US20050052319A1  Method for receiver autonomous integrity monitoring and fault detection and elimination  Google Patents
Method for receiver autonomous integrity monitoring and fault detection and elimination Download PDFInfo
 Publication number
 US20050052319A1 US20050052319A1 US10656956 US65695603A US2005052319A1 US 20050052319 A1 US20050052319 A1 US 20050052319A1 US 10656956 US10656956 US 10656956 US 65695603 A US65695603 A US 65695603A US 2005052319 A1 US2005052319 A1 US 2005052319A1
 Authority
 US
 Grant status
 Application
 Patent type
 Prior art keywords
 measurement
 plurality
 gps
 measurements
 correlation
 Prior art date
 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
 Granted
Links
Images
Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
 G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
 G01S19/01—Satellite radio beacon positioning systems transmitting timestamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
 G01S19/13—Receivers
 G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
Abstract
Description
 [0001]The present invention relates generally to Fault Detection and Elimination (FDE) in a discretetime controlled process, and particularly to methods for Receiver Autonomous Integrity Monitoring (RAIM) in global positioning systems (GPS).
 [0002]GPS uses satellites in space to locate objects on earth. With GPS, signals from the satellites arrive at a GPS receiver and are used to determine the position of the GPS receiver. Currently, two types of GPS measurements corresponding to each correlator channel with a locked GPS satellite signal are available for civilian GPS receivers. The two types of GPS measurements are pseudorange, and integrated carrier phase for two carrier signals, L1 and L2, with frequencies of 1.5754 GHz and 1.2276 GHz, or wavelengths of 0.1903 m and 0.2442 m, respectively. The pseudorange measurement (or code measurement) is a basic GPS observable that all types of GPS receivers can make. It utilizes the C/A or P codes modulated onto the carrier signals. The measurement records the apparent time taken for the relevant code to travel from the satellite to the receiver, i.e., the time the signal arrives at the receiver according to the receiver clock minus the time the signal left the satellite according to the satellite clock. The carrier phase measurement is obtained by integrating a reconstructed carrier of the signal as it arrives at the receiver. Thus, the carrier phase measurement is also a measure of a transit time difference as determined by the time the signal left the satellite according to the satellite clock and the time it arrives at the receiver according to the receiver clock. However, because an initial number of whole cycles in transit between the satellite and the receiver when the receiver starts tracking the carrier phase of the signal is usually not known, the transit time difference may be in error by multiple carrier cycles, i.e., there is a wholecycle ambiguity in the carrier phase measurement.
 [0003]With the GPS measurements available, the range or distance between a GPS receiver and each of a multitude of satellites is calculated by multiplying a signal's travel time by the speed of light. These ranges are usually referred to as pseudoranges (false ranges) because the receiver clock generally has a significant time error which causes a common bias in the measured range. This common bias from receiver clock error is solved for along with the position coordinates of the receiver as part of the normal navigation computation. Various other factors can also lead to errors or noise in the calculated range, including ephemeris error, satellite clock timing error, atmospheric effects, receiver noise and multipath error. With standalone GPS navigation, where a user with a GPS receiver obtains code and/or carrierphase ranges with respect to a plurality of satellites in view, without consulting with any reference station, the user is very limited in ways to reduce the errors or noises in the ranges.
 [0004]To eliminate or reduce these errors, differential operations are typically used in GPS applications. Differential GPS (DGPS) operations typically involve a base reference GPS receiver, a user GPS receiver, and a communication mechanism between the user and reference receivers. The reference receiver is placed at a known location and the known position is used to generate corrections associated with some or all of the above error factors. The corrections are supplied to the user receiver and the user receiver then uses the corrections to appropriately correct its computed position. The corrections can be in the form of corrections to the reference receiver position determined at the reference site or in the form of corrections to the specific GPS satellite clock and/or orbit. Corrections to the reference receiver position are not as flexible as GPS satellite clock or orbit corrections because, for optimum accuracy, they require that the same satellites be observed by the user receiver and the reference receiver.
 [0005]The fundamental concept of Differential GPS (DGPS) is to take advantage of the spatial and temporal correlations of the errors inherent in the GPS measurements to cancel the noise factors in the pseudorange and/or carrier phase measurements resulting from these error factors. However, while the GPS satellite clock timing error, which appears as a bias on the pseudorange or carrier phase measurement, is perfectly correlated between the reference receiver and the user receiver, most of the other error factors are either not correlated or the correlation diminishes in widearea applications, i.e., when the distance between the reference and user receivers becomes large.
 [0006]To overcome the inaccuracy of the DGPS system in widearea applications, various wide area DGPS (WADGPS) techniques have been developed. The WADGPS includes a network of multiple reference stations in communication with a computational center or hub. Error corrections are computed at the hub based upon the known locations of the reference stations and the measurements taken by them. The computed error corrections are then transmitted to users via a communication link such as satellite, phone, or radio. By using multiple reference stations, WADGPS provides more accurate estimates of the error corrections.
 [0007]Thus, a user with a GPS receiver may use different modes of navigation, i.e., standalone GPS, DGPS, WADGPS, carrierphase DGPS, etc. Whichever of the navigation modes is used, there is always the possibility that the range with respect to a satellite are computed based on a faulty measurement, such as a measurement with respect to a failed satellite. When this range is used in determining the position of the user, an erroneous or wrong position would result. Thus, a faulty measurement can cause serious degradation to the reliability and integrity of the GPS system. Therefore, various integrity monitoring techniques have been developed for fault detection and elimination (FDE) in GPS systems. Receiver autonomous integrity monitoring (RAIM) is the name coined by the FAA for methods of integrity monitoring in GPS using redundant GPS satellite measurements.
 [0008]The literature on RAIM and FDE procedures is extensive. Most of the procedures in the literature, however, are related to aviation use and attempt to bound the probable error in a position domain. As a result, they generally involve very extensive computations. One of the earliest papers describing a RAIM procedure is a paper by Brown and McBurney, “SelfContained GPS Integrity Check Using Maximum Solution Separation,” Navigation, Vol. 35, No. 1, pp 4153. In this paper, the authors suggest: (1) obtaining GPS measurements with respect to n satellites in view; (2) for each of the n satellites, solving for the user position based on measurements with respect to the other (n−1) satellites; (3) computing all possible distances between the solutions in the horizontal plane and determining a maximum distance among the possible distances; and (4) using the maximum distance as a test statistic and declaring a failure when the maximum distance exceeds a threshold. Clearly, this technique is very computationally intensive and does not isolate a particular measurement or satellite as being faulty.
 [0009]Another early paper is by Parkinson and Axelrad, “Autonomous GPS Integrity Monitoring Using the Pseudorange Residual,” Navigation, Vol. 35, No. 2, pp 255271. In this paper, the authors suggest an excellent test statistic based upon pseudorange measurement residuals, but when it comes to using the test statistic to isolate a failed satellite, they use a scheme similar to that used by Brown and McBurney, i.e., for each of a plurality of satellites, they compute a test statistic while leaving out the measurement with respect to the satellite. Again, this procedure presents an excessive computational burden.
