A method for MHSS FDE based on inter-satellite differential GPS / BDS / INS compact integrated navigation

Abstract

This invention discloses an MHSS FDE method for inter-satellite single-difference GPS / BDS / INS compact combination positioning: Initialization is performed to obtain the inter-system bias between GPS and BDS; an inter-satellite / inertial compact combination model based on inter-satellite difference is established; a fault subset is designed based on the number of satellites; the detection statistics and thresholds corresponding to each fault subset are solved, and fault detection and removal are performed. This invention can handle faults in multi-satellite observations and maximize the utilization of correct satellite observations. The method includes initialization to solve the inter-system bias between GPS and BDS; establishing a satellite / inertial compact combination model based on inter-satellite difference; designing a fault subset based on the number of satellites; constructing a test statistic based on the fault subset, performing fault detection, and designing an MHSS fault removal algorithm based on the detection results with the principle of "maximum fault contribution as the highest priority for removal"; finally, the positioning result is output.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation technology, and specifically relates to an MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation. Background Technology

[0002] Satellite / inertial integrated navigation (SINS) has become one of the most common methods for outdoor positioning due to the complementarity of satellite navigation and inertial navigation systems. Based on the integration method, SINS can be divided into loosely integrated, tightly integrated, and deeply integrated navigation. Tightly integrated SINS, using pseudorange / pseudorange rate as the measurement input, offers higher positioning accuracy and reliability than loosely integrated navigation, and lower computational cost and better implementation than deeply integrated navigation. With the development and improvement of global satellite navigation systems in various countries, the number of visible satellites has increased, improving the accuracy and availability of integrated navigation. However, this also increases the probability of simultaneous failures of multiple satellite observations. Observation failures are often caused by multipath effects, human interference, spoofing, and random hardware and software failures in satellite navigation, making them unpredictable and unmodelable. Therefore, multi-observation failure detection and elimination (FDE) algorithms are of great significance for reliable navigation based on inertial / satellite integration.

[0003] Currently, satellite information fault detection algorithms applied to integrated navigation systems include Receiver Autonomous Integrity Monitoring (RAIM) and Receiver Autonomous Integrity Extrapolation (AIME). These methods are highly sensitive to single faults but cannot effectively detect multiple faults. Multiple Hypothesis Solution Separation (MHSS) separates different faults into different subsets by performing combined operations on all satellites. It constructs a test statistic based on the difference between the subset solution and the full set solution, making it an effective method for multiple fault detection. It has been applied to Advanced Receiver Integrity Monitoring (ARAIM), but it is currently only applied to single receivers and is not well-suited to the integrated navigation framework. Summary of the Invention

[0004] To address the problems and difficulties of existing technologies, this invention proposes an MHSS FDE method for inter-satellite single-difference GPS / BDS / INS compact integrated positioning. This method integrates the GPS / BDS / INS compact integrated navigation framework with MHSS algorithm theory to detect and eliminate multi-observation faults, thereby ensuring the reliability and stability of the integrated navigation system.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention proposes a MHSS FDE method for inter-satellite single-difference GPS / BDS / INS compact combination positioning, which can handle multi-satellite observation faults and maximize the use of correct satellite observations. The method includes initializing and solving for the bias between the GPS and BDS systems; establishing a satellite / inertial compact combination model based on inter-satellite difference; designing a fault subset based on the number of satellites; constructing a test statistic based on the fault subset for fault detection; designing an MHSS fault removal algorithm based on the detection results, prioritizing the removal of faults with the largest contribution; and finally outputting the positioning result.

[0007] For the fault detection and removal section: Calculate the test statistics and thresholds for all fault subsets. If all test statistics are within the threshold, the system is considered fault-free; otherwise, a fault is considered present and needs to be removed. Fault removal follows the principle of "maximum fault contribution as the highest priority for removal." Only one fault hypothesis star corresponding to a fault subset is removed at a time. After removal, the measurement equation construction, fault subset design, fault detection, and removal processes are repeated.

[0008] like Figure 1 As shown, an MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation includes the following steps:

[0009] Step (1): Initialize and obtain the system deviation between GPS and BDS;

[0010] In step (1), the initialization phase obtains the prior system-to-system deviation between GPS and BDS before the system officially starts working. The method for solving the system-to-system deviation at epoch k is as follows:

[0011] δt τ,k =δt uG,k -δt uB,k (1)

[0012] Where: δt uG,k and δt uB,k These are the GPS receiver clock bias and BDS receiver clock bias obtained from pseudorange point positioning at epoch k, respectively, δt. τ,k To obtain the a priori inter-system deviation δt, we take the mean of the inter-system deviations obtained during the initialization phase for this epoch. τ :

[0013]

[0014] Where: j represents the j-th epoch, δt τ,j The inter-system bias is at epoch j.

