A federated filtering fault detection and isolation fault-tolerant integrated navigation method

Abstract

The application provides a fault detection and isolation federated filtering fault-tolerant integrated navigation method, according to the number N of fusion sensors required by integrated navigation, N-1 sub-filters and a main filter are constructed to construct a federated filter structure. The observation innovation in each sub-filter system and the corresponding covariance are calculated, a fault detection system of kernel multivariate exponentially weighted moving average control chart is constructed, whether the sub-filter needs to be isolated is judged according to the alarm threshold, i.e. the control limit of the control chart, if the constructed multivariate exponentially weighted moving average statistic is greater than the alarm threshold, a warning is given, and if four of the five consecutive monitored statistics exceed the alarm threshold, the sub-filter is isolated. The method can more accurately and quickly detect the occurrence of faults and isolate the fault sensors in time to improve the fault tolerance of the whole system.

Description

Technical Field

[0001] This invention relates to the field of fault-tolerant integrated navigation technology, and in particular to a federated filtering fault-tolerant integrated navigation method for fault detection and isolation. Background Technology

[0002] Reliability and safety are fundamental to ensuring the effective application of navigation systems in various scenarios. Redundancy technology in multi-sensor integrated navigation is crucial to ensuring that the navigation system can still achieve effective and autonomous real-time positioning even when malfunctions occur. Therefore, a real-time and effective fault detection system is indispensable in the field of fault-tolerant integrated navigation. It can provide the navigation system with correct positioning information, eliminate erroneous and invalid positioning information, and issue alarm prompts to the user, enabling operators to isolate, diagnose, and repair the corresponding sensors in a timely and effective manner.

[0003] Federated filtering, with its superior fault tolerance, is effectively applied in fault-tolerant integrated navigation systems. It can isolate fault information transmitted by faulty sensors by isolating and restoring sub-filters, preventing fault information from contaminating the entire system. However, the criteria for isolating sub-filters in federated filtering suffer from poor real-time performance, the need for manual alarm threshold settings, and insufficient sensitivity. Therefore, a judgment criterion is urgently needed to make the fault detection system more sensitive and effective, automatically isolating faults in sub-filters within the federated filter, thus enhancing the stability and reliability of the entire navigation system. Control chart technology, widely used in quality management, is a means of quickly, accurately, and effectively monitoring product quality. Therefore, leveraging its advantages to assist fault-tolerant integrated navigation in achieving more stable and reliable operation is promising. Summary of the Invention

[0004] To address the current issues related to fault-tolerant integrated navigation, this invention provides a federated filtering fault-tolerant integrated navigation method for fault detection and isolation. This method uses a kernel multivariate exponential weighted moving average control chart as the federated filtering method for the fault detection system, which can improve the system's sensitivity to fault detection and the fault tolerance capability of integrated navigation.

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

[0006] A fault-tolerant combined navigation method for fault detection and isolation using federated filtering, characterized by the following steps:

[0007] Step 1: Based on the number N of sensors required for integrated navigation, construct N-1 sub-filters and one master filter to build a federated filter structure. Calculate the observation innovation and corresponding covariance in each sub-filter system, and construct a fault detection system based on a kernel multivariate exponentially weighted moving average control chart. Determine whether a sub-filter needs isolation based on the alarm threshold, i.e., the control limit of the control chart. If the constructed multivariate exponentially weighted moving average statistic is greater than the alarm threshold, proceed to Step 2; otherwise, proceed to Step 3.

[0008] Step 2: Issue an early warning for the system and determine whether fault isolation is necessary based on the following criteria: continuously monitor five multivariate exponentially weighted moving average statistics to determine if they exceed the alarm threshold. If four statistics exceed the alarm threshold, the sub-filter corresponding to the fault detection system is isolated, while the remaining filters and the main filter operate normally. Otherwise, restore all isolated sub-filters and proceed to Step 3. In this scheme, the integrated navigation includes inertial, GPS, BeiDou, and astronomical navigation systems, with inertial as the main filter. Figure 1 The system operates based on a structure comprising three sub-filters and corresponding fault monitoring modules. One of these modules, a kernel-multivariate exponentially weighted moving average control chart, issues an early warning to the entire integrated navigation system if the constructed statistic exceeds the alarm threshold. If the condition described in step 2 occurs, the system... Figure 1 The sub-filters in the structure are used for fault isolation.