 [0010]A method for detecting and identifying a faulty measurement among a plurality of GPS measurements, obtained by a GPS receiver with respect to a plurality of satellites in view of the GPS receiver, determines whether the plurality of GPS measurements include a faulty measurement. In response to a determination that the plurality of GPS measurements include a faulty measurement, the method identifies a satellite contributing the faulty measurement by computing a correlation value associated with each of the plurality of satellites, and selecting a satellite associated with a highest correlation value as the satellite contributing the faulty measurement. In one embodiment, to insure that the correct satellite is identified, the satellite associated with the highest correlation value is selected when the highest correlation value exceeds a predetermined threshold value and the predetermined threshold value is sufficiently larger than a second highest correlation value. In an alternative embodiment, the satellite associated with the highest correlation value is selected when the difference between the highest correlation value and a second highest correlation value exceeds a predetermined threshold.
 [0011]In some embodiments, whether the GPS measurements include a faulty measurement is determined by computing test statistic using postfix residuals corresponding to the plurality of GPS measurements, and comparing test statistic with a threshold residual value, which is chosen based on a navigation mode used by the GPS receiver. If the test statistic exceeds the threshold residual value, a faulty measurement is detected.
 [0012]In some embodiments, the correlation value associated with a satellite is the absolute value of a correlation coefficient associated with the satellite. The correlation coefficient is computed based on a residual sensitivity matrix corresponding to the plurality of satellites and a residual vector including the postfix residuals corresponding to the plurality of GPS measurements.
 [0013]In some embodiments, the size of the error in the faulty GPS measurement is determined based on a residual sensitivity matrix corresponding to the plurality of satellites and the root mean square residual.
 [0014]
FIG. 1 is a block diagram of a computer system that can be used to carry out a method for detecting and identifying a faulty GPS measurement or a satellite contributing to the faulty GPS measurement.  [0015]
FIG. 2 is a flowchart illustrating the method for detecting and identifying a faulty GPS measurement or a satellite contributing to the faulty GPS measurement.  [0016]
FIG. 3 is a flowchart illustrating a method for determining whether a plurality of GPS measurements include a faulty GPS measurement.  [0017]
FIG. 4 is a flowchart illustrating a method for identifying a faulty GPS measurement among a plurality of GPS measurements.  [0018]
FIG. 5A is a flowchart illustrating a method for identifying a satellite with a highest correlation value as the satellite contributing to the faulty GPS measurement.  [0019]
FIG. 5B is a flowchart illustrating another method for identifying a satellite with a highest correlation value as the satellite contributing to the faulty GPS measurement.  [0020]
FIG. 6 is a flowchart illustrating a method for verifying that the satellite contributing to the faulty measurement has been identified correctly.  [0021]
FIG. 1 illustrates a computer system 100 that can be used to carry out the method for detecting and identifying a faulty GPS measurement among a plurality of GPS measurements. Each of the plurality of GPS measurements is taken by a GPS receiver 122 based on signals from one of a plurality of satellites 1101, 1102, . . . , 110n, where n is the number of satellites in view of the GPS receiver 122. The plurality of satellites, or any one or more of them, are sometimes referred to hereafter in this document as satellite(s) 110. In some embodiments, the GPS receiver 122 and the computer system 100 are integrated into a single device, within a single housing, such as a portable, handheld or even wearable position tracking device, or a vehiclemounted or otherwise mobile positioning and/or navigation system. In other embodiments, the GPS receiver 122 and the computer system 100 are not integrated into a single device.  [0022]As shown in
FIG. 1 , the computer system 100 includes a central processing unit (CPU) 126, memory 128, an input port 134 and an output port 136, and (optionally) a user interface 138, coupled to each other by one or more communication buses 129. The memory 128 may include highspeed random access memory and may include nonvolatile mass storage, such as one or more magnetic disk storage devices. The memory 128 preferably stores an operating system 131, a database 133, and GPS application procedures 135. The GPS application procedures may include procedures 137 for implementing the method for detecting and identifying the faulty GPS measurement, as described in more detail below. The operating system 131 and application programs and procedures 135 and 137 stored in memory 128 are for execution by the CPU 126 of the computer system 124. The memory 128 preferably also stores data structures used during execution of the GPS application procedures 135 and 137, including GPS pseudorange and/or carrierphase measurements 139, as well as other data structures discussed in this document.  [0023]The input port 134 is for receiving data from the GPS receiver 122, and output port 136 is used for outputting data and/or calculation results. Data and calculation results may also be shown on a display device of the user interface 138.
 [0024]
FIG. 2 illustrates a method 200 for detecting and identifying a faulty GPS measurement among a plurality of GPS measurements obtained by the GPS receiver 122 with respect to the plurality of satellites 110. As shown inFIG. 2 , method 200 includes step 210 for determining whether the plurality of GPS measurements include a faulty measurement. In response to a determination in step 210 that the plurality of GPS measurements include a faulty measurement, method 200 further includes step 220 in which the faulty measurement is isolated or identified among the plurality of GPS measurements, or the satellite contributing to the faulty measurement is isolated or identified among the plurality of satellites. With the satellite contributing the fault measurement identified, method 200 may include an optional step 230 in which a size of an error in the faulty measurement is determined, and an optional step 240 for verifying that the correct identification has been made.  [0025]
FIG. 3 illustrates an embodiment of a method 300 for determining whether the GPS measurements include a faulty measurement in step 210. As shown inFIG. 3 , method 300 includes step 310 in which postfix residuals corresponding to the plurality of GPS measurements are computed and step 320 in which a test statistics is formed using the postfix residuals and is compared with a threshold to determine whether the plurality of GPS measurements include a faulty measurement. A residual of a GPS measurement represents a disagreement between the GPS measurement and a prediction or expected value of the GPS measurement. Before the position and clock bias of the GPS receiver are adjusted, the residuals are often referred to as prefix residuals or measurement innovations. A measurement innovation can be computed based on the difference between a GPS measurement and a theoretical prediction of the GPS measurement. Alternatively, a measurement innovation corresponding to a GPS measurement can be computed as the difference between the GPS measurement and an expected value of the GPS measurement computed from an initial estimated state of the GPS receiver, as discussed in the following.  [0026]Whatever the navigation mode, navigating with GPS involves a discretetime controlled process that is governed by a linear stochastic difference equation:
Hx=z+n (1)
where x is a state vector of the discretetime controlled process and, in the case of GPS, it includes corrections to the position and clock bias of the GPS receiver, H is a measurement sensitivity matrix including direction cosines of the state vector or unit vectors from the GPS receiver to each of the n satellites, z is a measurement innovation vector including measurement innovations corresponding to the plurality of GPS measurements, and n is a measurement noise vector. In the case of carrierphase measurements, the state vector may include an unknown ambiguity factor.
The postfix residuals are usually obtained in a twostep process. First, a leastsquares solution for x is made, i.e.
{circumflex over (x)}=(H ^{T} H)^{−1} H ^{T} z (2)
or,
{circumflex over (x)}=(H ^{T} R ^{−1} H)^{−1} H ^{T} R ^{−1} z (3)
for a weighted least squares solution. R in Equation (4) is a measurement covariance matrix and$\begin{array}{cc}R=\left[\begin{array}{ccc}{\sigma}_{1}^{2}& \dots & 0\\ \vdots & \u22f0& \vdots \\ 0& \text{\hspace{1em}}& {\sigma}_{n}^{2}\end{array}\right]& \left(4\right)\end{array}$
where σ_{i}, i=1, 2, . . . , n, represents a standard deviation of GPS measurement noises with respect to the i^{th }satellite. An example of the methods for calculating σ_{i }can be found in “Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations,” by Peter Bona, GPS Solutions, Vol. 4, No. 2, Fall 2000, p. 313, or in “Tightly Integrated Attitude Determination Methods for LowCost Inertial Navigation: TwoAntenna GPS and GPS/Magnetometer,” by Yang, Y., Ph.D. Dissertation, Dept. of Electrical Engineering, University of California, Riverside, Calif. June 2001, both of which are hereby incorporated by reference.  [0032]The correction to the state as calculated in Equation (3) or (4) is used to transform the measurement innovations (prefix residuals) into a set of postfix residuals in step 310 of method 300, according to the following equations
