Fault-tolerant method for SINS and GNSS integrated navigation system based on LSTM neural network

Abstract

The application provides a SINS and GNSS combined navigation system fault-tolerant method based on an LSTM neural network, and a set of fault detection and system fault-tolerant method based on an LSTM neural network auxiliary is provided for sudden faults and slowly changing faults in a SINS / GNSS loosely coupled navigation system. A new information Mahalanobis distance auxiliary chi-square test algorithm is used to detect the sudden faults existing in the system in real time, and a sequential probability ratio algorithm is used to detect the slowly changing faults existing in the system. Robust Kalman filtering based on M estimation is used to complete the robustness enhancement of the system, thereby effectively inhibiting the influence of sudden faults on the system. The LSTM neural network is used in the form of replacement to effectively inhibit the influence of slowly changing faults on the system, and signal repair is realized. Through detection and fault tolerance of the two kinds of faults existing in the GNSS signal, the precision of the combined navigation positioning is improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of detection and fault-tolerant technology of sudden faults and slowly varying faults, and in particular to a SINS and GNSS combined navigation system fault-tolerant method based on an LSTM neural network. BACKGROUND

[0002] In a combined navigation system involved in an actual application scenario, due to complex sensor types and a large number of sensors, sudden (wild value) faults and slowly varying faults are often carried in sensor information. The slowly varying faults often have a small amplitude and weak trend, and exist in the sensors of the combined navigation system. Multi-source unknown interference and device aging also affect the accuracy of the final result of the combined navigation. Therefore, designing a fault-tolerant scheme capable of real-time detection and effective processing of sudden faults and slowly varying faults in the combined navigation system plays a crucial role in the accuracy of the final positioning result of the combined navigation.

[0003] In recent years, among the commonly used positioning technologies, the Strapdown Inertial Navigation System (SINS) is favored by scholars of various countries due to its strong autonomy, good concealment, high accuracy in a short time, fast update frequency and comprehensive navigation information. The Global Navigation Satellite System (GNSS) is also widely used in many technical fields due to its real-time and high accuracy. Considering that a single navigation mode has been difficult to meet the needs of today's actual tasks, and the inertial navigation has the characteristic of divergence over time, the combined navigation technology has become the core technology that must be broken through and sustainable developed in the navigation field. SINS / GNSS is a commonly used combined navigation mode. GNSS can provide real-time and high-precision navigation information for SINS to assist SINS information to be corrected in time and prevent errors from accumulating over time.

[0004] However, the accuracy of the SINS / GNSS combined navigation system is still affected by abnormal GNSS measurement signals. In actual application scenarios, complex environments and time-varying noise often affect GNSS measurement signals (such as position, speed, etc.). According to the degree of influence and the characteristics of the faults, they are divided into sudden faults (wild values) and slowly varying faults. The slowly varying faults are difficult to be detected due to their small changes and unobvious characteristics, and have a great influence on the positioning result. Although the sudden faults are relatively easy to be detected, the detection time and the fault-tolerant processing degree also affect the final positioning result. SUMMARY

[0005] The application provides an SINS and GNSS combined navigation system fault-tolerant method based on an LSTM neural network, which can be used to solve the technical problem that two types of faults in the SINS / GNSS combined navigation system cannot be accurately detected and processed.

[0006] The application provides an SINS and GNSS combined navigation system fault-tolerant method based on an LSTM neural network, which comprises the following steps:

[0007] Step 1: An SINS and GNSS combined navigation model is established; then, a MD chi-square test method based on a Markov distance auxiliary innovation sequence is used to test the sudden fault measurement outliers carried in the GNSS position data, and it is determined whether there is a sudden fault;

[0008] Step 2: A SPRT algorithm is used to detect the slowly varying fault carried in the GNSS position data; when the slowly varying fault occurs, a SPRT increment is constructed, a slowly varying fault discrimination model based on the SPRT increment is established, and a threshold is set; when the SPRT increment value is negative, it is determined that the SINS and GNSS system contains a slowly varying fault;

[0009] Step 3: According to the detection results of the MD chi-square algorithm and the SPRT algorithm in steps 1 and 2, it is determined whether the SINS and GNSS system contains a fault, and whether it contains a sudden fault and a slowly varying fault; as long as the system has a sudden fault or a slowly varying fault, it is determined that the SINS and GNSS system has a fault;

[0010] Step 4: The SINS and GNSS system is fault-tolerant; when the GNSS position information is detected to contain a slowly varying fault, an LSTM neural network model is introduced; the formation of the LSTM neural network includes a training phase and a prediction phase; when the GNSS position information is fault-free, the training phase of the LSTM is completed; when the GNSS position information contains a slowly varying fault, the trained position information of the LSTM is used to replace the original GNSS position information, and the online reconstruction of the system is completed;

[0011] Step 5: When the GNSS position information is detected to contain only a sudden fault, in order to suppress the influence of the measurement outliers on the combined navigation system, a weighted matrix restriction and a modified innovation matrix are introduced;

[0012] Step 6: The SINS and GNSS combined navigation is performed, and the navigation result is output.