[0009] Step 3: All sub-filters and the main filter function normally according to the relevant structure.

[0010] A fault detection and isolation federated filter fault-tolerant navigation method, characterized in that step 1 includes the specific steps of a federated filter structure for a kernel multivariate exponentially weighted moving average control chart fault detection system:

[0011] S1: The integrated navigation system can consist of multiple sensors. This invention uses inertial navigation systems, GPS navigation systems, BeiDou navigation systems, and astronomical navigation systems as examples for illustration. The state equation for the filter system is as follows:

[0012] X k =Φ k,k-1 X k-1 +W k-1

[0013] Z k =H k X k +V k

[0014]

[0015]

[0016] Where k represents the time information, updated using 15 states. Let be the state matrix, where These represent the attitude angle errors in the pitch, roll, and azimuth directions, respectively, δv=[δv E δv N δv U ] represent the velocity errors in the east, north, and sky directions, respectively, δp=[δp L δp λ δp H ] represents the positional error in latitude, precision, and altitude, respectively, δb g =[δb gx δb gy δb gz ] represents the drift error of the gyroscope in the three-axis directions, δb a =[δb aE δb aN δb aU [] represents the zero bias error of the accelerometer in three directions. Z = [V] INS -V GPS P INS -P GPS φ INS -φ CNS V INS -V BDS P INS -P BDS ] is the measurement matrix, where V IND =[V IND,E V IND,N V IND,U ] represent the velocity information of the inertial navigation system in the east, north, and sky directions, respectively. V GPS =[V GPS,E V GPS,N V GPS,U ] represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. INS =[P INS,L P INS,λ P INS,H ] represent the latitude, longitude, and altitude position information of the inertial navigation system, respectively. P GPS =[P GPS, L P GPS,λ P GPS,H ] represent the location information of the GPS navigation system in latitude, longitude, and altitude, respectively. φ INS =[φ INS,pitch φ INS,roll φ INS,yaw] represent the angle information in the pitch, roll, and azimuth directions of the inertial navigation system, respectively, φ CNS =[φ CNS,pitch φ CNS,roll φ CNS,yaw ] These represent the angle information in the directions of pitch, roll, and azimuth of the celestial navigation system, respectively. BDS =[V BDS,E V BDS,E V BDS,U ] represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. BDS =[P BDS,L P BDS,λ P BDS,H ] These represent the latitude, longitude, and altitude location information of the GPS navigation system, respectively. Φ k,k-1 H k Given the known system structural parameters, where Φ k,k-1 =eye(15),eye(n) represents an n-dimensional square matrix with diagonal elements of 1 and the rest of the elements of 0. Let w be the system variance matrix. eb The gyroscope randomly walks in three directions, w db Acceleration random walks are performed in three directions. Let σ be the noise observation matrix. GPS , σ CNS , σ BDS These are the standard deviations of positioning noise for GPS navigation systems, astronomical navigation systems, and BeiDou navigation systems, respectively.

[0017] S2: Calculate the filtering innovation, i.e., the residual, for each sub-filter, expressed as:

[0018]

[0019] Next, we need to calculate the filtered innovation r. k The covariance is expressed as:

[0020]

[0021] in, Let be the state one-step mean square error matrix, where Let be the mean square error matrix of the state estimation, where This is the optimal estimate from the previous moment.

[0022] S3: Calculate the statistics used for monitoring in the fault detection system corresponding to each sub-filter, expressed as:

[0023] zt k =λrk +(1-λ)r k

[0024]

[0025] EWMA k =zt k Sz k -1 zt T

[0026] Where λ is the coefficient of the exponentially weighted moving average, which is related to the drift δ x =(μ T Σ -1 The value is proportional to μ, which can be obtained directly through Markov chains, Monte Carlo methods, or by querying the corresponding table. Here, μ is the sample mean of the data, and Σ is the sample covariance of the data.