Δ=Sz. (5)
where Δ is a residual vector including as its elements postfix residuals corresponding to the plurality of GPS measurements, and S is a residual sensitivity matrix:
S=(1−H(H ^{T} H)^{−1} H ^{T}) (5a)
or,
S=(1−H(H ^{T} R ^{−1} H)^{−1} H ^{T} R ^{−1}) (5b)  [0035]S is called the residual sensitivity matrix because it is a matrix whose elements are the residuals corresponding to unit changes in the measurement innovations. This can be explained through the following discussions. Equation (1) can be expanded to include a set of state vectors corresponding to a set of arbitrary measurement innovation vectors:
HX=Z (6)
where X includes a set of state vectors x_{1},x_{2}, . . . ,x_{n }corresponding to a set of arbitrary measurement innovation vectors z_{1},z_{2}, . . . ,z_{n}. Now, if we let Z be an identity matrix, we get the state vectors corresponding to a set of measurement innovation vectors each representing a single unit change (e.g., one meter or any arbitrary unit) in the measurement innovation of a different respective one of the plurality of satellites while the measurement innovations of the other satellites are kept unchanged, as shown in the following equation:
HX=I (7)
The leastsquares solution for X is then:
{circumflex over (X)}=(H ^{T} H)^{−1} H ^{T} (8)
For a weighted leastsquares solution this becomes:
{circumflex over (X)}=(H ^{T} R ^{−1} H)^{−1} H ^{T} R ^{−1} (9)  [0039]Multiplying equation (8) by H gives a prediction about the measurement innovations of each satellite based on the leastsquares solution:
H{circumflex over (X)}=H(H ^{T} H)^{−1} H ^{T} (10)
Subtracting this prediction from the input value of the innovations, i.e., the identity matrix, we obtain a matrix including the residuals of unit changes in the measurement innovations, which is the residual sensitivity matrix S in Equation (5a) or (5b). As shown in Equation (5), the S matrix can be used to directly map the prefix residuals (measurement innovations) into the postfix residuals.  [0041]Thus, each column (or row) of the S matrix includes residuals corresponding to a unit change in the measurement innovation of one of the plurality of satellites while the measurement innovations of the other ones of the plurality of satellites are kept unchanged. The S matrix has a number of interesting properties: it is symmetric; it is idempotent, i.e., S=S^{2}=S^{3}= . . . ; the sum of the elements in any row or column equals zero; and the length of any row or column is equal to the square root of an associated diagonal element. Since the state vector, x, has four elements for most navigation modes, the rank of S is n−4, where n is the number of satellites.
 [0042]With the S matrix, the postfix residuals in the residual vector Δ can be computed according to Equation (5) in step 310. The postfix residuals can be used to compute a root mean square residual δ, which is the norm value (or length) of a residual vector Δ divided by the number of measurements, n, i.e.,
$\begin{array}{cc}\delta =\sqrt{\frac{{\Delta}^{T}\Delta}{n}}& \left(11\right)\end{array}$  [0043]After computing the postfix residuals in step 310, method 300 further includes step 320 in which the postfix residuals or the root mean square residual are used to form a test statistic, which is then compared with a fault threshold to determine whether the plurality of GPS measurements include a faulty measurement. The test statistic can be the root mean square residual. Or, it can be the length of the postfix residual vector scaled by appropriate normalization for the number of satellites, such as the square root of (n−4), as in the following equation
$\begin{array}{cc}\sigma =\sqrt{\frac{{\Delta}^{T}\Delta}{\left(n4\right)}}& \left(12\right)\end{array}$
Alternatively, when one is not concerned with very small errors, the fault threshold can be set large enough so that the scaling is relatively insignificant. Thus, the test statistic σ can simply be the length of the postfix residual vector, i.e.,
σ={square root}{square root over (Δ^{T}Δ)} (12a).  [0045]When the test statistic is larger than the fault threshold, it is determined that the plurality of GPS measurements include a faulty measurement. Since the level of measurement noise (or the position accuracy) of the GPS receiver 122 often depends on the navigation mode in which the GPS receiver is operating, in some embodiments the fault threshold value is selected to correspond to the navigation mode used by the GPS receiver 122.
 [0046]
FIG. 4 illustrates an embodiment of a method 400 for identifying the faulty measurement or a satellite contributing the faulty measurement in step 220 of method 200. As shown inFIG. 4 , method 400 includes step 410 in which a correlation value associated with each of the plurality of measurements or with each of the plurality of satellites is computed, and step 420 in which a satellite associated with a highest correlation value among the plurality of satellites 110 is identified as the satellite contributing the faulty measurement, or the GPS measurement with respect to the satellite associated with the highest correlation value is identified as the faulty measurement.  [0047]In some embodiments, the correlation value associated with each one of the plurality of satellites is computed based on a correlation coefficient associated with the satellite or with the one of the plurality of GPS measurements with respect to the satellite. The correlation coefficient associated with a satellite, e.g., the j^{th }satellite, where j=1, 2, . . . , n, represents a correlation between the residuals of the plurality of GPS measurements and the residuals corresponding to a unit change in the measurement innovations with respect to the j^{th }satellite, while the measurement innovations of the other satellites are kept unchanged. Thus, the correlation coefficient associated with the j^{th }satellite can be computed using the S matrix and the residual vector Δ according to the following equation:
$\begin{array}{cc}{\rho}^{j}=\frac{\sum _{i}{\Delta}_{i}\xb7{s}_{i}^{j}}{\left\Delta {s}^{j}\right}& \left(13\right)\end{array}$
where ρ^{j }is the correlation coefficient associated with the j^{th }satellite, Δ_{i }is the i^{th }element of the residual vector Δ, s_{i} ^{j }is the element in the i^{th }row and j^{th }column of the S matrix, Δ is the norm value of the residual vector Δ, s^{j }represents the j^{th }column of the S matrix, and the summation is over all elements of Δ or of the j^{th }column of the S matrix. Note that the length of s^{j}, s^{j}, is equal to the square root of the diagonal element, s_{j} ^{j}.  [0049]In one embodiment, the correlation value associated with a satellite is equal to the absolute value of the correlation coefficient associated with the satellite. With the correlation values thus computed, the satellite associated with a highest correlation value among the correlation values associated with the plurality of satellites can generally be identified in step 420 as the satellite contributing to the faulty measurement. However, an additional check may be required to ensure that the correct satellite is identified.
 [0050]When only five satellites are available, the correlation coefficient associated with every satellite should be about one (or minus one). This is because the degree of freedom is only one (one more satellite than the number of unknowns in the state vector). With only five measurements corresponding to the five satellites, each column in the S matrix is perfectly correlated with the residual vector, except that the length of the columns are different. In other words, the large root mean square residual, which indicated a fault in step 210 of method 200, could be caused by a faulty measurement from any one of the satellites. Moreover, even when the number of satellites is greater than 5, a similar phenomenon can occur with a degenerate geometry. Such a degenerate geometry is indicated if more than one satellite are associated with correlation coefficients close to one or minus one.
 [0051]Thus, to insure that the satellite contributing to the faulty measurement be identified correctly, method 500A or 500B, as shown in