[0013] Further, step 1, the SINS and GNSS integrated navigation model is established; then, for the sudden fault measurement outliers carried in the GNSS position data, a residual chi-square test method based on innovation sequence Markov distance auxiliary, namely MD chi-square, is used for testing to determine whether there is a sudden fault; including:

[0014] Step 11, the SINS / GNSS integrated navigation system model is established;

[0015] According to the analysis of the SINS error model, the Northeast geodetic coordinate system is used as the navigation coordinate system, and the SINS / GNSS integrated navigation system is established, and the discrete state space model is:

[0016] X k =Φ k,k-1 X k-1 +Γ k-1 W k-1

[0017] In the formula, Φ k,k-1 represents the state one-step transfer matrix of the SINS / GNSS integrated navigation system; Γ k-1 represents the noise distribution or driving matrix of the system; W k-1 is the system noise; and W k-1 ~N(0,Q k ) satisfies; X k and X k-1 are state variables of the integrated navigation system at k and k-1 time, respectively, wherein:

[0018]

[0019] In the formula, the vector φ=[φ E φ N φ U ] T represents the inertial platform angle error information; the vector δv=[δv E δv N δv U ] T represents the inertial velocity error information; the vector δp=[δλδLδh] T is the inertial position error information; ε b , are first-order Markov processes of gyroscopes and accelerometers three-axis errors respectively;

[0020] The measurement equation of the integrated navigation system is represented as:

[0021] Z k =H k X k +V k

[0022] where the measurement vector Z k is the difference between the three-dimensional position and velocity of the inertial navigation system (SINS) and GNSS; H k is the measurement matrix; V k is the measurement noise, which is approximately white noise, and V k satisfies V k ~ N(0, R k );

[0023] Step 12, auxiliary chi-square detection using the Mahalanobis distance of the new measurement sequence;

[0024] The Mahalanobis distance of the new measurement is established as:

[0025]

[0026] where δZ k = Z k - H k X kk-1 represents the new measurement, and the variance is:

[0027]

[0028] where μ z represents the mean of the measurement vector Z k , and P k,k-1 represents the error covariance;

[0029] The statistic quantity M is constructed, i.e., M k obeys the chi-square distribution with a parameter of 1;

[0030] When the measurement information output by GNSS contains outliers, i.e., the system has a sudden fault, the square of the Mahalanobis distance of the new measurement will no longer obey the chi-square distribution;

[0031] The hypothesis testing idea in probability statistics is used to evaluate the system; first, set the significance level α of the chi-square test, then the Mahalanobis distance probability under the condition that the significance level α is established satisfies Further, the discrimination condition of whether the GNSS output information has a sudden fault is established:

[0032] If , it is determined that the SINS / GNSS integrated navigation system has a sudden fault;

[0033] If , it is determined that the SINS / GNSS integrated navigation system has no sudden fault;

[0034] Further, for the existence of slowly varying faults in GNSS position data, the sequential probability ratio algorithm SPRT is adopted, when the slowly varying fault occurs, the sequential probability ratio increment is constructed, the slowly varying fault discrimination model based on the sequential probability ratio increment is established, and the threshold is set, when the sequential probability ratio increment value is negative, it is judged that the SINS and GNSS system contains slowly varying fault, including:

[0035] Firstly, it is assumed that the residual value at time k is v(k); the independent random sample sequence belonging to its continuous k times is {v(1), v(2), …, v(k)}, according to the central limit theorem of probability theory, it is known that: Wherein And (σ(k)) 2 Respectively represent the sample mean and sample variance; when the GNSS output information has no slowly varying fault, i.e. the original hypothesis H0, and has slowly varying fault, i.e. the alternative hypothesis H1, the maximum likelihood function is respectively:

[0036]

[0037] Based on the above two hypothesis testing theory, the residual sequence of k independent times {v(1), v(2), …, v(k)} is taken, then the likelihood ratio is:

[0038]

[0039] Taking the logarithm of the likelihood ratio function on both sides, and then using the sample mean Substitute μ, then the likelihood ratio is:

[0040]

[0041] The sequential probability ratio increment is:

[0042] Considering the concepts of false alarm rate and missed detection rate of fault detection, the following test threshold is set:

[0043]

[0044] Wherein, P M Represents the missed detection rate, P F Represents the false alarm rate;

[0045] Based on the above analysis, the discrimination condition of whether the GNSS output information has slowly varying fault is established:

[0046] If λ(k)≥T(H1), it is judged that the original hypothesis H0 is false, and the alternative hypothesis H1 is true;

[0047] If λ(k)≤T(H0), it is judged that the original hypothesis H0 is true, and the alternative hypothesis H1 is false;

[0048] If T(H0)≤λ(k)≤T(H1), more GNSS data information needs to be added to continue the test.