[0015] Step (2): Establish a satellite / inertial compact combination model based on inter-satellite difference;

[0016] The establishment of the measurement equations in the satellite / inertial compact combination model based on interplanetary difference in step (2) includes the following steps:

[0017] Step (21) corrects the satellite clock error, ionospheric error and tropospheric error of the satellite pseudorange observations obtained at the current epoch, and subtracts the inter-system bias from the pseudorange observations of the BDS system. The final value is the pseudorange observations used for subsequent calculations.

[0018] Step (22): Select the satellite with the highest satellite elevation angle as the reference satellite L in the star difference calculation, and calculate the satellite pseudorange interplanetary difference value respectively. Interstellar difference with inertial navigation pseudorange

[0019]

[0020] in: and The pseudorange values ​​are divided into those for non-reference satellite i and reference satellite L. and These are the predicted pseudoranges of non-reference satellite i and reference satellite L, respectively, calculated by the inertial navigation system. and The value corresponds to the geometric distance between the satellite and the receiver. Assuming the total number of satellites is N, the measurement Z... k and measurement matrix H k They are respectively:

[0021]

[0022] in, and These are the inertial recursive pseudorange inter-satellite difference values ​​and the satellite observation pseudorange inter-satellite difference values ​​corresponding to the first satellite, respectively. and These are the inter-satellite difference values ​​for the inertial recursive pseudorange and the inter-satellite difference values ​​for the satellite observation pseudorange corresponding to the (N-1)th satellite; These correspond to the 1st, i-th, and N-1th satellites, respectively. Defined as the unit observation vector difference between each satellite and the reference satellite, i.e. and The unit observation vectors for the i-th satellite and the reference satellite L are respectively. Let be the rotation matrix from navigation frame n to Earth frame e.

[0023] Step (3): Design a fault subset based on the number of satellites;

[0024] Step (3) includes the following steps:

[0025] Step (31): Considering first-order and second-order faults (single-satellite fault, dual-satellite fault, single-constellation fault, and simultaneous single-constellation and single-satellite faults), and ignoring faults in the reference satellite L observations, calculate the number of fault subsets:

[0026] N fault =2N+(N-1)(N-2) / 2 (7)

[0027] Where N is the total number of satellites, N fault This represents the number of fault subsets.

[0028] Step (32), calculate N fault Class identity matrix Each subset of faults has a corresponding class identity matrix; The corresponding fault subset γ q The diagonal elements corresponding to the faulty satellite are assumed to be 0.

[0029] like Figure 2 As shown, in step (4), the detection statistics and thresholds corresponding to each fault subset are solved, and fault detection and elimination are performed.

[0030] Step (4) includes the following steps:

[0031] Step (41): Calculate the filter gain K at epoch k under the fault-free assumption. k,0 ;

[0032] Step (42), calculate the fault subset γ q , q=1,…,N fault The filter gain matrix corresponding to epoch k

[0033]

[0034] Where: N fault γ represents the number of fault subsets. q This refers to the q-th fault subset, where q represents the index of the fault subset. Each fault subset has a corresponding class identity matrix.

[0035] Step (43) Calculate the state variables obtained from all satellites and the corresponding fault subset γ q Difference of state quantities

[0036]

[0037] Wherein: γ k The EKF innovation vector;

[0038] Step (44), calculate The corresponding covariance matrix

[0039]

[0040] Where: E{·} represents expectation, and T is the transpose symbol. For the new interest amount γ k covariance matrix P k / k-1 R is the covariance matrix for predicting state values ​​in one step. k To measure the covariance matrix;

[0041] Step (45), calculate the fault subset γ q The corresponding MHSS detection statistics Its variance:

[0042]

[0043] Where |·| represents the modulus of the vector; The 7th to 9th dimensions of the representation; variance for The corresponding covariance matrix The largest eigenvalue in the matrix is ​​and the standard deviation is .