[0027] S4: In offline mode, the system automatically estimates the alarm threshold using kernel density based on collected fault-free data, expressed as:

[0028]

[0029]

[0030]

[0031] h = 1.06 min(s, IQR / 1.34)n-1 / 5

[0032] in, Let be the probability density function. K(t) is the distribution function, K(t) is the kernel function (the Epanechnikov kernel is used here), n is the sample size, h is the smoothing coefficient (obtained through the Silverman rule), α is the significance level (used to adjust the strictness of the system), AL is the alarm threshold, s is the standard deviation of the sample, and IQR is the interquartile range.

[0033] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0034] 1) By using control chart technology, system faults can be identified more quickly and sensitively, thus providing early warnings to the system and preventing the faults from further contaminating the signal.

[0035] 2) Using statistical methods to calculate alarm thresholds can eliminate the interference of random factors, enabling more accurate and automatic acquisition of alarm thresholds.

[0036] 3) By constructing a fault-tolerant integrated navigation federated filtering structure, the fault tolerance of the entire system is improved, enabling more accurate and effective navigation and positioning when integrated navigation malfunctions. This scheme is applicable to various fault-tolerant integrated navigation systems and has generalization capabilities. In practical applications, it eliminates the need for manually setting alarm thresholds, as can be added in point 2. Attached Figure Description

[0037] Figure 1 This is a diagram of the federated filter structure based on the kernel multivariate exponential weighted moving average control chart of the present invention;

[0038] Figure 2 This is a flowchart illustrating the specific steps of the present invention;

[0039] Figure 3 This is a flowchart illustrating the construction principle of the nuclear multivariate index-weighted moving average control chart of the present invention.

[0040] Figure 4 The fault detection results are shown in the nuclear multivariate index-weighted moving average control chart in the embodiment.

[0041] Figure 5 This example compares the positioning accuracy of the present invention with that of centralized filtering. Detailed Implementation

[0042] The following will take the inertial / GPS / BeiDou / astronomical integrated navigation system as an example, and in conjunction with the accompanying drawings of the embodiments of the present invention, clearly and completely describe the technical solutions of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] Example 1: As Figure 1 As shown, a fault detection and isolation federated filtering fault-tolerant combined navigation method includes the following steps:

[0044] Step 1: Based on the requirement of 4 fusion sensors for integrated navigation, construct 3 sub-filters and 1 main filter to build a federated filter structure. Calculate the observation innovation and corresponding covariance in each sub-filter system, and construct a fault detection system based on a kernel multivariate exponentially weighted moving average control chart. Determine whether a sub-filter needs isolation based on the alarm threshold, i.e., the control limit of the control chart. If the constructed multivariate exponentially weighted moving average statistic is greater than the alarm threshold, proceed to Step 2; otherwise, proceed to Step 3.

[0045] Step 2: Issue an early warning to the system and determine whether fault isolation is required based on the following criteria: continuously detect five multivariate exponential weighted moving average statistics to determine whether they exceed the alarm threshold. If four statistics exceed the alarm threshold, isolate the sub-filter corresponding to the fault detection system, while the remaining filters and the main filter operate normally. Otherwise, restore all isolated sub-filters and proceed to Step 3.

[0046] Step 3: All sub-filters and the main filter function normally according to the relevant structure.

[0047] In step 1, the federated filter structure of the kernel multivariate exponential weighted moving average control chart fault detection system is as follows: Figure 2 As shown, the specific steps are as follows:

[0048] S1: The integrated navigation system can consist of multiple sensors. This invention uses an inertial navigation system, a GPS navigation system, a BeiDou navigation system, and an astronomical navigation system as examples for illustration. The entire process takes 965 seconds. A sinusoidal slow fault is injected into the GPS navigation system from the 600th to the 700th second, and a ramp slow fault is injected into the BeiDou navigation system from the 300th to the 400th second. For the filter system state equation:

[0049] X k =Φ k,k-1 X k-1 +W k-1

[0050] Z k =H k X k +V k

[0051]

[0052]