[0049] Further, in step 3, according to the results of the MD chi-square algorithm and the SPRT algorithm in steps 1 and 2, it is judged whether the SINS and GNSS system contains a fault, and whether it contains a sudden fault and a slowly varying fault; as long as the system has a sudden fault or a slowly varying fault, it is determined that the SINS and GNSS system has a fault; including:

[0050] For the MD chi-square-sequential probability ratio algorithm, the sudden fault and the slowly varying fault existing in the GNSS output information can be tested at the same time; when the sequential probability ratio increment is positive, it is considered that the system has a slowly varying fault, then step 4 is executed to perform online reconstruction using the LSTM neural network method; when the sequential probability ratio increment is negative, step 5 is executed to perform robust enhancement based on the M-estimate robust Kalman filter algorithm to eliminate the influence of the sudden fault on the positioning result.

[0051] Further, in step 4, the formation of the LSTM neural network includes the following steps:

[0052] Step 41, training phase: when the system has no fault, the output of the accelerometer and the gyroscope is used as the input of the LSTM, and the position information output by the GNSS is used as the output of the LSTM to complete the LSTM training phase;

[0053] Step 42, prediction phase: when the system contains a slowly varying fault, the output of the trained LSTM model is used to replace the GNSS information containing the slowly varying fault to complete the reconstruction of the system; after the reconstruction is completed, the combined navigation is performed again.

[0054] Further, in step 5, when the GNSS position information is detected to contain only a sudden fault, in order to suppress the influence of the measurement outliers on the combined navigation system, a weighting matrix restriction and a modified innovation matrix are introduced, including:

[0055] When the sequential probability ratio increment is negative, the MD chi-square detection result is referred to at this time; if the MD chi-square detection result indicates that the system has a sudden fault, the robust Kalman filter algorithm based on M-estimation is used to enhance the robustness of the system;

[0056] The criterion function is defined as shown in the following formula:

[0057]

[0058] In the formula, the function ρ(·) is a continuously convex function selected appropriately, is the i-th element of the innovation at time k, m is the dimension of the measurement; a robust scale adjustment parameter is introduced The innovation is normalized, and the criterion function is rewritten as

[0059]

[0060] where is the i-th element of the innovation at time k, m is the dimension of the measurement; a robust scale adjustment parameter is introduced is called the normalized innovation; is calculated by

[0061]

[0062] where MAD denotes the median absolute deviation, defined as

[0063]

[0064] where med denotes the median, is the innovation sequence of the i-th measurement component up to the current time;

[0065] Taking the derivative with respect to X and setting it to zero gives

[0066]

[0067] where

[0068] is defined as and the matrix ω(·) is called the weight function, and thus the matrix form is written as

[0069] H k ω k e k =0

[0070] The above is the principle of M-estimation; therefore, the application of M-estimation in Kalman filtering is to introduce the matrix ω k as the weighting matrix of the innovation, i.e.

[0071]

[0072] The robust Kalman filtering algorithm based on M-estimation is obtained.

[0073] When the SINS / GNSS system only contains abrupt faults (measurement outliers), the existence of outliers will pollute the data innovation of GNSS, and thus the combined result contains uncontrollable errors, therefore, the robust KF filtering algorithm based on M-estimation is adopted, a new type of criterion function is defined, and a robust scale adjustment parameter is introduced to standardize the innovation. The constructed weight function is used as the weighting matrix of the innovation, so as to suppress the outliers in the position information output by GNSS and improve the accuracy of SINS / GNSS integrated navigation.

[0074] The present application uses the fault detection method of steps 1 and 2 to judge the abrupt faults and slowly changing faults existing in the SINS / GNSS integrated navigation system, and then uses the fault-tolerant scheme proposed in steps 4 and 5 to perform online reconstruction and robustness enhancement on the system, thereby improving the accuracy of integrated navigation.

[0075] Compared with the prior art, the new SINS / GNSS integrated navigation system fault-tolerant scheme provided by the present application can better detect abrupt faults in combination with the Mahalanobis distance of innovation. Although the traditional chi-square detection algorithm can identify abrupt faults, it is still not sensitive enough. If the system is detected to have only slowly changing faults, the robust Kalman filtering algorithm based on M-estimation is used for robustness enhancement processing. The MD chi-square-sequential probability ratio fault diagnosis machine proposed in the present application can be sensitive to slowly changing faults, and the LSTM network proposed is used to perform online reconstruction on the system state at this time, so as to ensure that the integrated navigation can be carried out smoothly under the condition of ensuring high accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 The method overall framework provided by the embodiment of the present application is provided.

