A method for GNSS positioning state domain multi-fault elimination

Abstract

A method for gradually eliminating multiple faults in the state domain of GNSS positioning, through GNSS extended Kalman filtering, using a state domain fault detection algorithm for detection, if there is no fault in the current epoch, the next epoch detection is performed, if there is a fault, the epoch observation values ​​of the current fault are arranged from small to large according to the normalized new information, the first n satellite observation values ​​are taken to calculate the posterior state estimation value and the covariance matrix for detection, if there is a fault, it means that the fault cannot be eliminated, and an alarm is issued to the user; if there is no fault, the observation value corresponding to the maximum new information is deleted, and the posterior state estimation value and the covariance matrix are calculated using the remaining satellite observation values ​​for detection, if there is a fault, the observation value corresponding to the maximum new information in the remaining observation values ​​is deleted, and this step is repeated until the fault is eliminated; if there is no fault, the next epoch detection is performed. The present invention is expanded from the state domain, and while ensuring the calculation efficiency, multiple faults existing in the GNSS are accurately eliminated to improve the positioning accuracy.

Description

Technical Field

[0001] The invention relates to a GNSS positioning state domain multi-fault elimination method, belonging to the technical field of satellite positioning fault elimination. Background Art

[0002] With the development of global navigation satellite system (GNSS) positioning technology, the integration and fusion of multiple systems has become a trend. At the same time, the probability of multiple faults occurring simultaneously has also greatly increased. The traditional receiver autonomous integrity monitoring algorithm has poor ability to detect and eliminate multiple faults, which will seriously affect the positioning accuracy of GNSS.

[0003] In the field of fault detection and elimination, the residual chi-square test method detects faults based on Kalman filter new information (i.e., measurement prediction error). It can detect faults in GNSS in a timely manner with less computational effort, and then perform a separate normality test on each satellite to eliminate single or multiple faults. However, due to the nonlinear relationship in the tightly coupled system, this method provides a direct assessment of the measurement prediction error, which is in contrast to the indirect assessment of the filter state estimation error. In addition, the measurement domain dimension in the residual chi-square test method is often high due to the number of satellites and the type of observations, resulting in a high fault detection threshold and thus missed alarms. In order to solve the problem of multiple fault detection and elimination, the prior art proposes a multi-hypothesis solution separation method based on the theory of the maximum distance method of the solution, and theoretically analyzes its feasibility. The main principle is to divide the Kalman filter into three levels in the GNSS / INS tightly coupled system, and perform multiple fault detection and elimination through the differences in the state estimation values ​​of the main filter, sub-filter, and secondary sub-filter, but the calculation is complex, and the amount of calculation will increase exponentially with the increase in the number of visible satellites and the number of faults. Therefore, under the premise of ensuring computational efficiency, multiple fault detection and elimination in GNSS positioning is still a problem that needs to be solved urgently. Summary of the invention

[0004] The present invention provides a method for gradually eliminating multiple faults in the state domain of GNSS positioning. The method can develop a fault detection and elimination algorithm from the state domain, directly evaluate the a posteriori state estimation error while ensuring the calculation efficiency, eliminate the faults one by one, and improve the positioning accuracy of GNSS.

[0005] In order to achieve the above object, the present invention provides a GNSS positioning state domain multiple fault elimination method, comprising the following steps:

[0006] S1: Obtain the posterior state estimate of k epochs through GNSS extended Kalman filtering and its covariance matrix P xx,k, use the state domain fault detection algorithm to perform fault detection on each epoch. If there is no fault in the current epoch, directly perform fault detection and elimination on the next epoch. If there is a fault in the current epoch, proceed to the next step;

[0007] S2: Rearrange the GNSS observations of the current faulty epoch from small to large according to the normalized new information, and take the first n satellite observations to calculate the posterior state estimate and the covariance matrix P 0,xx,k , perform fault detection on it. If there is a fault, it means that the positioning result calculated by the current n satellite observation values ​​is unreliable, the observation value quality of the current epoch is poor, and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated; if there is no fault, it means that the fault can be eliminated and proceed to the next step;

