers of radio transmitters based on the plurality of received signal strengths measured at the i=1,..., N s number of sensors. Furthermore, the invention also relates to a computer program, a computer program product, and a central processing unit thereof.
Description
Technical Field
The present invention relates to a method for determining the power and position of a radio transmitter. Furthermore, the invention relates to a computer program, a computer program product and a central processing unit thereof.
Background
Passive transmitter positioning via sensor networks is an important issue in many wireless applications, as positioning of unknown radio sources is likely to become a critical component in future generation wireless communication networks. A central control panel or other associated wireless network management entity is given the ability to sense and record wireless activity in the surrounding environment, and corresponding actions can be efficiently planned, decided and executed through their network.
In general, environmental awareness with location information of unknown transmitters is likely to become very important in future ad hoc networks, where power, frequency or other critical wireless parameters are (automatically) adapted, e.g. based on environmental information collected from large sensor networks and their related measurements ("observations", "observation data"). For example, next generation cellular networks may benefit from such ad hoc capabilities by increasing cost efficiency (reducing operating cost, OPEX) and by increasing spectrum and energy efficiency.
Benefits may be obtained by both the operator and the administrator; the former improves network operation, and the latter detects and locates malicious and unauthorized spectrum users.
Most designs and expectations regarding future cellular networks predict that the number of wireless transmitters will increase substantially. One key contributing factor to providing higher data rates is the densification of the network infrastructure, i.e., more transmitters per unit area.
FIG. 1 illustrates a problem scenario addressed by the present invention. In the area of interest, two or more active wireless transmitters operate in a certain frequency band. The location, power, type, or any other relevant parameter of these wireless transmissions is unknown. The number of active wireless transmitters is also unknown. There may be a large number of distributed sensors performing measurements of Received Signal Strength (RSS) produced by these unknown transmitters at respective sensor locations and forwarding these respective measurement data to the central network node. The forwarded measurement data may contain relevant tags such as time of measurement, frequency band of measurement, location/coordinates of the sensor, etc.
A common problem that arises in these multiple transmitter scenarios is that: distinguishing the measured RSS components generated by different wireless transmitters is highly complex. This complicates the multi-emitter positioning problem.
The problem then is to accurately determine the unknown number, unknown power(s), and unknown location(s) of wireless transmitters in the area.
RSS-based transmitter location technique(s) are the most popular techniques due to their simplicity and ability to be directly applied to off-the-shelf wireless hardware. However, the literature fully addresses the single-source localization problem in the multi-source case where less attention is paid due to inherent difficulties arising from the following reasons:
i. commercial scenarios lacking multiple non-orthogonal sources overlapping in the same frequency band; and
a rather high cost for deploying a large number of sensors, which is a prerequisite for accurate positioning.
However, the potential for cognitive wireless applications (see coexistence issues in IEEE 802.19 and 802.22) coupled with the cost reduction of sensors is changing reality. There are several approaches to solving the positioning problem in the prior art.
ML estimation
Maximum Likelihood (ML) is a popular estimation method due to its asymptotic optimality. However, the likelihood function in a lognormal propagation environment typically has multiple maxima, thus creating a non-convex optimization problem. This becomes the most obvious disadvantage of the ML method. The standard techniques for such non-convex optimization tend to be very complex. In addition, the computation grows exponentially with the number of sources, which is another major drawback of the ML estimation method.
The problem of local maxima for a single source has been solved by convex set Projection (POCS). The algorithm has low complexity, is robust to local maxima, and has distributable computations. The distance estimation also employs RSS, but the algorithm can also be used for any positioning method where sensor source distance estimates are available in some way. This method, which is referred to as "round robin" POCS, works well when the (single) source node is located inside the convex sensor hull defined by the peripheral nodes in the sensor network. The method also requires knowledge of parameters such as path loss and transmission power. The disadvantage of this solution is that it only addresses the single source case.