[0077] Figure 2 The structure diagram of LSTM provided by the embodiment of the present application is provided.

[0078] Figure 3 The integrated navigation error graph before and after improvement provided by the embodiment of the present application is provided.

[0079] Figure 4 The method flowchart provided by the embodiment of the present application is provided. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0081] In order to effectively deal with two types of faults in SINS / GNSS integrated navigation system, a SINS / GNSS integrated navigation system fault-tolerant method based on neural network processing is proposed. A model of SINS / GNSS integrated navigation system fault detection, robust enhancement and online reconstruction is built. The position information output by GNSS is fault detected to effectively determine whether it contains abrupt faults and slowly changing faults. For abrupt faults, the robustness is enhanced by using the M-estimate based robust Kalman filter algorithm. For slowly changing faults, considering that LSTM can effectively process time series data in SINS / GNSS integrated navigation, especially in dealing with nonlinear, long-term dependence and signal loss problems. LSTM neural network can learn the time sequence pattern of sensor data through its own learning, and provide more accurate and reliable navigation information when GNSS signal is interrupted or data is unreliable. Therefore, for slowly changing faults, when its existence affects the position information output by GNSS, the robust filter algorithm cannot effectively suppress outliers, and LSTM is needed for online reconstruction of the system. After the above fault-tolerant scheme, the influence of GNSS two types of faults on the results of SINS / GNSS integrated navigation system is effectively suppressed, and the accuracy of SINS / GNSS integrated navigation is improved.

[0082] Step 1, establish SINS and GNSS integrated navigation model; then, for the abrupt fault measurement outliers carried in GNSS position data, the residual chi-square test method assisted by innovation sequence Mahalanobis distance, namely MD chi-square, is used for testing to determine whether there is an abrupt fault.

[0083] Step 2, for the slowly changing faults carried in GNSS position data with a certain probability, the sequential probability ratio algorithm SPRT is used. When the slowly changing fault occurs, the sequential probability ratio increment is constructed, the slowly changing fault discrimination model based on the sequential probability ratio increment is established, and the threshold is set. When the sequential probability ratio increment value is negative, it is determined that the SINS and GNSS system contains slowly changing faults.

[0084] Step 3, according to the results of MD chi-square algorithm and SPRT algorithm in step 1 and step 2, determine whether the SINS and GNSS system contains faults, and determine whether it contains abrupt faults and slowly changing faults. As long as the system has abrupt faults or slowly changing faults, it is determined that the SINS and GNSS system has faults.

[0085] Step 4, fault-tolerant processing is carried out on the SINS and GNSS system, when the GNSS position information is detected to contain a slowly varying fault, an LSTM neural network model is introduced; the formation of the LSTM neural network is divided into a training stage and a prediction stage; when the position information of the GNSS is fault-free, the training stage of the LSTM is completed; when the position information of the GNSS contains a slowly varying fault, the trained position information of the LSTM is used to replace the original position information of the GNSS, and the online reconstruction of the system is completed.

[0086] Step 5, when the GNSS position information is detected to contain only a sudden fault, in order to suppress the influence of the measurement outliers on the integrated navigation system, a weighted matrix restriction and a correction innovation matrix are introduced, the influence of the measurement outliers on the integrated navigation result is effectively reduced, and the robust enhancement of the system is completed.

[0087] Step 6, SINS and GNSS integrated navigation is carried out, and the navigation result is output.

[0088] The application provides a SINS and GNSS integrated navigation system fault-tolerant method based on neural network processing, as shown in Figure 1 As shown in the figure, the MD chi-square-sequence probability ratio joint fault diagnosis machine is formed based on MD chi-square detection and sequential probability ratio algorithm, the GNSS output information is diagnosed, and the sudden fault and slowly varying fault contained in the GNSS output information are mainly aimed at.

[0089] When the SINS / GNSS system is detected to contain a slowly varying fault, online reconstruction is carried out by using the LSTM. When the GNSS data is normal, the training stage of the LSTM is first completed; when the GNSS data contains a slowly varying fault, the output of the trained LSTM is used to replace the fault data of the GNSS, and the reconstruction of the system is completed. When the SINS / GNSS system is detected to contain only a sudden fault, the robust Kalman filter based on M estimation is used for system robustness enhancement.