FIG. 5A or 5B, respectively, can be used in step 420. Method 500A includes step 510A in which the highest correlation value is identified among the correlation values associated with the plurality of satellites. Method 500A further includes step 520A for determining that the highest correlation value exceed a predetermined threshold value and step 530A for determining that the predetermined threshold value is sufficiently larger than a second highest correlation value among the correlation values associated with the plurality of satellites. Alternatively, method 500B is used, which includes step 510B in which the highest and the second highest correlation values are identified, step 520B in which the difference between the highest and second highest correlation values are computed, and step 530B for determining that the difference exceeds a predetermined minimum difference value.  [0052]With the satellite contributing the faulty measurement identified, method 200 may further include step 230 in which the size of any error in the faulty measurement (or the size of the fault) is estimated. Estimating the size of the fault is sometimes useful, especially when method 200 is used to identify a faulty measurement in a RealTime Kinematic (RTK) navigation mode. Since RTK navigations usually involve carrier phase measurements and thus resolutions of wholecycle ambiguities, a measurement fault can be the result of a cycle slip in a tracking loop or an improper determination of the wholecycle ambiguity. When this is the case, the size of the fault will be a multiple of the carrier wavelength. Given that the satellite, such as satellite 110k, where k is 1, 2, . . . , or n, with the highest correlation value is identified, a best estimate of the size of the error, e_{k}, is given by the root mean square residual divided by the length of the column of the S matrix associated with the satellite 100j. So, e_{k }is the root mean square residual corresponding to a unit change in the measurement innovation of satellitek while the measurement innovations for the rest of the plurality of satellites are kept unchanged. Since the length of the column of the S matrix is equal to the square root of the corresponding diagonal element of the S matrix, we have:
$\begin{array}{cc}{e}_{k}=\frac{\delta \sqrt{n}}{\sqrt{{s}_{k}^{k}}}& \left(14\right)\end{array}$
Note that with poor geometry the diagonal element can be small. However, the smaller the diagonal element, the larger the measurement error from the corresponding satellite must be before it can cause the root mean square residual to exceed the detection threshold.  [0054]With the size of the error in the faulty measurement estimated, method 200 may further include step 240 for verifying that there is only one faulty measurement among the plurality of GPS measurements and that the identification of the satellite contributing the faulty measurement is correctly made.
FIG. 6 illustrates a method 600 for performing the verification in step 240. As shown inFIG. 6 , method 600 includes step 610 in which the residual vector Δ is adjusted to account for the error according to the following equation:
Δ′=Δ+SE (15)
where E is a vector with zero elements corresponding to satellites whose measurements are without error and an element having the value of e_{k }for the satellite 100k that contributed the faulty measurement. Method 600 further includes step 620 in which the test statistic is recalculated according to Equation (11), (12), or (12a) after the adjusted residual vector Δ′ is used to replace the residual vector Δ in the equation. If the fault identification has been made correctly, the recalculated test statistic should now pass the threshold test for the test statistic, indicating that the fault has been removed. Thus, method 600 further includes step 630 in which the recalculated test statistic is compared with the fault threshold to verify that there is only one faulty measurement among the plurality of GPS measurements and the identification of the satellite contributing the faulty measurement is correctly made.  [0056]The above described method for identifying a faulty GPS measurement is computationally efficient because it works entirely in the measurement domain. When there are more than five satellites being tracked, the method can be used to dramatically improve the reliability of positioning and navigation using GPS, with only a small cost in additional computational complexity.
Claims (50)
 1. A method for identifying a faulty measurement among a plurality of measurements that are used to determine a state of a discretetime controlled process, comprising:computing a plurality of correlation values, each correlation value associated with one of the plurality of measurements; andselecting a measurement among the plurality of measurements as the faulty measurement based on the correlation values.
 2. The method of
claim 1 wherein the correlation values represent a correlation between residuals of the plurality of measurements and residuals corresponding to a change in one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  3. The method of
claim 1 wherein computing the correlation values comprises:computing a residual sensitivity matrix;computing residuals corresponding to the plurality of measurements; andcomputing a correlation coefficient associated with the one of the plurality of measurements based on the residuals of the plurality of measurements and the residual sensitivity matrix.  4. The method of
claim 3 wherein computing the residuals corresponding to the plurality of measurements comprises:obtaining a leastsquares solution of the state of the discretetime controlled process;computing expected values of the plurality of measurements based on the leastsquare solution; andcomputing differences between the plurality of measurements and the expected values of the plurality of measurements.  5. The method of
claim 3 wherein the residuals corresponding to the plurality of measurements are computed using the residual sensitivity matrix.  6. The method of
claim 1 wherein selecting a measurement among the plurality of measurements as the faulty measurement comprises:identifying a highest correlation value; andselecting a measurement associated with the highest correlation value as the faulty measurement.  7. The method of
claim 6 , wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:identifying a second highest correlation value; andselecting the measurement associated with the highest correlation value as the faulty measurement when the difference between the highest correlation value and the second highest correlation value exceeds a predetermined threshold value.  8. The method of
claim 6 wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:determining that the highest correlation value exceeds a first predetermined threshold value;identifying a second highest correlation value; anddetermining that the second highest correlation value is smaller than the first predetermined threshold value and the difference between the first predetermined threshold value and the second highest correlation value exceeds a second predetermined threshold value.  9. The method of
claim 1 wherein the state of the discretetime controlled process includes corrections to a position and a clock bias of a GPS receiver and the plurality of measurements are GPS range measurements obtained by the GPS receiver with respect to a plurality of satellites, each of the plurality of measurements corresponding to one of the plurality of satellites.  10. The method of
claim 9 wherein the number of the plurality of satellites is greater than 5.  11. The method of
claim 1 , further comprising:determining a size of an error in the faulty measurement.  12. The method of
claim 11 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a root mean square residual corresponding to a unit change in the one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  13. The method of
claim 11 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a square root of a diagonal element corresponding to the faulty measurement in a residual sensitivity matrix.  14. A method for detecting and identifying a faulty measurement among a plurality of GPS measurements obtained by a GPS receiver with respect to a plurality of satellites, comprising:determining whether the plurality of GPS measurements include a faulty measurement; andin response to a determination that the plurality of GPS measurements include a faulty measurement, identifying a satellite contributing the faulty measurement by:computing a plurality of correlation values, each correlation value associated with one of the plurality of satellites; andselecting a satellite among the plurality of satellites as the satellite contributing the faulty measurement based on the correlation values.
 15. The method of
claim 14 wherein determining whether the GPS measurements include a faulty measurement comprises:computing a test statistic using postfix residuals corresponding to the plurality of GPS measurements; anddetermining whether the test statistic exceeds a fault threshold.  16. The method of
claim 15 wherein the fault threshold is a function of a navigation mode used by the GPS receiver.  17. The method of
claim 15 , further comprising:determining a size of an error in the faulty GPS measurement.  18. The method of
claim 17 , further comprising:verifying that the satellite contributing to the faulty measurement has been correctly identified.  19. The method of
claim 18 wherein verifying that the satellite contributing to the faulty measurement has been correctly identified comprises:adjusting the postfix residuals based on the size of the error in the faulty GPS measurement;computing the test statistic using the adjusted postfix residuals; andverifying that the test statistic does not exceed the fault threshold.  20. The method of
claim 14 wherein computing the correlation value associated with a respective satellite comprises:computing a residual sensitivity matrix;computing residuals corresponding to the plurality of GPS measurements; andcomputing a correlation coefficient associated with the respective satellite based on the residuals and the residual sensitivity matrix.  21. The method of