[0008] S3: Delete the GNSS observation corresponding to the maximum innovation, and use the remaining satellite observations to calculate the posterior state estimate and the covariance matrix P test,xx,k , perform fault detection on it. If a fault exists, it means that the fault has not been completely eliminated. Delete the GNSS observation value corresponding to the maximum innovation in the remaining observation values, repeat this step until the fault is completely eliminated, and perform fault detection and elimination for the next epoch; if no fault exists, it means that the fault has been eliminated, and directly perform fault detection and elimination for the next epoch.

[0009] Repeat the above steps until the fault detection and elimination of k epochs are completed.

[0010] Furthermore, the fault detection statistic of the state domain fault detection algorithm used in step S1 is The detection threshold is in, P dd,k =P x ' x,k -P xx,k , is the prior state estimate, P x ' x,k is its covariance matrix; P dd,k is the residual d k The covariance matrix of P dd,k The eigenvector matrix of dd,k P dd,k The eigenvalue matrix of For dd,k The maximum eigenvalue of The i in the equation is the component corresponding to the maximum eigenvalue, erf -1 (·) is the inverse function of the Gaussian error function, P FAis the false alarm rate of the specific application field of navigation and positioning. Then go to step S2; if Then carry out fault detection and elimination for the next epoch.

[0011] Furthermore, the GNSS observation value of the epoch currently experiencing a fault in step S2 is z k =[z 1 ,z 2 ,z 3 ,…,z N ], and the normalized new information is arranged from small to large. Where N is the total number of observations, and the normalized innovation calculation formula is: in,

[0012] h k (·) is the measurement function, 1≤i≤N, R k is the measurement noise matrix, Indicates that the state vector x obeys the mean Covariance matrix cov[x] = P x ' x Gaussian distribution of

[0013] The observation vector composed of the first n observations is Depend on The calculated a posteriori state estimate The covariance matrix P 0,xx,k =P x ' x,k -K 0,k P 0 ' ,zz,k (K 0,k ) T , Kalman filter gain K 0,k =P 0 ' ,xz,k (P 0 ' ,zz,k ) -1 , The prior measurement value of The covariance matrix of and The cross covariance matrix of Among them, h 0,k (·)for The measurement function, R 0,k for The corresponding measurement noise matrix, based on the a posteriori state estimate and its covariance matrix P0,xx,k Constructing Fault Detection Statistics The detection threshold is in P 0,dd,k =P x ' x,k -P 0,xx,k , P 0,dd,k The eigenvector matrix of 0,dd,k P 0,dd,k The eigenvalue matrix of For 0,dd,k The maximum eigenvalue of The i in is the component corresponding to the maximum eigenvalue. It means that the quality of the observation data of the current epoch is poor and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated. Then proceed to step S3.

[0014] Furthermore, after deleting the GNSS observation value corresponding to the maximum innovation in step S3, the observation vector is By z test,k The calculated a posteriori state estimate The covariance matrix P test,xx,k =P x ' x,k -K test, k P te ' st,zz,k (K test,k ) T , Kalman filter gain K test,k =P te ' st,xz,k (P te ' st,zz,k ) -1 , z test,k The prior measurement value of The covariance matrix of and The cross covariance matrix of where h test,k (·) is z test,k The measurement function, R test,k For z test,k The corresponding measurement noise matrix, based on the a posteriori state estimate and its covariance matrix P test,xx,k Constructing Fault Detection Statistics The detection threshold is in, P test,dd,k =P x ' x,k -P test,xx,k , P test,dd,k The eigenvector matrix of test,dd,k P test,dd,k The eigenvalue matrix of For test,dd,k The maximum eigenvalue of The i in is the component corresponding to the maximum eigenvalue. Indicates that the fault has not been completely eliminated. Delete the GNSS observation value corresponding to the maximum innovation in the remaining observation values, repeat this step until the fault is completely eliminated, and then perform fault detection and elimination for the next epoch; if This means that the fault has been eliminated and the next epoch of fault detection and elimination can be carried out directly.