[0090] The specific steps of the implementation method are as follows:

[0091] Step 1, SINS / GNSS model establishment and sudden fault detection includes:

[0092] Step 11, SINS / GNSS integrated navigation system mathematical model

[0093] According to the analysis of the SINS error model, the northeast geodetic coordinate system is used as the navigation coordinate system, the SINS / GNSS integrated navigation system is established, and the discrete state space model is:

[0094] X k =Φ k,k-1 X k-1 +Γ k-1 W k-1

[0095] where Φ k,k-1 represents the state step transition matrix of the SINS / GNSS integrated navigation system; Γ k-1 represents the noise distribution or driving matrix of the system; W k-1 is the system noise; and W k-1 ~N(0, Q k ) satisfies; X k and X k-1 are the state variables of the integrated navigation system at time k and k-1, respectively, where:

[0096]

[0097] where the vector φ = [φ E φ N φ U ] T represents the inertial platform angular error information; the vector δv = [δv E δv N δv U ] T represents the inertial velocity error information; the vector δp = [δλ δL δh] T is the inertial position error information; ε b , are the first-order Markov processes of the three-axis errors of the gyroscopes and accelerometers, respectively;

[0098] The measurement equation of the integrated navigation system is represented as:

[0099] Z k = H k X k + V k

[0100] where the measurement vector Z k is taken as the difference between the three-dimensional positions and velocities of the inertial SINS and GNSS; H k is the measurement matrix; V k is the measurement noise, which is approximately white noise, and V k satisfies V k ~N(0, R k );

[0101] Step 12, using the innovation sequence Mahalanobis distance to assist chi-square detection;

[0102] In order to more accurately and quickly track the characteristics of the abrupt fault, the Mahalanobis distance of the measurement innovation is established as:

[0103]

[0104] where δZ k= Z k - H k X kk-1 denotes the measurement innovation, and the variance is:

[0105]

[0106] where μ z denotes the mean of the measurement vector Z k , P k,k-1 denotes the error covariance;

[0107] The statistic M is constructed, i.e., M k obeys the chi-square distribution with 1 degree of freedom.

[0108] When the measurement information output by the GNSS contains outliers, i.e., the system has a sudden fault, the Mahalanobis distance square of the measurement innovation will no longer obey the chi-square distribution;

[0109] Based on the above analysis, the hypothesis testing idea in probability statistics is used to evaluate the system; first, the significance level α of the chi-square test is set, and then the Mahalanobis distance probability under the condition that the significance level α is satisfied satisfies Further, the discrimination condition of whether the GNSS output information has a sudden fault is established:

[0110] If , it is determined that the SINS / GNSS integrated navigation system has a sudden fault;

[0111] If , it is determined that the SINS / GNSS integrated navigation system has no sudden fault;

[0112] Step 2, detection of slowly varying faults, specifically including:

[0113] In order to detect whether the GNSS measurement information contains a slowly varying fault, the sequential probability ratio algorithm is used in the scheme. The main steps of the sequential probability ratio algorithm are as follows.

[0114] First, assume that the residual value at time k is v(k); the independent random sample sequence belonging to it at the continuous k times is {v(1), v(2), …, v(k)}, and by the central limit theorem of probability theory, it is known that: where and (σ(k)) 2 respectively denote the sample mean and the sample variance; when the GNSS output information has no slowly varying fault, i.e., the original hypothesis H0, and has a slowly varying fault, i.e., the alternative hypothesis H1, the maximum likelihood functions are respectively:

[0115]

[0116] Based on the above two binary hypothesis testing theory, now take k independent time residual sequence {v(1), v(2), …, v(k)}, then the likelihood ratio is:

[0117]

[0118] Take the logarithm of the likelihood ratio function, and then use the sample mean Substitute μ, then the likelihood ratio is:

[0119]

[0120] The sequential probability ratio increment is:

[0121] Considering the concepts of false alarm rate and missed detection rate of fault detection, set the following test threshold:

[0122]

[0123] Where, P M represents the missed detection rate, P F represents the false alarm rate;

[0124] Based on the above analysis, establish the discrimination condition of whether the GNSS output information exists a slowly varying fault:

[0125] If λ(k)≥T(H1), then the original hypothesis H0 is false, and the alternative hypothesis H1 is true.

[0126] If λ(k)≤T(H0), then the original hypothesis H0 is true, and the alternative hypothesis H1 is false.

[0127] If T(H0)≤λ(k)≤T(H1), then more GNSS data information needs to be added to continue the test.

[0128] Step 3, MD chi-square-sequential probability ratio algorithm detection result judgment, including:

[0129] For MD chi-square-sequential probability ratio algorithm, it can simultaneously realize the test of sudden fault and slowly varying fault existing in GNSS output information; the chi-square detection algorithm based on Mahalanobis distance is more sensitive to sudden fault, and the sequential probability ratio algorithm can track the slowly varying characteristics of slowly varying fault in real time; when the sequential probability ratio increment is positive, it is considered that the system has a slowly varying fault, then step 4 is executed, and the LSTM neural network method is used for online reconstruction; when the sequential probability ratio increment is negative, step 5 is executed, and the robustness of the Kalman filter algorithm based on M estimation is enhanced to eliminate the influence of sudden fault on the positioning result.