claim 14 wherein selecting a satellite among the plurality of satellites as the satellite contributing the faulty measurement comprises:identifying a highest correlation value; andselecting the satellite associated with the highest correlation value as the satellite contributing the faulty measurement.  22. A computer readable medium comprising computer executable program instructions that when executed by a processor in a digital processing system, causes the digital processing system to perform the operations of:computing a plurality of correlation values, each correlation value associated with one of the plurality of measurements; andselecting the measurement associated with a highest correlation value among the plurality of correlation values as the faulty measurement.
 23. The computer readable medium of
claim 22 wherein the method further comprises:determining a size of an error in the faulty measurement.  24. A computerreadable medium containing thereon instructions, which, when executed by a processor in a digital processing system, causes the digital processing system to determine a state of a discretetime controlled process by performing the operations of:computing a plurality of correlation values, each correlation value associated with one of the plurality of measurements; andselecting a measurement among the plurality of measurements as the faulty measurement based on the correlation values.
 25. The computerreadable medium of
claim 24 wherein the operations that the instructions cause the digital processing system to perform further comprise:determining a size of an error in the faulty measurement.  26. The computerreadable medium of
claim 25 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a root mean square residual corresponding to a unit change in one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  27. The computerreadable medium of
claim 25 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a square root of a diagonal element corresponding to the faulty measurement in a residual sensitivity matrix.  28. The computerreadable medium of
claim 24 wherein the correlation values represent a correlation between residuals of the plurality of measurements and residuals corresponding to a change in the one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  29. The computerreadable medium of
claim 24 wherein computing the correlation values comprises:computing a residual sensitivity matrix;computing residuals corresponding to the plurality of measurements; andcomputing a correlation coefficient associated with the one of the plurality of measurements based on the residuals of the plurality of measurements and the residual sensitivity matrix.  30. The computerreadable medium of
claim 29 wherein computing the residuals corresponding to the plurality of measurements comprises:obtaining a leastsquares solution of a state of a discretetime controlled process;computing expected values of the plurality of measurements based on the leastsquare solution; andcomputing differences between the plurality of measurements and the expected values of the plurality of measurements.  31. The computerreadable medium of
claim 29 wherein the residuals corresponding to the plurality of measurements are computed using the residual sensitivity matrix.  32. The computerreadable medium of
claim 24 wherein selecting a measurement among the plurality of measurements as the faulty measurement comprises:identifying a highest correlation value; andselecting the measurement associated with the highest correlation value as the faulty measurement.  33. The computerreadable medium of
claim 32 , wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:identifying a second highest correlation value; andselecting the measurement associated with the highest correlation value as the faulty measurement when the difference between the highest correlation value and the second highest correlation value exceeds a predetermined threshold value.  34. The computerreadable medium of
claim 32 wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:determining that the highest correlation value exceeds a first predetermined threshold value;identifying a second highest correlation value; anddetermining that the second highest correlation value is smaller than the first predetermined threshold value and the difference between the first predetermined threshold value and the second highest correlation value exceeds a second predetermined threshold value.  35. The computerreadable medium of
claim 24 wherein the state of the discretetime controlled process includes corrections to a position and a clock bias of a GPS receiver and the plurality of measurements are GPS range measurements obtained by the GPS receiver with respect to a plurality of satellites, each of the plurality of measurements corresponding to one of the plurality of satellites.  36. The computerreadable medium of
claim 35 wherein the number of the plurality of satellites is greater than 5.  37. A system capable of identifying a faulty measurement among a plurality of measurements that are used to determine a state of a discretetime controlled process, comprising:a processor;a memory including instructions, which, when executed by the processor, causes the processor to perform the operations of:computing a plurality of correlation values, each correlation value associated with one of the plurality of measurements; andselecting a measurement among the plurality of measurements as the faulty measurement based on the correlation values.
 38. The system of
claim 37 wherein the correlation values represent a correlation between residuals of the plurality of measurements and residuals corresponding to a change in the one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  39. The system of
claim 37 wherein computing the correlation values comprises:computing a residual sensitivity matrix;computing residuals corresponding to the plurality of measurements; andcomputing a correlation coefficient associated with the one of the plurality of measurements based on the residuals of the plurality of measurements and the residual sensitivity matrix.  40. The system of
claim 39 wherein computing the residuals corresponding to the plurality of measurements comprises:obtaining a leastsquares solution of the state of the discretetime controlled process;computing expected values of the plurality of measurements based on the leastsquare solution; andcomputing differences between the plurality of measurements and the expected values of the plurality of measurements.  41. The system of
claim 39 wherein the residuals corresponding to the plurality of measurements are computed using the residual sensitivity matrix.  42. The system of
claim 37 wherein selecting a measurement among the plurality of measurements as the faulty measurement comprises:identifying a highest correlation value; andselecting the measurement associated with the highest correlation value as the faulty measurement.  43. The system of
claim 42 , wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:identifying a second highest correlation value; andselecting the measurement associated with the highest correlation value as the faulty measurement when the difference between the highest correlation value and the second highest correlation value exceeds a predetermined threshold value.  44. The system of
claim 42 wherein selecting the measurement associated with the highest correlation value as the faulty measurement comprises:determining that the highest correlation value exceeds a first predetermined threshold value;identifying a second highest correlation value; anddetermining that the second highest correlation value is smaller than the first predetermined threshold value and the difference between the first predetermined threshold value and the second highest correlation value exceeds a second predetermined threshold value.  45. The system of
claim 37 wherein the state of the discretetime controlled process includes corrections to a position and a clock bias of a GPS receiver and the plurality of measurements are GPS range measurements obtained by the GPS receiver with respect to a plurality of satellites, each of the plurality of measurements corresponding to one of the plurality of satellites.  46. The system of
claim 45 wherein the number of the plurality of satellites is greater than 5.  47. The system of
claim 37 , wherein the operations further comprise:determining a size of an error in the faulty measurement.  48. The system of
claim 47 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a root mean square residual corresponding to a unit change in one of the plurality of measurements while the rest of the plurality of measurements are unchanged.  49. The system of
claim 47 wherein determining the size of the error in the faulty measurement comprises:dividing a root mean square residual of the plurality of measurements by a square root of a diagonal element corresponding to the faulty measurement in a residual sensitivity matrix.  50. A system for identifying a faulty measurement among a plurality of measurements that are used to determine a state of a discretetime controlled process, comprising:means for computing a plurality of correlation values, each correlation value associated with one of the plurality of measurements; andmeans for selecting a measurement among the plurality of measurements as the faulty measurement based on the correlation values.
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