[0015] The present invention avoids high threshold missed alarms caused by high measurement domain dimension by directly developing fault detection and elimination algorithms from the state domain of the GNSS system. Compared with the existing multi-hypothesis solution separation method, it adopts a multi-fault gradual elimination strategy, which greatly reduces the computational burden brought by the multi-stage filter. The algorithm has a simple structure, a small amount of calculation, and can operate online in real time, realizing multi-fault elimination from the perspective of positioning results. Under the premise of ensuring computational efficiency, the posterior state estimation error is directly evaluated, and faults are eliminated one by one, thereby improving the positioning accuracy of GNSS. In addition, the present invention can be used not only for single systems such as GPS, GLONASS, BDS and GALILEO, but also for combined positioning of different satellite systems and inertial systems, with a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flow chart of the present invention;

[0017] Figure 2 1 is a diagram of the fault detection result of the tightly combined small-amplitude fault simulation data experiment in the embodiment of the present invention, wherein (a) is a diagram of the RCTM fault detection result, (b) is a diagram of the MHSS fault detection result, and (c) is a diagram of the SRCTM fault detection result;

[0018] Figure 3 1 is a position error diagram of a tightly combined double-fault simulation data experiment in an embodiment of the invention, wherein (a) is a position error diagram in the east direction, (b) is a position error diagram in the north direction, and (c) is a position error diagram in the sky direction;

[0019] Figure 41 is a velocity error diagram of a tightly combined double-fault simulation data experiment in an embodiment of the invention, wherein (a) is a velocity error diagram in the east direction, (b) is a velocity error diagram in the north direction, and (c) is a velocity error diagram in the sky direction;

[0020] Figure 5 It is a posture error diagram of a tightly combined double-fault simulation data experiment in an embodiment of the invention, wherein (a) is a roll angle error diagram, (b) is a pitch angle error diagram, and (c) is a heading angle error diagram. DETAILED DESCRIPTION

[0021] The present invention will be further described below in conjunction with the accompanying drawings.

[0022] like Figure 1 As shown, a GNSS positioning state domain multi-fault gradual elimination method comprises the following steps:

[0023] S1: Obtain the posterior state estimate of k epochs through GNSS extended Kalman filtering and its covariance matrix P xx,k , use the state domain fault detection algorithm to perform fault detection on each epoch. If there is no fault in the current epoch, directly perform fault detection and elimination on the next epoch. If there is a fault in the current epoch, proceed to the next step;

[0024] S2: Rearrange the GNSS observations of the current faulty epoch from small to large according to the normalized new information, and take the first n satellite observations to calculate the posterior state estimate and the covariance matrix P 0,xx,k , perform fault detection on it. If there is a fault, it means that the positioning result calculated by the current n satellite observation values ​​is unreliable, the observation value quality of the current epoch is poor, and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated; if there is no fault, it means that the fault can be eliminated and proceed to the next step;

[0025] S3: Delete the GNSS observation corresponding to the maximum innovation, and use the remaining satellite observations to calculate the posterior state estimate and the covariance matrix P test,xx,k , perform fault detection on it. If a fault exists, it means that the fault has not been completely eliminated. Delete the GNSS observation value corresponding to the maximum innovation in the remaining observation values, repeat this step until the fault is completely eliminated, and perform fault detection and elimination for the next epoch; if no fault exists, it means that the fault has been eliminated, and directly perform fault detection and elimination for the next epoch.