[0053] Where k represents the time information, updated using 15 states. Let be the state matrix, where These represent the attitude angle errors in the pitch, roll, and azimuth directions, respectively, δv=[δv E Vv N δv U ] represent the velocity errors in the east, north, and sky directions, respectively, δp=[δp L δp λ δp H ] represents the positional error in latitude, precision, and altitude, respectively, δb g =[δb gx δb gy δb gz] represents the drift error of the gyroscope in the three-axis directions, δb a =[δb aE δb aN δb aU [] represents the zero bias error of the accelerometer in three directions. Z = [V] INS -V GPS P INS -P GPS φ INS -φ CNS V INS -V BDS P INS -P BDS ] is the measurement matrix, where V INS =[V INS,E V INS,N V INS,U ] represent the velocity information of the inertial navigation system in the east, north, and sky directions, respectively. V GPS =[V GPS,E V BPS,N V GPS,U ] represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. INS =[P INS,L P INS,λ P INS,H ] represent the latitude, longitude, and altitude position information of the inertial navigation system, respectively. P GPS =[P GPS, L P GPS,λ P GPS,H ] represent the location information of the GPS navigation system in latitude, longitude, and altitude, respectively. φ INS =[φ INS,pitch φ INS,roll φ INS,yaw ] represent the angle information in the pitch, roll, and azimuth directions of the inertial navigation system, respectively, φ CNS =[φ CNS,pitch φ CNS,roll φ CNS,yaw ] These represent the angle information in the directions of pitch, roll, and azimuth of the celestial navigation system, respectively. BDS =[V BDS,E V BDS,N V BDS,U ] represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. BDS =[P BDS,L P BDS,λ P BDS,H ] These represent the latitude, longitude, and altitude location information of the GPS navigation system, respectively. Φ k,k-1 H kGiven the known system structural parameters, where Φ k,k-1 =eye(15),eye(n) represents an n-dimensional square matrix with diagonal elements of 1 and the rest of the elements of 0. Let w be the system variance matrix. eb The gyroscope randomly walks in three directions, w db Acceleration random walks are performed in three directions. Let σ be the noise observation matrix. GPS , σ CNS , σ BDS These are the standard deviations of positioning noise for GPS navigation systems, astronomical navigation systems, and BeiDou navigation systems, respectively.

[0054] S2: Calculate the filtering innovation, i.e., the residual, for each sub-filter, expressed as:

[0055]

[0056] Next, we need to calculate the filtered innovation r. k The covariance is expressed as:

[0057]

[0058] in, Let be the state one-step mean square error matrix, where Let be the mean square error matrix of the state estimation, where This is the optimal estimate from the previous moment.

[0059] S3: Calculate the statistics used for monitoring in the fault detection system corresponding to each sub-filter, expressed as:

[0060] zt k =λr k +(1-λ)r k

[0061]

[0062] EWMA k =zt k Sz k -1 zt T

[0063] Where λ is the coefficient of the exponentially weighted moving average, which is related to the drift δ x =(μ T Σ -1 The value is proportional to μ, which can be obtained directly through Markov chains, Monte Carlo methods, or by querying the corresponding table. Here, μ is the sample mean of the data, and Σ is the sample covariance of the data.

[0064] S4: The kernel multivariate index-weighted moving average control chart fault detection system, in offline mode, collects fault-free data and calculates the kernel density to estimate the alarm threshold, expressed as:

[0065]

[0066]

[0067]

[0068] h = 1.06 min(s, IQR / 1.34)n-1 / 5

[0069] Among them, X i For monitoring purposes, Let be the probability density function. K(t) is the distribution function, K(t) is the kernel function (the Epanechnikov kernel is used here), n is the sample size, h is the smoothing coefficient (obtained through the Silverman rule), α is the significance level (used to adjust the strictness of the system), AL is the alarm threshold, s is the standard deviation of the sample, and IQR is the interquartile range.

[0070] According to step 2, as Figure 4 As shown, the fault detection times for the BeiDou and GPS navigation systems are ultimately at 318 seconds and 614 seconds, respectively, demonstrating timely detection of sensor malfunctions. Furthermore, compared to conventional federated filtering, such as... Figure 5 As shown, the federated filtering based on the kernel multivariate index-weighted moving average control chart can promptly isolate sensor malfunctions and achieve higher positioning accuracy.