US10656956 US6864836B1 (en)  20030905  20030905  Method for receiver autonomous integrity monitoring and fault detection and elimination 
Applications Claiming Priority (8)
Application Number  Priority Date  Filing Date  Title 

US10656956 US6864836B1 (en)  20030905  20030905  Method for receiver autonomous integrity monitoring and fault detection and elimination 
EP20040786560 EP1660903B1 (en)  20030905  20040819  Method for receiver autonomous integrity monitoring and fault detection and elimination 
DE200460009590 DE602004009590T2 (en)  20030905  20040819  A process for Receiver Autonomous Integrity Monitoring and error detection and correction 
CN 200480025390 CN1846147A (en)  20030905  20040819  Method for receiver autonomous integrity monitoring and fault detection and elimination 
CA 2535713 CA2535713A1 (en)  20030905  20040819  Method for receiver autonomous integrity monitoring and fault detection and elimination 
PCT/US2004/027344 WO2005027283A3 (en)  20030905  20040819  Method for receiver autonomous integrity monitoring and fault detection and elimination 
ES04786560T ES2294549T3 (en)  20030905  20040819  Method for monitoring the integrity of an autonomous receiver, detecting and removing faults. 
JP2006526112A JP2007504469A (en)  20030905  20040819  The receiver automatic integrity monitoring, as well as a method of fault detection and removal 
Publications (2)
Publication Number  Publication Date 