[0026] Embodiment: The GNSS positioning state domain multi-fault elimination method of the present invention can be used not only for single systems such as GPS, GLONASS, BDS and GALILEO, but also for combined positioning of different satellite systems and inertial systems. The following embodiment is the application of the present invention in BDS pseudorange single point positioning, which specifically includes the following steps:

[0027] S1: Extend the Kalman filter through BDS pseudo-range single point positioning to obtain the posterior state estimate of k epochs and its covariance matrix P xx,k , use the state domain fault detection algorithm to perform fault detection on each epoch. If there is no fault in the current epoch, directly perform fault detection and elimination on the next epoch. If there is a fault in the current epoch, proceed to the next step;

[0028] S1.1: Define the receiver initial state value and false alarm rate

[0029] Define the a priori state estimate of the receiver at epoch k and its covariance matrix is ​​P x ' x,k , And determine the false alarm rate as P FA ,in Indicates that the state vector x obeys the mean Covariance matrix cov[x] = P x ' x Gaussian distribution, let k = 0, then the system is in the initial state;

[0030] S1.2: Get the pseudo-range observation value of the BDS system:

[0031] P=ρ-cδt+I+T+ε (1)

[0032] Where P is the pseudorange, ρ is the geometric distance from the satellite to the receiver, cδt is the speed of light multiplied by the receiver clock error, I is the ionospheric delay error, T is the tropospheric delay error, and ε is the pseudorange observation noise. Formula (1) is linearized at the approximate coordinates of the station:

[0033] P-ρ 0 -D=ldX+mdY+ndZ+cδt (2)

[0034] In the formula, ρ 0 is the geometric distance from the satellite to the approximate coordinates of the receiver, D = I + T + ε, ((l, m, n) is the direction cosine from the receiver to the satellite, (dX, dY, dZ) is the coordinate correction number;

[0035] S1.3: Posterior state estimate for k epochs via BDS extended Kalman filter and its covariance matrix Pxx,k :

[0036] S1.3.1: Define the state equation and measurement equation of the BDS system:

[0037] x k+1 =f k (x k )+w k (3)

[0038] z k =h k (x k )+v k (4)

[0039] In the formula, x k is the state vector, including the receiver coordinate correction and clock correction; f k is the state transfer function; w k is the system process noise, and its covariance matrix is ​​Q k ; z k is the BDS pseudorange measurement value in equation (2), h k is the measurement function, v k is the measurement noise, and its covariance matrix is ​​R k ;

[0040] S1.3.2: Extended Kalman filtering is performed on the BDS to obtain the posterior state estimate of k epochs and its covariance matrix P xx,k :

[0041]

[0042] P xx,k =P x ' x,k -K k P z ' z,k (K k ) T (6)

[0043] in:

[0044] K k = P x ' z,k (P z ' z,k ) -1 (7)

[0045] P xx,k =P x ' x,k -K k P z ' z,k(K k ) T (8)

[0046]

[0047] In the formula, K k is the Kalman filter gain, is the prior measurement value, P x ' z,k is the state measurement cross covariance matrix, P z ' z,k is the measurement covariance matrix;

[0048] S1.4: Fault detection using state domain fault detection algorithm

[0049] S1.4.1:

[0050]

[0051] in, P dd,k =P x ' x,k -P xx,k , P dd,k The eigenvector matrix of dd,k P dd,k The eigenvalue matrix of For dd,k The maximum eigenvalue of The i in the equation is the component corresponding to the maximum eigenvalue, erf -1 (·) is the inverse function of the Gaussian error function;

[0052] S1.4.2: If Perform fault detection and troubleshooting for the next epoch. Then proceed to step S2;

[0053] S2: Rearrange the GNSS observations of the current faulty epoch from small to large according to the normalized new information, and take the first n satellite observations to calculate the posterior state estimate and the covariance matrix P 0,xx,k , perform fault detection on it:

[0054] S2.1: Let the original satellite observation value z k =[z 1 ,z 2 ,z 3 ,…,z N ], and the normalized new information is arranged from small to large. Where N is the total number of observations, and the normalized innovation calculation formula is:

[0055]

[0056] In the formula, 1≤i≤N;

[0057] S2.2: Take the observation vector consisting of the first n observations n can be 4 in an open environment and 6 in a harsh environment to increase the robustness of the navigation and positioning algorithm. Compute the posterior state estimate and its covariance matrix P 0,xx,k :