[0130] Step 4, the online reconstruction method of the SINS / GNSS integrated navigation system based on LSTM, comprises:

[0131] When the detection result of the chi-square-sequence probability ratio algorithm is a positive value, it is determined that the system has a slowly varying fault; at this time, the signal containing the slowly varying fault is reconstructed, and the LSTM neural network is introduced to complete the online reconstruction of the system. As shown in Figure 2 The LSTM neural network has the characteristics of strong learning ability and high fitting degree, can relatively accurately provide the original accurate information, and reduces the influence of the GNSS position information containing the slowly varying fault on the integrated positioning result through online reconstruction. The online reconstruction using the LSTM neural network comprises the following two stages:

[0132] Step 41, training stage: when the system has no fault, the output of the accelerometer and the gyroscope is taken as the input of the LSTM, and the position information output by the GNSS is taken as the output of the LSTM to complete the LSTM training stage;

[0133] Step 42, prediction stage: when the system contains a slowly varying fault, the output of the trained LSTM model is used to replace the GNSS information containing the slowly varying fault to complete the reconstruction of the system; after the reconstruction is completed, the integrated navigation is performed again.

[0134] Step 5, robustness enhancement of the system, comprising:

[0135] When the sequence probability ratio increment is a negative value, the MD chi-square detection result is used as a reference at this time; if the MD chi-square detection result indicates that the system has a sudden fault, the robustness of the system is enhanced by using the robust Kalman filtering algorithm based on M estimation, and the main principle is to define a new criterion function and introduce a robust scale adjustment parameter to standardize the innovation. The constructed weight function is used as the weighting matrix of the innovation, so as to suppress the outliers in the position information output by the GNSS. Compared with the traditional robust filtering algorithm, the algorithm can more accurately adjust the weight to suppress the sudden fault and improve the positioning result precision of the SINS / GNSS integrated navigation. The main process of the robust Kalman filtering algorithm based on M estimation is as follows.

[0136] Taking the robust filtering algorithm based on Huber-M estimation as an example, the robustness enhancement algorithm of the integrated navigation system is performed.

[0137] M estimation, i.e. generalized maximum likelihood estimation, is a commonly used robust estimation method, which is different from the least square estimation that uses the residual square sum minimum as the criterion function, but defines the criterion function as shown in the following formula:

[0138]

[0139] where ρ(·) is a properly chosen continuous convex function, is the i th element of innovation at time k, and m is the dimension of measurements; to further optimize the robustness of the above criterion function, a robust scale adjustment parameter is usually introduced The innovation is normalized, and the criterion function is rewritten as:

[0140]

[0141] where is the i th element of innovation at time k, and m is the dimension of measurements; to further optimize the robustness of the above criterion function, a robust scale adjustment parameter is usually introduced is called the normalized innovation; is calculated by:

[0142]

[0143] where MAD denotes the median absolute deviation, defined as:

[0144]

[0145] where med denotes the median, is the innovation sequence of the i th measurement component up to the current time;

[0146] Taking the derivative with respect to X and setting it to 0 gives:

[0147]

[0148] where

[0149] is defined as and matrix ω(·) is called the weight function, and thus the matrix form is written as:

[0150] H k ω k e k =0

[0151] The above is the principle of M-estimation; therefore, the application of M-estimation in Kalman filtering is to introduce the matrix ω k as the weighting matrix of innovation, i.e., as follows:

[0152]

[0153] The robust Kalman filtering algorithm based on M-estimation (abbreviated as MKF) is obtained. By introducing the weighting matrix to limit and correct the innovation, the influence of measurement gross errors on filtering accuracy can be effectively reduced, and the robustness of filtering can be enhanced.

[0154] Step 6, fault-tolerant integrated navigation, comprising:

[0155] According to steps (1) to (5), sudden change faults and slow change faults in the position information output by the GNSS sensor can be detected and fault-tolerantly processed.

[0156] As described above, sudden outliers in the system can be detected using the MD chi-square test. For slowly varying faults with small amplitudes and small variations, the sequential probability ratio algorithm is used for fault detection. After detecting these two types of faults, systematic fault tolerance is required. For sudden outliers in the system, the robust Kalman filter algorithm based on M-estimation described above can effectively suppress the impact of outliers on integrated navigation positioning results. For slowly varying faults in the system, using robust filtering algorithms alone is insufficient to repair the system. Therefore, this solution uses an LSTM neural network to reconstruct signals affected by slowly varying faults. When the system is free of sudden outliers and slowly varying faults, the LSTM neural network is pre-trained. The LSTM neural network training phase is completed using normal information. When a slowly varying fault is detected in the GNSS signal, the output of the trained LSTM replaces the original GNSS signal affected by the slowly varying fault.