US6864836B1 US6864836B1 (en)  20050308 
US20050052319A1 true true US20050052319A1 (en)  20050310 
Family
ID=34218150
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

US10656956 Active US6864836B1 (en)  20030905  20030905  Method for receiver autonomous integrity monitoring and fault detection and elimination 
Country Status (8)
Country  Link 

US (1)  US6864836B1 (en) 
EP (1)  EP1660903B1 (en) 
JP (1)  JP2007504469A (en) 
CN (1)  CN1846147A (en) 
CA (1)  CA2535713A1 (en) 
DE (1)  DE602004009590T2 (en) 
ES (1)  ES2294549T3 (en) 
WO (1)  WO2005027283A3 (en) 
Cited By (10)
Publication number  Priority date  Publication date  Assignee  Title 

US20060047413A1 (en) *  20031202  20060302  Lopez Nestor Z  GNSS navigation solution integrity in noncontrolled environments 
US20070139263A1 (en) *  20051215  20070621  Gang Xie  Method and apparatus for improving fault detection and exclusion systems 
US20090070635A1 (en) *  20070706  20090312  Thales  Method of improving the integrity and safety of an avionics system 
US20100033370A1 (en) *  20031202  20100211  Gmv Aerospace And Defence, S.A.  Gnss navigation solution integrity in noncontrolled environments 
WO2010059439A2 (en) *  20081124  20100527  Andrew Llc  System and method for determining falsified geographic location of a mobile device 
US7956802B1 (en) *  20070521  20110607  Rockwell Collins, Inc.  Integrityoptimized receiver autonomous integrity monitoring (RAIM) for vertical integrity monitoring 
CN103308929A (en) *  20130524  20130918  北京东方计量测试研究所  Satellite navigation signal simulator used for pseudorange precision index measurement 
CN103308928A (en) *  20130524  20130918  北京东方计量测试研究所  Pseudorange precision measurement system of satellite navigation signal simulator 
CN103308930A (en) *  20130524  20130918  北京东方计量测试研究所  Pseudorange precision measurement method of satellite navigation signal simulator 
US9854398B1 (en) *  20160803  20171226  International Business Machines Corporation  System, method and recording medium for location verification 
Families Citing this family (14)
Publication number  Priority date  Publication date  Assignee  Title 

US7212155B2 (en) *  20040507  20070501  Navcom Technology, Inc.  GPS navigation using successive differences of carrierphase measurements 
JP4548604B2 (en) *  20050614  20100922  三菱自動車工業株式会社  Vehicletovehicle communication system 
US7501981B2 (en) *  20051118  20090310  Texas Instruments Incorporated  Methods and apparatus to detect and correct integrity failures in satellite positioning system receivers 
US7733268B2 (en) *  20060516  20100608  Andrew Corporation  Method and apparatus for determining the geographic location of a device 
FR2905006B1 (en) *  20060821  20081017  Airbus France Sas  Process for monitoring the integrity of an aircraft position calculated on board 
US7436354B2 (en) *  20060907  20081014  The Mitre Corporation  Methods and systems for mobile navigational applications using global navigation satellite systems 
CN100582811C (en) *  20061220  20100120  北京航空航天大学  Method for monitoring GNSS receiver autonomous integrity based on multisatellite failure recognition 
US20130138338A1 (en) *  20111130  20130530  Honeywell International Inc.  Graphical presentation of receiver autonomous integrity monitoring outage regions on an aircraft display 
US9547086B2 (en)  20130326  20170117  Honeywell International Inc.  Selected aspects of advanced receiver autonomous integrity monitoring application to kalman filter based navigation filter 
CN103592658A (en) *  20130930  20140219  北京大学  New method for RAIM (receiver autonomous integrity monitoring) based on satellite selecting algorithm in multimode satellite navigation system 
CN103592657B (en) *  20130930  20160831  北京大学  Under lowvisibility satellite based clock errorassisted singlemode implementation raim 
US9784844B2 (en)  20131127  20171010  Honeywell International Inc.  Architectures for high integrity multiconstellation solution separation 
CN104297557B (en) *  20141008  20170426  北京航空航天大学  Suitable for freeflying aircraft multijoint navigation Autonomous Integrity Monitoring 
DE102016224804A1 (en) *  20161213  20180614  Bayerische Motoren Werke Aktiengesellschaft  A method for determining the position of a charging station for the wireless transmission of electric energy to a vehicle 
Citations (12)
Publication number  Priority date  Publication date  Assignee  Title 

US5412584A (en) *  19921130  19950502  Kabushiki Kaisha Toyota Chuo Kenkyusho  Dynamic system diagnosing apparatus, tire air pressure diagnosing apparatus and vehicle body weight change detecting apparatus using same 
US5544308A (en) *  19940802  19960806  Giordano Automation Corp.  Method for automating the development and execution of diagnostic reasoning software in products and processes 
US5680409A (en) *  19950811  19971021  FisherRosemount Systems, Inc.  Method and apparatus for detecting and identifying faulty sensors in a process 
US5841399A (en) *  19960628  19981124  Alliedsignal Inc.  Fault detection and exclusion used in a global positioning system GPS receiver 
US5931889A (en) *  19950124  19990803  Massachusetts Institute Of Technology  Clockaided satellite navigation receiver system for monitoring the integrity of satellite signals 
US6114988A (en) *  19961231  20000905  Honeywell Inc.  GPS receiver fault detection method and system 
US6204806B1 (en) *  19990226  20010320  Rockwell Collins, Inc.  Method of enhancing receiver autonomous GPS navigation integrity monitoring and GPS receiver implementing the same 
US6502042B1 (en) *  20001026  20021231  Bfgoodrich Aerospace Fuel And Utility Systems  Fault tolerant liquid measurement system using multiplemodel state estimators 
US6515618B1 (en) *  20001129  20030204  Trimble Navigation Ltd.  Fault detection and exclusion in a positioning system receiver 
US6691066B1 (en) *  20000828  20040210  Sirf Technology, Inc.  Measurement fault detection 
US20040089051A1 (en) *  20010309  20040513  Camenisch Johann L.  Method and device for evaluating a liquid dosing process 
US20040148940A1 (en) *  20030130  20040805  General Electric Company  Method and apparatus for monitoring the performance of a gas turbine system 
Patent Citations (12)
Publication number  Priority date  Publication date  Assignee  Title 

US5412584A (en) *  19921130  19950502  Kabushiki Kaisha Toyota Chuo Kenkyusho  Dynamic system diagnosing apparatus, tire air pressure diagnosing apparatus and vehicle body weight change detecting apparatus using same 
US5544308A (en) *  19940802  19960806  Giordano Automation Corp.  Method for automating the development and execution of diagnostic reasoning software in products and processes 
US5931889A (en) *  19950124  19990803  Massachusetts Institute Of Technology  Clockaided satellite navigation receiver system for monitoring the integrity of satellite signals 
US5680409A (en) *  19950811  19971021  FisherRosemount Systems, Inc.  Method and apparatus for detecting and identifying faulty sensors in a process 
US5841399A (en) *  19960628  19981124  Alliedsignal Inc.  Fault detection and exclusion used in a global positioning system GPS receiver 
US6114988A (en) *  19961231  20000905  Honeywell Inc.  GPS receiver fault detection method and system 
US6204806B1 (en) *  19990226  20010320  Rockwell Collins, Inc.  Method of enhancing receiver autonomous GPS navigation integrity monitoring and GPS receiver implementing the same 
US6691066B1 (en) *  20000828  20040210  Sirf Technology, Inc.  Measurement fault detection 
US6502042B1 (en) *  20001026  20021231  Bfgoodrich Aerospace Fuel And Utility Systems  Fault tolerant liquid measurement system using multiplemodel state estimators 
US6515618B1 (en) *  20001129  20030204  Trimble Navigation Ltd.  Fault detection and exclusion in a positioning system receiver 
US20040089051A1 (en) *  20010309  20040513  Camenisch Johann L.  Method and device for evaluating a liquid dosing process 
US20040148940A1 (en) *  20030130  20040805  General Electric Company  Method and apparatus for monitoring the performance of a gas turbine system 
Cited By (15)
Publication number  Priority date  Publication date  Assignee  Title 