[0058]

[0059] P 0,xx,k =P x ' x,k -K 0,k P 0 ' ,zz,k (K 0,k ) T (16)

[0060] The Kalman filter gain K 0,k =P 0 ' ,xz,k (P 0 ' ,zz,k ) -1 , The prior measurement value of The covariance matrix of and The cross covariance matrix of Among them, h 0,k (·)for The measurement function of

[0061] R 0,k for The corresponding measurement noise matrix;

[0062] S2.2: Based on the posterior state estimate and its covariance matrix P 0,xx,k Construct fault detection statistics and calculate detection thresholds:

[0063]

[0064] in P 0,dd,k =P x ' x,k -P0,xx,k ,

[0065] P 0,dd,k The eigenvector matrix of 0,dd,k P 0,dd,k The eigenvalue matrix of For 0,dd,k The maximum eigenvalue of The i in is the component corresponding to the maximum eigenvalue. It means that the quality of the observation data of the current epoch is poor and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated. Then proceed to step S3;

[0066] S3: Delete the GNSS observation corresponding to the maximum innovation, and use the remaining satellite observations to calculate the posterior state estimate and the covariance matrix P test,xx,k , perform fault detection on it:

[0067] S3.1: After deleting the GNSS observation value corresponding to the maximum innovation, the observation vector is Using z test,k Compute the posterior state estimate and its covariance matrix P test,xx,k :

[0068]

[0069] P test,xx,k =P x ' x,k -K test,k P te ' st,zz,k (K test,k ) T (20)

[0070] In the formula, the Kalman filter gain K test,k =P te ' st,xz,k (P te ' st,zz,k ) -1 , z test,k The prior measurement value of The covariance matrix of and The cross covariance matrix of where h test,k (·) is z test,k The measurement function, R test,k For z test,k The corresponding measurement noise matrix;

[0071] S3.2: Based on the posterior state estimate and its covariance matrix P test,xx,k Construct fault detection statistics and calculate detection thresholds:

[0072]

[0073] In the formula, P test,dd,k =P x ' x,k -P test,xx,k , P test,dd,k The eigenvector matrix of test,dd,k P test,dd,k The eigenvalue matrix of For test,dd,k The maximum eigenvalue of The i in is the component corresponding to the maximum eigenvalue. Indicates that the fault has not been completely eliminated, return to step S3.1 until the fault is completely eliminated, and then proceed to the next step; if It means the fault has been eliminated and you can proceed to the next step directly.

[0074] S4: Continue to detect and eliminate faults in the next epoch, and predict the prior state estimate of the next epoch by the following formula: and its covariance matrix P x ' x,k+1 :

[0075]

[0076] Let k=k+1 and return to step S1.2.

[0077] In order to further illustrate the characteristics and advantages of the present invention, the GNSS / INS pseudo-range tight combination simulation data is used for experimental verification and analysis. Firstly, the fault detection performance of the method SRCTM used in the present invention, the prior art RCTM (based on the measurement residual method), and the MHSS (multiple hypothesis solution separation method) are compared and verified. Secondly, the double fault is taken as an example to conduct experimental verification of multi-fault detection and elimination. At the same time, the multi-fault detection and elimination efficiency of the present invention and MHSS are compared. The false alarm rate of fault detection and elimination in the experiment is 10 -6 ;

[0078] The modified GPSoft toolbox is used to simulate the simple uniform linear motion of the aircraft in the sky. The single-frequency pseudorange and pseudorange rate of GPS are used to perform differential tight combination with INS. The standard deviations of pseudorange and pseudorange rate are 1m and 0.1m / s respectively. The sampling frequency of the receiver is 1Hz, and the sampling frequency of INS is 200Hz. Its technical parameters are shown in Table 1. It can be seen that the number of satellites is always 6, and the value of n in the present invention is 4.