[0157] The novel fault diagnosis and fault-tolerant processing method provided by the present invention can, on the one hand, detect sudden faults and slowly varying faults carried in the GNSS output signal in a more real-time and accurate manner. On the other hand, it can perform effective fault-tolerant processing after detecting the two types of faults, thereby reducing the impact on the final positioning result. Compared with traditional algorithms, it has better real-time performance and accuracy. Therefore, for sudden wild values ​​and slowly varying faults, the present invention can be used to perform real-time detection and effective fault-tolerant processing, and then re-perform combined navigation, and verify the reliability of this solution through the results of combined navigation. Figure 3 As shown in Figure 2, the combined navigation error diagram of the algorithm before and after improvement is shown. Figure 3 It shows that compared with the KF method, the algorithm proposed in this scheme has smaller combined navigation error and has effectively improved the estimation accuracy.

[0158] The above-described embodiments of the present application do not constitute a limitation on the scope of protection of the present application.

Claims

1. A fault-tolerant method for a SINS and GNSS integrated navigation system based on an LSTM neural network, characterized in that, The method comprises: Step 1, a SINS and GNSS integrated navigation model is established; then, a residual chi-square test method based on innovation sequence Markov distance assistance, namely MD chi-square, is used to test the sudden fault measurement outliers carried in the GNSS position data, and it is judged whether there is a sudden fault; Step 2, for the slowly varying fault existing in the GNSS position data with a certain probability, a sequential probability ratio algorithm SPRT is used, when the slowly varying fault occurs, a sequential probability ratio increment is constructed, a slowly varying fault discrimination model based on the sequential probability ratio increment is established, and a threshold is set, when the sequential probability ratio increment value is negative, it is judged that the SINS and GNSS system contains a slowly varying fault; Step 3, according to the results of the MD chi-square algorithm and the SPRT algorithm in steps 1 and 2, it is judged whether the SINS and GNSS system contains a fault, and whether it contains a sudden fault and a slowly varying fault; as long as the system has a sudden fault or a slowly varying fault, it is judged that the SINS and GNSS system has a fault; Step 4, fault-tolerant processing is performed on the SINS and GNSS system; when the GNSS position information is detected to contain a slowly varying fault, an LSTM neural network model is introduced; the formation of the LSTM neural network includes a training phase and a prediction phase; when the GNSS position information is fault-free, the training phase of the LSTM is completed; when the GNSS position information contains a slowly varying fault, the trained position information of the LSTM is used to replace the original GNSS position information, and the online reconstruction of the system is completed; Step 5, when the GNSS position information is detected to contain only a sudden fault, in order to suppress the influence of the measurement outliers on the integrated navigation system, a weighted matrix restriction and a modified innovation matrix are introduced; Step 6, SINS and GNSS integrated navigation is performed, and navigation results are output.

2. The method of claim 1, wherein, Step 1, a SINS and GNSS integrated navigation model is established; then, a residual chi-square test method based on innovation sequence Markov distance assistance, namely MD chi-square, is used to test the sudden fault measurement outliers carried in the GNSS position data, and it is judged whether there is a sudden fault; including: Step 11, a SINS / GNSS integrated navigation system model is established; According to the analysis of the SINS error model, the northeast geodetic coordinate system is used as the navigation coordinate system, the SINS / GNSS integrated navigation system is established, and the discrete state space model is: X k = Φ k,k-1 X k-1 + Γ k-1 W k-1 wherein Φ k,k-1 represents a state step transition matrix of the SINS / GNSS integrated navigation system; Γ k-1 represents a noise distribution or driving matrix of the system; W k-1 is a system noise; and W k-1 ~ N(0, Q k ) satisfies; X k and X k-1 are state variables of the integrated navigation system at time k and time k-1, respectively, wherein: In the formula, vector φ = [φ E φ N φ U ] T represents inertial platform angular error information; vector δv = [δv E δv N δv U ] T represents inertial velocity error information; vector δp = [δλ δL δh] T is the error information of inertial position; ε b , is the first-order Marf process of gyro, accelerometer three-axis error respectively; The measurement equation of the integrated navigation system is represented as: Z k = H k X k + V k where the measurement vector Z k is the difference between the three-dimensional position and velocity of the inertial navigation system SINS and GNSS; H k is the measurement matrix; V k is the measurement noise, which is approximated as white noise, and V k satisfies V k ~ N(0, R k ). Step 12, innovation sequence Markov distance auxiliary chi-square detection is used; The Markov distance of the measurement innovation is established as: where δZ k = Z k - H k X kk-1 denotes the measurement innovation, with variance: where μ z denotes the mean of the measurement vector Z k , P k,k-1 denotes the error covariance; Constructing statistics i.e. M k obeys a chi-squared distribution with 1 degree of freedom; When the measurement information output by the GNSS contains outliers, that is, the system has a sudden fault, the square of the Markov distance of the measurement innovation will no longer satisfy the chi-square distribution; The system is evaluated by using the hypothesis testing idea in probability statistics. First, the significance level α of the chi-square test is set, and then the Mahalanobis distance probability under the condition that the significance level α is met satisfies Further, a discrimination condition for determining whether a sudden fault exists in the GNSS output information is established. If then determine that the SINS / GNSS integrated navigation system has a sudden fault; If then it is determined that the SINS / GNSS integrated navigation system has no abrupt fault.