Another approach for addressing the non-convexity of conventional ML is the semi-definite programming (SDP) relaxation technique. The idea here is to transform the non-convex quadratic distance constraint into a linear constraint by introducing a relaxation that removes the quadratic term in the formula. This SDP method has only been applicable to the single source case. In addition, the transmit power of the wireless transmitter must be known.
Method for using simplified channel model and known number of sources
For multiple sources, research has focused primarily on the AWGN model, which is effective for acoustic sources. The same AWGN model has been applied in wireless applications, but this is an oversimplification of the lognormal shadow environment. Other prior art proposes global optimization methodologies. Clustering algorithms have been introduced based on k-means for enhancing convergence and reducing overall complexity. For the same AWGN model, a quasi-EM approach has been proposed. All of the above techniques assume knowledge of the number of sources. Intrinsic sparsity (small number of sources, large number of measurements) has been adopted in order to improve the estimation method by appropriately modifying at least the absolute contraction and selection operator (LASSO).
Grid-based method
The first attempt at maturing ML is by approximating the sum of lognormal random variables. The problem of unknown number of sources is solved by placing a large number of hypothetical sources on the grid (i.e., each grid point corresponds to one potential source), resulting in an over-fitting problem. The mentioned overfitting problem leads to poor performance.
Other methods
Other prior art approaches address this problem by employing deterministic methods. The disadvantage here is that shadow fading is not taken into account and the robustness of the method in such an environment becomes poor.
Accordingly, there is a need in the art for an improved method for determining the power and location of wireless transmitters in an area.
Disclosure of Invention
It is an object of the present invention to provide a solution that alleviates or solves the disadvantages and problems of the prior art solutions. It is a further object of the present invention to provide a simplified solution to the above-mentioned problems.
According to a first aspect of the invention, the above mentioned object is achieved by a method comprising: based on the equation i 1SPower and position of K wireless transmitters are determined from a plurality of received signal strengths measured at the sensors, where K and N aresAre respectively positive integers, and K is more than or equal to 2 and NsNot less than 1; the method comprises the following steps:
using an expectation maximization method for a method based on a maximum of 1SThe power P of K wireless transmitters is determined from a plurality of received signal strengths measured at each sensor to determine j 1jAnd position Xj。
Preferred embodiments of the invention are defined in the appended dependent claims. Any of the methods according to the present invention may be implemented as a computer program in a processing device and may be included in a computer program product.
According to a second aspect of the invention, the above mentioned object is achieved with a central processing unit comprising processing means for processing data and a memory for storing dataAn apparatus, and further comprising receiving means and transmitting means for receiving and transmitting data, respectively, the central processing unit being arranged to determine the value of the parameter based on the value of 1SPower and position of K wireless transmitters are determined from a plurality of received signal strengths measured at the sensors, where K and N aresAre respectively positive integers, and K is more than or equal to 2 and Ns≧ 1, the central processing unit is further arranged to use an expectation maximization method for a maximum value based on a maximum value of 1SThe power P of K wireless transmitters is determined from a plurality of received signal strengths measured at each sensor to determine j 1jAnd position Xj。
The present invention provides a scheme with improved computational complexity (e.g., relative to a mature ML method). In addition, compared with the prior art, the scheme has better performance in the aspect of higher accuracy of the estimated value.
Further applications and advantages of the present invention will become apparent from the detailed description that follows.
Drawings
The attached drawings are intended to illustrate and explain various embodiments of the present invention, in which:
fig. 1 shows an example problem scenario for 2 wireless transmitters and 5 sensors, in which these 2 transmitters operate at unknown locations in an area. The 5 distributed sensors measure the received signal strength from the wireless transmitter and forward the measurements to the central processing unit; and
fig. 2 shows a flow chart of an embodiment of the invention.
Detailed Description
To achieve the above and other objects, the present invention relates to the following methods: the power and location of active wireless transmitters in an area is determined based on received signal strengths measured at a plurality of sensors distributed over the area. As mentioned above, this particular problem leads to a very complex mathematical problem, but the method provides a simplified model that makes it possible to solve the problem.