[0079] Table 1 IMU technical parameters of tight combination simulation data experiment

[0080]

[0081] Since there are no faults in the observations in the tightly combined simulation data, the navigation positioning results are highly accurate. In order to compare the fault detection differences between SRCTM and RCTM, a small-amplitude fault scheme is set: starting from 100s, a small-amplitude fault of 6-8m is artificially added to a pseudorange observation every 100s. Figure 2 (a), (b), and (c) are the fault detection statistics and detection thresholds of RCTM, MHSS, and SRCTM, respectively. It can be seen that MHSS and SRCTM have a relatively lower detection threshold by transferring the measurement residuals to state residuals, and thus have better small-amplitude fault detection performance than RCTM;

[0082] In order to verify the multi-fault detection and elimination performance of the present invention, a double fault scheme is set up: 20m and 30m gross errors are artificially added to the two pseudo-range observation values ​​of 101-105s, 301-305s and 501-505s respectively. Figures 3 to 5 They are the position error diagram, velocity error diagram, and attitude error diagram of the double fault experiment respectively; among them, Figure 3 (a) is the position error map in the east direction, (b) is the position error map in the north direction, and (c) is the position error map in the sky direction. Figure 4 (a) is the velocity error diagram in the east direction, (b) is the velocity error diagram in the north direction, and (c) is the velocity error diagram in the sky direction. Figure 5 (a) is the roll angle error diagram, (b) is the pitch angle error diagram, and (c) is the heading angle error diagram. Figures 3 to 5 It can be seen that the double faults artificially added at different epochs can be effectively eliminated by the present invention, thereby improving the navigation positioning accuracy;

[0083] Table 2 shows the root mean square (RMS) of the position, velocity and attitude errors before fault elimination, after single fault elimination and after double fault elimination in the double fault experiment. It can be seen that the accuracy of each component is improved to varying degrees after all faults are eliminated by the present invention, among which the position accuracy is improved most significantly. Compared with eliminating a single fault, the position accuracy in the east, north and sky directions before fault elimination is improved by -50.30%, 61.34% and 76.49% respectively. After eliminating a single fault, although the accuracy in the north and sky directions is increased, the accuracy in the east direction is reduced. This is because the two new information elements containing the fault, the Kalman filter gain elements corresponding to the north and sky positions are both positive, and there is a superposition effect, while the Kalman filter gain elements corresponding to the east position are one positive and one negative, and there is a cancellation effect; compared with eliminating a single fault, the position accuracy in the northeast, north and sky directions is improved by 59.31%, 54.40% and 82.96% respectively after eliminating double faults;

[0084] Table 2 Experimental RMS error of tight combination double fault simulation data

[0085]

[0086] To compare the double fault detection and elimination efficiency of MHSS and the present invention, Table 3 summarizes the average processing time of MHSS and the present invention in three fault time periods:

[0087] Table 3 Tightly combined double fault simulation data experiment MHSS and processing time of the present invention

[0088]

[0089] It can be seen from Table 3 that the present invention adopts a multi-fault elimination strategy to eliminate faults one by one, which effectively avoids the complex calculation caused by the blind assumption of faults by MHSS and greatly improves the efficiency of fault detection and elimination.