US20060047413A1 (en) *  20031202  20060302  Lopez Nestor Z  GNSS navigation solution integrity in noncontrolled environments 
US20100033370A1 (en) *  20031202  20100211  Gmv Aerospace And Defence, S.A.  Gnss navigation solution integrity in noncontrolled environments 
US8131463B2 (en)  20031202  20120306  Gmv Aerospace And Defence, S.A.  GNSS navigation solution integrity in noncontrolled environments 
US20070139263A1 (en) *  20051215  20070621  Gang Xie  Method and apparatus for improving fault detection and exclusion systems 
US7286083B2 (en) *  20051215  20071023  Motorola, Inc.  Method and apparatus for improving fault detection and exclusion systems 
US7956802B1 (en) *  20070521  20110607  Rockwell Collins, Inc.  Integrityoptimized receiver autonomous integrity monitoring (RAIM) for vertical integrity monitoring 
US20090070635A1 (en) *  20070706  20090312  Thales  Method of improving the integrity and safety of an avionics system 
WO2010059439A3 (en) *  20081124  20100805  Andrew Llc  System and method for determining falsified geographic location of a mobile device 
US7800533B2 (en)  20081124  20100921  Andrew, Llc  System and method for determining falsified geographic location of a mobile device 
US20100127920A1 (en) *  20081124  20100527  Andrew Llc  System and method for determining falsified geographic location of a mobile device 
WO2010059439A2 (en) *  20081124  20100527  Andrew Llc  System and method for determining falsified geographic location of a mobile device 
CN103308929A (en) *  20130524  20130918  北京东方计量测试研究所  Satellite navigation signal simulator used for pseudorange precision index measurement 
CN103308928A (en) *  20130524  20130918  北京东方计量测试研究所  Pseudorange precision measurement system of satellite navigation signal simulator 
CN103308930A (en) *  20130524  20130918  北京东方计量测试研究所  Pseudorange precision measurement method of satellite navigation signal simulator 
US9854398B1 (en) *  20160803  20171226  International Business Machines Corporation  System, method and recording medium for location verification 
Also Published As
Publication number  Publication date  Type 

US6864836B1 (en)  20050308  grant 
EP1660903A2 (en)  20060531  application 
EP1660903B1 (en)  20071017  grant 
CA2535713A1 (en)  20050324  application 
ES2294549T3 (en)  20080401  grant 
WO2005027283A2 (en)  20050324  application 
CN1846147A (en)  20061011  application 
JP2007504469A (en)  20070301  application 
WO2005027283A3 (en)  20050602  application 
DE602004009590D1 (en)  20071129  grant 
DE602004009590T2 (en)  20080724  grant 
Similar Documents
Publication  Publication Date  Title 

Hatch  Instantaneous ambiguity resolution  
US6205377B1 (en)  Method for navigation of moving platform by using satellite data supplemented by satellitecalibrated baro data  
US6268824B1 (en)  Methods and apparatuses of positioning a mobile user in a system of satellite differential navigation  
US5557284A (en)  Spoofing detection system for a satellite positioning system  
US6633256B2 (en)  Methods and systems for improvement of measurement efficiency in surveying  
US6885940B2 (en)  Navigation processing for a satellite positioning system receiver  
US20100109950A1 (en)  Tightlycoupled gnss/imu integration filter having speed scalefactor and heading bias calibration  
US6215442B1 (en)  Method and apparatus for determining time in a satellite positioning system  
US7292185B2 (en)  Attitude determination exploiting geometry constraints  
US6181274B1 (en)  Satellite navigation receiver for precise relative positioning in real time  
US5831576A (en)  Integrity monitoring of location and velocity coordinates from differential satellite positioning systems signals  
US5583774A (en)  Assuredintegrity monitoredextrapolation navigation apparatus  
US20050231423A1 (en)  Automatic decorrelation and parameter tuning realtime kinematic method and apparatus  
US6515618B1 (en)  Fault detection and exclusion in a positioning system receiver  
Serrano et al.  A GPS velocity sensor: how accurate can it be?–a first look  
US5825326A (en)  Realtime highaccuracy determination of integer ambiguities in a kinematic GPS receiver  
US20110148698A1 (en)  GNSS Signal Processing Methods and Apparatus with Scaling of Quality Measure  
US6424914B1 (en)  Fullycoupled vehicle positioning method and system thereof  
US6618670B1 (en)  Resolving time ambiguity in GPS using overdetermined navigation solution  
US5506588A (en)  Attitude determining system for use with global positioning system, and laser range finder  
US20090189804A1 (en)  Satellite differential positioning receiver using multiple baserover antennas  
US6861979B1 (en)  Method and apparatus for detecting anomalous measurements in a satellite navigation receiver  
US20030098810A1 (en)  System for determining precise orbit of satellite and method thereof  
US6421003B1 (en)  Attitude determination using multiple baselines in a navigational positioning system  
US5760737A (en)  Navigation system with solution separation apparatus for detecting accuracy failures 
Legal Events
Date  Code  Title  Description 

AS  Assignment 
Owner name: NAVCOM TECHNOLOGY, INC., CALIFORNIA Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:HATCH, RONALD R.;SHARPE, RICHARD T.;YANG, YUNCHUN;REEL/FRAME:014479/0443 Effective date: 20030904 

FPAY  Fee payment 
Year of fee payment: 4 

REMI  Maintenance fee reminder mailed  
FPAY  Fee payment 
Year of fee payment: 8 

AS  Assignment 
Owner name: DEERE & COMPANY, ILLINOIS Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:NAVCOM TECHNOLOGY, INC.;REEL/FRAME:034761/0398 Effective date: 20150109 

FPAY  Fee payment 
Year of fee payment: 12 