Referring to the problem statement, the received power at sensor i using a linear scale is (lower case letters indicate linear scale) is:
where K is the number of wireless transmitters (radio frequency sources) in the area. Position SiThe slave distance d of the ith sensori，jAt a transmission power of PjReceived energy RSS of source ji，j(capital letters indicate dB scale) is
RSSi，j＝Pj+L0-PL(xj，si)+ni，j (2)
Wherein L is0Is referred to the path loss and ni，jIs having a varianceIs the lognormal shadow fading component of (b), PL (x)j，si) Is a suitable deterministic path loss function. One possible choice for this function is:
wherein d is0Is a reference distance, typically close to the selected transmitter, such that d0Path loss equal to L (in free space)0And α is the path loss index.
Equation (1) becomes the sum of lognormal variables by equation (2), and in the case of approximating calculation (1) using the standard gaussian approximation of the sum of lognormal variables, the received power at sensor i is distributed with the mean μiSum varianceGaussian function of (d):
the mean and variance are:
and
wherein
mi，j(θj)＝Pj-PL(xj，si) (6)
Is the average energy received at the ith sensor when only the jth source is active, θ ═ x1，y1，P1，x2，y2，P2，...，xK，yx，PK]Is the 3K length vector (x-coordinate, y-coordinate and power) of the parameter to be estimated,is a common shadow fading variance, andnormalized constants are scaled in dB.
By means of such a signal model, the problem solved by the invention is then to find the (large) number NsIndividual observed values rssiThe position and power collected by the medium vector theta. N is a radical ofsEach of the sensors gives one such observation.
One solution to this problem is found by the ML estimation method, which involves minimization of a negative log-likelihood function with respect to θ (see [ 14 ]):
whereinIs a vector of observation measurements, an
Wherein N issIs the number of sensors in the area. This minimization (search θ) involves a non-convex optimization of dimension 3K with multiple minima. In general, this minimization is very complicated.
However, the inventors have enforced an approximation for each received power sample, which allows mapping the original problem to a Gaussian Mixture Model (GMM) fitting problem. GMM is a probability model that represents the occurrence of several gaussian variables at the bottom of the observed data. It is a probabilistic model for representing the existence of sub-populations within the overall population, and does not require observation data sets to identify which individual observation a sub-population belongs to. Each observation data sample is modeled as having been generated from one of a set of gaussian distributions (typically with different means and variances); however, it is not known by which generation is being made within the time of observation. The process of relating collected observations to these distributions and also finding their corresponding moments is often referred to as "clustering". In general, GMM involves a random variable y modeled as a weighted sum of gaussian variables, namely:the model represents not only the mean and variance of the component gaussian distributions, but also the prior probability (or prior mixing weight) of each component, which is indicative of the prior probability that the observation sample originated from that particular component.
The approximation includes assigning a dominant source to each sensor. If it is assumed that a single source contributes most of the measured power to each sensor:
rssi≈maxjrssi，j (9)
empirical practice has shown that this is effective, especially for indoor scenarios where the path loss is a high number. For example, assume that the sensor is at approximately the same distance from two equivalent power sources. The total received power will be just 3dB higher than the single source case. These 3dB fall well within the standard deviation of the usual indoor shading. In this hypothetical case, the model becomes the GMM. That is, using equation (9) (in dB), the measurement is then approximated as NsIndividual sample of identical distribution (it is derived from having K correlation parametersThe GMM of the component of).
Furthermore, it is assumed that each signal measurement originates from exactly one of the unknown gaussian distributions. The mean of the K components is parameterized by i, since the mean of each mode at the ith sensor depends on its position.
Unknown parameter mu applied to estimate GMMj、And wjThe EM algorithm of (A) is
Where it is applied to the specific case where the variance of all gaussian components is the same (i.e. for all j,) The positioning problem and model derived in the previous section.