[0044] Step (46), calculate the fault subset γ q The corresponding MHSS detection threshold

[0045]

[0046] Where: q represents the index of the fault subset. It is a 3×(Num-1) matrix. That is, only the elements corresponding to the positions in the gain matrix are extracted; b borm K represents the continuity deviation value. fa The upper 1-P of the standard normal distribution FA The 2 / 2 quantile is given by the following formula:

[0047]

[0048] Among them: Q -1 P is the inverse function of the cumulative function of the standard normal distribution. FA The preset false alarm rate;

[0049] Step (47), determine the fault subset γ qCheck whether the corresponding fault hypothesis is true and record it; if all fault subsets have been checked for whether the fault hypothesis is true or false, proceed to step (48); otherwise, q = q + 1, proceed to step (42).

[0050] Step (48) is to detect faults in k-epoch. If the fault hypothesis corresponding to all fault subsets is not true, then there is no fault and proceed to step (410). Otherwise, there is a fault and proceed to step (49) to remove the fault.

[0051] Step (49) involves fault elimination at epoch k; selecting the fault subset with the smallest number of fault stars and the valid fault hypothesis from all fault subsets, and then searching within these fault subsets. The satellite corresponding to the maximum fault hypothesis is deleted. Fault elimination is completed. Proceed to step (3) until the fault-free hypothesis is established.

[0052] Step (410): Output the combined navigation results.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) By using inter-satellite differential, the GPS / BDS / INS tight combination no longer needs to estimate the receiver clock bias, which reduces the state variables that need to be estimated, avoids the problem of inaccurate receiver clock bias modeling, and improves positioning accuracy.

[0055] (2) The MHSS FDE algorithm based on the inter-satellite differential GPS / BDS / INS compact combination fully integrates the framework of compact combination and the theory of MHSS, which can effectively detect and eliminate multiple fault observations and ensure the reliability of navigation and positioning. Attached Figure Description

[0056] Figure 1 This is a diagram of the algorithm structure of the present invention;

[0057] Figure 2 This is the FDE algorithm flow based on MHSS in this invention;

[0058] Figure 3 These are comparison diagrams of positioning errors under fault conditions in the simulation of this invention; where: (a) is the comparison diagram of eastward error, (b) is the comparison diagram of northward error, and (c) is the comparison diagram of celestial error. Detailed Implementation

[0059] The present invention will be further described below with reference to embodiments.

[0060] Simulation Description

[0061] To verify the effectiveness of the proposed MHSS FDE algorithm, simulated step faults were added to the experimental data. The fault size exceeded 100 meters, and the fault order was first-order and second-order, including single-satellite faults, dual-satellite faults, single-constellation faults, and simultaneous single-satellite and single-constellation faults. The specific fault conditions are shown in Table 1 below.

[0062] Table 1 Simulation Fault Status Table

[0063]

[0064] like Figure 3 The figure shows a comparison of positioning errors under fault simulation conditions using MHSS FDE, without MHSS FDE, and without fault simulation. Without the FDE algorithm, positioning errors in all three directions increase rapidly, and the celestial error fails to converge for a long time after the fault disappears. Using the MHSS FDE algorithm effectively suppresses error divergence under fault conditions, keeping positioning errors in the east, north, and celestial directions at normal levels. The method described in this invention can adapt to the tightly integrated framework of inter-satellite differential GPS / BDS / INS, effectively identify and eliminate multi-satellite observation faults, significantly improve positioning accuracy, and effectively ensure the integrity and reliability of positioning.

[0065] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for MHSS FDE based on inter-satellite differential GPS / BDS / INS tightly integrated navigation, characterized in that, Includes the following steps, Step (1): Initialize and obtain the system deviation between GPS and BDS; Step (2): Establish a satellite / inertial compact combination model based on inter-satellite difference; Step (3): Design a fault subset based on the number of satellites; Step (4) solve for the detection statistics and thresholds corresponding to each fault subset, and perform fault detection and removal; Step (4) includes the following steps: Step (41): Calculate the filter gain K at epoch k under the fault-free assumption. k,0 ; Step (42), calculate the fault subset γ q , q=1,…,N fault The filter gain matrix corresponding to epoch k Where: N fault γ represents the number of fault subsets. q This refers to the q-th fault subset, where q represents the index of the fault subset. Each fault subset has a corresponding class identity matrix. Step (43): Calculate the difference between the state variables obtained from all satellites and the state variables corresponding to the fault subset γ. Where: r k The EKF innovation vector; Step (44), calculate The corresponding covariance matrix Where: E{·} represents expectation, and T is the transpose symbol. For new information quantity r k covariance matrix P k / k-1 H is the covariance matrix for predicting state values ​​in one step. k For the measurement matrix, R k To measure the covariance matrix; Step (45), calculate the fault subset γ q The corresponding MHSS detection statistics Its variance: Where |·| represents the modulus of the vector; The 7th to 9th dimensions of the representation; variance for The corresponding covariance matrix The largest eigenvalue in the matrix is ​​and the standard deviation is . Step (46), calculate the fault subset γ q The corresponding MHSS detection threshold Where: q represents the index of the fault subset. It is a 3×(Num-1) matrix. That is, only the elements corresponding to the positions in the gain matrix are extracted; b borm K represents the continuity deviation value. fa The upper 1-P of the standard normal distribution FA The 2 / 2 quantile is given by the following formula: Among them: Q -1 P is the inverse function of the cumulative function of the standard normal distribution. FA The preset false alarm rate; Step (47), determine the fault subset γ q Check whether the corresponding fault hypothesis is true and record it; if all fault subsets have been checked for whether the fault hypothesis is true or false, proceed to step (48); otherwise, q = q + 1, proceed to step (42). Step (48) is to detect faults in k-epoch. If the fault hypothesis corresponding to all fault subsets is not true, then there is no fault and proceed to step (410). Otherwise, there is a fault and proceed to step (49) to remove the fault. Step (49) involves fault elimination at epoch k; selecting the fault subset with the smallest number of fault stars and the valid fault hypothesis from all fault subsets, and then searching within these fault subsets. The satellite corresponding to the maximum fault hypothesis is deleted. Fault elimination is completed. Proceed to step (3) until the fault-free hypothesis is established. Step (410): Output the combined navigation results.