3. The method of claim 2, wherein, For the slowly varying fault existing in the GNSS position data with a certain probability, a sequential probability ratio algorithm SPRT is used, when the slowly varying fault occurs, a sequential probability ratio increment is constructed, a slowly varying fault discrimination model based on the sequential probability ratio increment is established, and a threshold is set, when the sequential probability ratio increment value is negative, it is judged that the SINS and GNSS system contains a slowly varying fault, including: Firstly, assume the residual value at time k is v(k); the independent random sample sequence belonging to its continuous k times is {v(1), v(2), …, v(k)}, by the central limit theorem of probability theory, it is known that: Wherein And (σ(k)) 2 Respectively represent the sample mean and sample variance; when the GNSS output information has no gradual failure, i.e. the original hypothesis H0, and has gradual failure, i.e. the alternative hypothesis H1, the maximum likelihood functions are respectively: Based on the above two binary hypothesis testing theory, now take k independent time residual sequence {v(1), v(2), …, v(k)}, then the likelihood ratio is: Taking the logarithm of the likelihood ratio function on both sides, and using the sample mean Substituting the approximation for μ, we obtain the likelihood ratio as The sequential probability ratio increment is: Considering the concept of false alarm rate and missed detection rate of fault detection, the following test threshold is set: where P M represents the false negative rate, P F represents the false positive rate; Based on the above analysis, the discrimination condition of whether the GNSS output information exists slowly varying fault is established: If λ(k)≥T(H1), it is determined that the original hypothesis H0 is false, and the alternative hypothesis H1 is true; If λ(k)≤T(H0), it is determined that the original hypothesis H0 is true, and the alternative hypothesis H1 is false; If T(H0)≤λ(k)≤T(H1), more GNSS data information needs to be added for further testing.

4. The method of claim 3, wherein, Step 3, according to the results of MD chi-square algorithm and SPRT algorithm detection in step 1 and step 2, judge whether there is a fault in SINS and GNSS system, and judge whether there is a sudden fault and a slowly varying fault; As long as the system has a sudden fault or a slowly varying fault, it is determined that the SINS and GNSS system has a fault; including: For MD chi-square-sequential probability ratio algorithm, it can realize the test of sudden fault and slowly varying fault in GNSS output information at the same time; When the sequential probability ratio increment is positive, it is considered that the system has a slowly varying fault, then step 4 is executed to use LSTM neural network method for online reconstruction; when the sequential probability ratio increment is negative, step 5 is executed to use robust Kalman filter algorithm based on M estimation for robust enhancement to eliminate the influence of sudden fault on positioning results.

5. The method of claim 4, wherein, Step 4, the formation of LSTM neural network includes the following steps: Step 41, training phase: when the system has no fault, the output of accelerometer and gyroscope is used as the input of LSTM, and the position information of GNSS output is used as the output of LSTM to complete the training phase of LSTM; Step 42, prediction phase: when the system has a slowly varying fault, the output of the trained LSTM model is used to replace the GNSS information containing slowly varying fault to complete the reconstruction of the system; after the reconstruction is completed, the integrated navigation is restarted.

6. The method of claim 5, wherein, Step 5, when the GNSS position information is detected to contain only sudden fault, in order to suppress the influence of measurement outliers on integrated navigation system, a weighted matrix restriction and a modified innovation matrix are introduced, including: When the sequential probability ratio increment is negative, the MD chi-square detection result is referred; if the MD chi-square detection result shows that the system has a sudden fault, the robust Kalman filter algorithm based on M estimation is used for system robustness enhancement; The criterion function is defined as shown in the following formula: where the function p(·) is a continuously convex function chosen appropriately, is the i-th element of the innovation at time k, and m is the dimension of the measurement; a robust scaling parameter is introduced The criterion function is then rewritten as wherein is also the estimate of the variance of the i-th element of the innovation at time k, is called the normalized innovation; is calculated by the equation: Where MAD represents the median absolute deviation, defined as: where med denotes the median, is the innovation sequence of the i-th measurement component up to the current time instant. Take the derivative with respect to the estimated value X and set it to 0: wherein Definitions and matrices ω(·) is called a weight function, so the matrix form is written as: H k ω k e k =0 The above is the M estimation principle; therefore, the application of M estimation in Kalman filtering is to introduce the matrix ω k The weighted matrix of the innovation, that is, as shown in the following formula: Get the robust Kalman filter algorithm based on M estimation.

Images