Then, the log-likelihood function of GMM in equation (10) is
Where the variance is no longer a function of distance because the shadows of all emitters are modeled as being the same.
Thus, by careful study of the above problem and by the above mentioned assumptions, the ML problem can now be solved using the EM algorithm. Thus, by using the EM algorithm on the signal strength measured at the sensor, the above problem can be solved as a simpler ML problem, i.e. (GMM). It should be noted that the EM algorithm has never been used before to solve this type of problem.
The method steps of an embodiment of the present invention (for a fixed number of wireless transmitters) are given in the flow chart of fig. 2 and table I below.
Table 1: n for channel model in equation (2)sEM-GMM based positioning algorithm for K wireless transmitter sources in a sensor survey (where d0And L0Is the reference distance and power loss, α is the path loss exponent, and the variance of the lognormal shadow fading component is)。
In a first initialization step, the vector θ and the weights w are calculated (e.g. randomly)jOf the position and power. These initialization values completely determine the RSS. A (scalar) likelihood of such an initial solution theta is also calculated.
In a desired step, for a hypothetical RSS, the probability that the measurement i is caused by the wireless transmitter j is calculated.
In the maximization step, nowRecalculating estimates of position and power in the vector θ and the sum weight w using the resulting probabilities in the desired stepjAn estimate of (d).
In the convergence step, a scalar likelihood of the solution θ is computed, and if such likelihood exhibits an increase above a certain threshold (which may be an arbitrarily small number heuristically chosen to control convergence), a new iteration is started by jumping back to the desired step.
The specific equations involved in each step are shown in table 1. The maximization step involves an optimization step, but, in contrast to the original ML search, this step now involves the standard non-linear weighted Least Squares (LS) problem, which is typically encountered in the problem of locating a single emitter source. Regardless of the search algorithm used to solve this optimization, the complexity of such a search only grows linearly with the number of transmitters K.
According to a preferred embodiment of the invention, the number of wireless transmitters K can also be determined, which is a further advantage with the present method. Up to now it has been assumed that the number of radio sources K is known. Since the actual number is usually not known in advance, the Akage Information Criterion (AIC) or the Minimum Description Length (MDL) theorem is applied.
The basic idea is to perform the method of table 1 for different numbers of hypothesized numbers K of transmitters and to select the number K for the one with the highest likelihood. Since likelihood increases with K, the AIK and MDL methods in the literature provide a way to normalize likelihood for K and are used in sequentially searching the stopping criteria for K. In table 2, the additional method steps of the proposed positioning algorithm without a priori assumptions about the number of radio transmitters K are summarized.
Table 2: EM-GMM localization for an unknown number of wireless transmitter sources
In either case, the EM algorithm is executed for K that is increasing continuously, starting with K ═ 1, and stopping increasing K when the criterion value stops decreasing, that is, when the following occurs:
C(K)≥C(K-1) (11)
the criterion value generally decreases when K is 1, 2 … …. However, for a specific value of K, the descent is stopped and the algorithm terminates.
According to another embodiment of the invention, the AIC is calculated as follows:
C(K)＝-L(K)+K (12)
wherein L (K) is the likelihood value calculated in step d) above.
According to yet another embodiment of the invention, the MDL is calculated as follows:
wherein L (K) is the likelihood value calculated in step d) above.
The sensors are distributed over an area and may each include only one receiving antenna. There is no limitation on the distribution of sensors in an area, so they may be, for example, random or deterministic. With respect to wireless transmitters, it is assumed that they operate in overlapping frequency bands, and often in the same frequency band. For example, the wireless transmitter may be a base station of a cellular operating system, such as LTE.