Claims

1. A method for gradually eliminating multiple faults in the GNSS positioning state domain, characterized in that: The steps include: S1: Obtain the posterior state estimate of k epochs through GNSS extended Kalman filtering and its covariance matrix P xx,k , use the state domain fault detection algorithm to perform fault detection on each epoch. If there is no fault in the current epoch, directly perform fault detection and elimination on the next epoch; if there is a fault in the current epoch, proceed to the next step; Among them, the fault detection statistics using the state domain fault detection algorithm is The detection threshold is in, P dd,k =P x ' x,k -P xx,k , is the prior state estimate, P x ' x,k is its covariance matrix; P dd,k is the residual d k The covariance matrix of P dd,k The eigenvector matrix of dd,k P dd,k The eigenvalue matrix of For dd,k The maximum eigenvalue, erf -1 (·) is the inverse function of the Gaussian error function, P FA is the false alarm rate of the specific application field of navigation and positioning. Then go to step S2; if Then the fault detection and elimination of the next epoch is carried out; S2: Rearrange the GNSS observations of the current faulty epoch from small to large according to the normalized new information, and take the first n satellite observations to calculate the posterior state estimate and the covariance matrix P 0,xx,k , perform fault detection on it. If there is a fault, it means that the positioning result calculated by the current n satellite observation values ​​is unreliable, the observation value quality of the current epoch is poor, and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated; if there is no fault, it means that the fault can be eliminated and proceed to the next step; S3: Delete the GNSS observation corresponding to the maximum innovation, and use the remaining satellite observations to calculate the posterior state estimate and the covariance matrix P test,xx,k , perform fault detection on it. If a fault exists, it means that the fault has not been completely eliminated. Delete the GNSS observation value corresponding to the maximum innovation in the remaining observation values, repeat this step until the fault is completely eliminated, and perform fault detection and elimination for the next epoch; if no fault exists, it means that the fault has been eliminated, and directly perform fault detection and elimination for the next epoch.

2. The GNSS positioning state domain multiple fault elimination method according to claim 1, characterized in that: The GNSS observation value of the epoch with the current fault in step S2 is z k =[z1,z2,z3,…,z N ], and the normalized new information is arranged from small to large. Where N is the total number of observations, and the normalized innovation calculation formula is: in, h k (·) is the measurement function, 1≤i≤N, R k is the measurement noise matrix, Represents the state vector x k Subordinate to the mean The covariance matrix cov[x k ]=P x ' x,k Gaussian distribution of The observation vector composed of the first n observations is Depend on The calculated a posteriori state estimate The covariance matrix P 0,xx,k =P x ' x,k -K 0,k P0′ ,zz,k (K 0,k ) T , Kalman filter gain K 0,k =P0′ ,xz,k (P0′ ,zz,k ) -1 , The prior measurement value of The covariance matrix of and The cross covariance matrix of Among them, h 0,k (·)for The measurement function, R 0,k for The corresponding measurement noise matrix, based on the a posteriori state estimate and its covariance matrix P 0,xx,k Constructing Fault Detection Statistics The detection threshold is in P 0,dd,k =P x ' x,k -P 0,xx,k , P 0,dd,k The eigenvector matrix of 0,dd,k P 0,dd,k The eigenvalue matrix of For 0,dd,k The maximum eigenvalue of It means that the quality of the observation data of the current epoch is poor and the fault cannot be eliminated. An alarm is issued to the user and the troubleshooting of the current epoch is terminated. Then proceed to step S3.

3. The GNSS positioning state domain multiple fault elimination method according to claim 2, characterized in that: After deleting the GNSS observation value corresponding to the maximum innovation in step S3, the observation vector is By z test,k The calculated a posteriori state estimate The covariance matrix P test,xx,k =P x ' x,k -K test,k P te ' st,zz,k (K test,k ) T , Kalman filter gain K test,k =P te ' st,xz,k (P te ' st,zz,k ) -1 , z test,k The prior measurement value of The covariance matrix of and The cross covariance matrix of where h test,k (·) is z test,k The measurement function, R test,k For z test,k The corresponding measurement noise matrix, based on the a posteriori state estimate and its covariance matrix P test,xx,k Constructing Fault Detection Statistics The detection threshold is in, P test,dd,k =P x ' x,k -P test,xx,k , P test,dd,k The eigenvector matrix of test,dd,k P test,dd,k The eigenvalue matrix of For test,dd,k The maximum eigenvalue of Indicates that the fault has not been completely eliminated. Delete the GNSS observation value corresponding to the maximum innovation in the remaining observation values, repeat this step until the fault is completely eliminated, and then perform fault detection and elimination for the next epoch; if This means that the fault has been eliminated and the next epoch of fault detection and elimination can be carried out directly.

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