2. The MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation as described in claim 1, characterized in that, In step (1), the initialization phase obtains the prior system-to-system deviation between GPS and BDS before the system officially starts working. The method for solving the system-to-system deviation at epoch k is as follows: δt τ,k =δt uG,k -δt uB,k (1) Where: δt uG,k and δt uB,k These are the GPS receiver clock bias and BDS receiver clock bias obtained from pseudorange point positioning at epoch k, respectively, δt. τ,k To obtain the a priori inter-system deviation δt, we take the mean of the inter-system deviations obtained during the initialization phase for this epoch. τ : Where: j represents the j-th epoch, δt τ,j The inter-system bias is at epoch j.

3. The MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation as described in claim 1, characterized in that, The establishment of the measurement equations in the satellite / inertial compact combination model based on interplanetary difference in step (2) includes the following steps: Step (21) corrects the satellite clock error, ionospheric error and tropospheric error of the satellite pseudorange observations obtained at the current epoch, and subtracts the inter-system bias from the pseudorange observations of the BDS system. The final value is the pseudorange observations used for subsequent calculations. Step (22): Select the satellite with the highest satellite elevation angle as the reference satellite L in the star difference calculation, and calculate the satellite pseudorange interplanetary difference value respectively. Interstellar difference with inertial navigation pseudorange in: and The pseudorange values ​​are divided into those for non-reference satellite i and reference satellite L. and These are the predicted pseudoranges of non-reference satellite i and reference satellite L, respectively, calculated by the inertial navigation system. and The value corresponds to the geometric distance between the satellite and the receiver. Assuming the total number of satellites is N, the measurement Z... k and measurement matrix H k They are respectively: in, and These are the inertial recursive pseudorange inter-satellite difference values ​​and the satellite observation pseudorange inter-satellite difference values ​​corresponding to the first satellite, respectively. and These are the inter-satellite difference values ​​for the inertial recursive pseudorange and the inter-satellite difference values ​​for the satellite observation pseudorange corresponding to the (N-1)th satellite; These correspond to the 1st, i-th, and N-1th satellites, respectively. Defined as the unit observation vector difference between each satellite and the reference satellite, i.e. i = 1, ..., N-1; and Let be the unit observation vectors of the i-th satellite and the reference satellite L, respectively. Let be the rotation matrix from navigation frame n to Earth frame e.

4. The MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation as described in claim 1, characterized in that, Step (3) includes the following steps: Step (31): Considering first-order and second-order faults, but ignoring faults in the reference satellite L observations, calculate the number of fault subsets: N fault =2N+(N-1)(N-2) / 2 (7) Where N is the total number of satellites, N fault This represents the number of fault subsets. Step (32), calculate N fault Class identity matrix Each subset of faults has a corresponding class identity matrix; The corresponding fault subset γ q The diagonal elements corresponding to the faulty satellite are assumed to be 0.

5. The MHSS FDE method based on inter-satellite differential GPS / BDS / INS tightly integrated navigation according to claim 4, characterized in that, The second-order faults include single-star faults, dual-star faults, single-constellation faults, and simultaneous faults of a single constellation and a single star.

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