Furthermore, as will be appreciated by a person skilled in the art, any method according to the present invention may also be implemented in a computer program having code means which, when executed by processing means, causes the processing means to perform the steps of the method. The computer program is embodied in a computer readable medium of a computer program product. The computer-readable medium may include essentially any memory, such as ROM (read-only memory), PROM (programmable read-only memory), EPROM (erasable PROM), flash memory, EEPROM (electrically erasable PROM), or hard disk drive.
Furthermore, the invention relates to a central processing unit arranged to perform the method. It is thus realized that the central processing unit may be modified, suitably adapted, according to different embodiments of the method.
The central processing unit comprises processing means for processing the data and memory means for storing the data, and further comprises suitable means, such as receiving means and transmitting means for receiving and transmitting data, such as received signal strength measured at the sensor. The present device is further arranged to use the EM method described above for determining the power P of a plurality of wireless transmitters based on a plurality of received signal strengths measured at the sensorjAnd position Xj。
The central processing unit may be integrated into a communication node of a Radio Access Network (RAN), such as a base station or a radio network controller, according to an embodiment. Costs can be reduced by integrating the central processing unit into the communication nodes of the RAN.
However, the central processing unit may also be implemented in, and become part of, an operation and management (Q & M) entity controlled by the mobile operator instead. Thus, information about the number, location and power of wireless transmitters is directly available at the network layer, which means that the information can be used for benign operation and management of the wireless network.
Finally, it is to be understood that the invention is not limited to the embodiments described above, but relates to and incorporates all embodiments within the scope of the appended independent claims.
Claims (20)
1. A method for processing a signal based on the method disclosed in 1SMethod for determining the power and position of K radio transmitters, where K and N are measured at a plurality of received signal strengths measured at a sensor to determine j 1SAre respectively positive integers, and K is more than or equal to 2 and NsThe method comprises the following steps:
using an expectation-maximization (EM) method for a data transmission based on a data transmission scheme selected at said i ═ 1SDetermining the power P of the j-1jAnd position Xj。
2. The method of claim 1, wherein the received power at sensor i is, on a linear scale, atAnd the method further comprises the steps of:
suppose rssi≈maxj rssi，j。
3. The method of claim 2, wherein the step of using involves the steps of:
a) determining K initial powers and K initial positions of the K wireless transmitters, and determining an initial likelihood value L based on the initial powers and initial positions(0)；
b) Based on the equation 1, NSCalculating a probability gamma for each sensor wireless transmitter pair i, j from the plurality of received signal strengths measured at the plurality of sensors
c) The probability gamma based on each sensor wireless transmitter pair i, jTo determine updated K powersAnd K positions
d) K powers based on the updateAnd K positionsTo determine a likelihood value L(m+1)(ii) a And
e) repeating steps b) through d) more than m times until a convergence criterion based on the likelihood values is satisfied, wherein m is an iteration index.
4. The method of claim 3, wherein step a) involves:
calculating the initial likelihood value as
Wherein,is represented as having the value RSSiMean value of evaluationSum varianceIs a gaussian distribution function ofRepresenting the weight value associated with the jth transmitter.
5. The method of claim 3, wherein step b) involves:
calculating the probability gamma for each sensor wireless transmitter pair i, jIs composed of
Wherein,is represented as having the value RSSiMean value of evaluationSum varianceIs a gaussian distribution function ofRepresenting the weight value associated with the jth transmitter.
6. The method of claim 3, wherein step c) involves:
calculating the updated K positionsAnd the associated K powersIs composed of
Wherein, <math>
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<mo>,</mo>
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</math>
and wherein PL (x, s)i) Is a deterministic path loss function, and siIs the location of the ith sensor.
7. The method of claim 3, wherein step d) involves:
calculating the likelihood value L(m+1)Is composed of
Wherein,is represented as having the value RSSiMean value of evaluationSum varianceIs a gaussian distribution function ofRepresenting the weight value associated with the jth transmitter.
8. The method of claim 3, wherein the convergence criterion is, compared to a threshold such that | L(m+1)-L(m)|＜。
9. A method according to claim 3, wherein said steps a) to d) are repeated with an assumed number of wireless transmitters until a stop criterion is met in order to obtain a number K of wireless transmitters.
10. The method of claim 9, wherein the stopping criterion is the akage information criterion AIC and is based on the following values: c(K) -L (K) + K, where L (K) is the likelihood value L determined in step d)(0)。
11. The method of claim 9, wherein the stopping criterion is a Minimum Description Length (MDL) criterion and is based on:wherein L (K) is the likelihood value determined in step d).
12. The method of claim 1, wherein the method further comprises the steps of:
reception is performed when i 1SThe plurality of received signal strengths measured at the plurality of sensors.
13. The method of claim 1, wherein i ═ 1.., NSThe sensors are distributed over an area.
14. The method of claim 1, wherein i ═ 1.., NSEach of the sensors includes only one receiving antenna.
15. The method of claim 1, wherein the j 1.
16. A computer program, characterized in that code means cause processing means to execute the method according to any of claims 1 to 15 when said processing means run said code means.
17. A computer program product comprising a computer readable medium and a computer program according to claim 16, wherein the computer program is comprised in the computer readable medium and comprises one or more from the group of: ROM (read only memory), PROM (programmable ROM), EPROM (erasable RPOM), flash memory, EEPROM (electrically EPROM), and hard disk drives.
18. A central processing unit comprising processing means for processing data and memory means for storing data, and further comprising receiving means and transmitting means for receiving and transmitting data, respectively, said central processing unit being arranged to be based on the algorithm i 1SPower and position of K wireless transmitters are determined from a plurality of received signal strengths measured at the sensors, where K and N areSAre respectively positive integers, and K is more than or equal to 2 and NsNot less than 1; the central processing unit is further arranged to use an expectation-maximization (EM) method for estimating an expected maximum (i.e., N) based on the estimated average value of i ═ 1SDetermining the power P of the j-1jAnd position Xj。
19. The central processing unit of claim 18, wherein the central processing unit is integrated into a communication node of a Radio Access Network (RAN).
20. The central processing unit of claim 18, wherein the central processing unit is part of a operations and management (QM) entity.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| PCT/EP2012/074174 WO2014082686A1 (en) | 2012-11-30 | 2012-11-30 | Method for determining powers and locations of radio transmitters |
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| CN104871615A true CN104871615A (en) | 2015-08-26 |
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| CN201280077285.8A Pending CN104871615A (en) | 2012-11-30 | 2012-11-30 | Method for determining powers and locations of radio transmitters |
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| CN107454618A (en) * | 2017-05-27 | 2017-12-08 | 柳州天艺科技有限公司 | More primary user's localization methods based on EM |
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| US20090258660A1 (en) * | 2008-04-15 | 2009-10-15 | Apple Inc. | Location determination using formula |
| CN101965050A (en) * | 2009-07-21 | 2011-02-02 | 北方电讯网络有限公司 | Use multi-beam to launch the method and apparatus of the position of estimating wireless station |
| CN102066969A (en) * | 2008-05-16 | 2011-05-18 | 苹果公司 | Location determination |
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- 2012-11-30 WO PCT/EP2012/074174 patent/WO2014082686A1/en active Application Filing
- 2012-11-30 CN CN201280077285.8A patent/CN104871615A/en active Pending
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| US20090258660A1 (en) * | 2008-04-15 | 2009-10-15 | Apple Inc. | Location determination using formula |
| CN102066969A (en) * | 2008-05-16 | 2011-05-18 | 苹果公司 | Location determination |
| CN101965050A (en) * | 2009-07-21 | 2011-02-02 | 北方电讯网络有限公司 | Use multi-beam to launch the method and apparatus of the position of estimating wireless station |
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| CN107454618A (en) * | 2017-05-27 | 2017-12-08 | 柳州天艺科技有限公司 | More primary user's localization methods based on EM |
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| WO2014082686A1 (en) | 2014-06-05 |
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