[0071] In summary, this paper proposes a fault-tolerant integrated navigation method based on federated filtering for fault detection and isolation. During integrated navigation, sensor faults can be detected in a timely manner and effectively predicted. Fault isolation can be performed simultaneously when necessary. At the same time, this method can improve the positioning accuracy of the system, thereby ensuring fault tolerance and reliability in integrated navigation.

Claims

1. A fault-tolerant combined navigation method for fault detection and isolation using federated filtering, characterized in that, Includes the following steps: Step 1: Determine the number of sensors required for integrated navigation. , build A federated filter structure is constructed using a combination of sub-filters and a master filter. The observational information and corresponding covariance in each sub-filter system are calculated. A fault detection system based on a kernel multivariate exponentially weighted moving average control chart is constructed. In the offline phase, an alarm threshold is calculated based on the constructed monitoring statistics. In the online phase, i.e., the actual detection and operation phase, the need for sub-filter isolation is determined based on the alarm threshold, i.e., the control limit of the control chart. If the constructed multivariate exponentially weighted moving average statistic is greater than the alarm threshold, step 2 is executed; otherwise, step 3 is executed. Step 2: Issue an early warning for the system and determine whether fault isolation is necessary based on the following criteria: continuously monitor five multivariate exponentially weighted moving average statistics to determine if they exceed the alarm threshold. If four statistics exceed the alarm threshold, isolate the sub-filter corresponding to the fault detection system, while the remaining filters and the main filter operate normally. Otherwise, restore all isolated sub-filters and proceed to Step 3. Step 3: All sub-filters and the main filter function normally according to the relevant structure; The specific steps for constructing the federated filter structure of the kernel multivariate exponential weighted moving average control chart fault detection system in step 1 are as follows: S1: The integrated navigation system consists of multiple sensors, exemplified by inertial navigation system, GPS navigation system, BeiDou navigation system, and astronomical navigation system. The state equation for the filter system is as follows: in, For time-based information, a 15-dimensional state matrix is ​​used for updating. Let be the state matrix, where These represent the attitude angle errors in the pitch, roll, and azimuth directions, respectively. These represent the velocity errors in the east, north, and sky directions, respectively. These represent the positional errors of latitude, longitude, and altitude, respectively. This represents the drift error of the gyroscope in the three-axis directions. This indicates the zero bias error of the accelerometer in three directions. Here is the measurement matrix, where These represent the velocity information of the inertial navigation system in the east, north, and sky directions, respectively. These represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. These represent the latitude, longitude, and altitude position information of the inertial navigation system, respectively. These represent the latitude, longitude, and altitude location information of the GPS navigation system, respectively. These represent the angle information in the pitch, roll, and azimuth directions of the inertial navigation system, respectively. These represent the angle information in the directions of pitch, roll, and azimuth of the celestial navigation system. These represent the speed information in the east, north, and sky directions of the GPS navigation system, respectively. These represent the location information of the GPS navigation system in terms of latitude, longitude, and altitude, respectively. , Given the known system structural parameters, where , express A square matrix with diagonal elements all being 1 and the rest being 0. , Let be the system variance matrix, where The gyroscope moves randomly in three directions, taking its angles in each direction. Acceleration random walk in three directions, Here is the noise observation matrix, where , These are the standard deviations of positioning noise for GPS navigation systems, astronomical navigation systems, and BeiDou navigation systems, respectively. S2: Calculate the filtering innovation, i.e., the residual, for each sub-filter, expressed as: Next, the filtered innovation needs to be calculated. The covariance is expressed as: in, Let be the state one-step mean square error matrix, where , , Let be the mean square error matrix of the state estimation, where , This is the optimal estimate from the previous moment. S3: Calculate the statistics used for monitoring in the fault detection system corresponding to each sub-filter, expressed as: in, The coefficients of the exponentially weighted moving average are related to the drift. Proportional, obtained through Markov chains, Monte Carlo methods, or by directly querying the corresponding table, among which... The sample mean of the data. The sample covariance of the data, S4: The kernel multivariate index-weighted moving average control chart fault detection system, in offline mode, collects fault-free data and calculates the kernel density to estimate the alarm threshold, expressed as: in, For monitoring purposes, Let be the probability density function. The distribution function, For the kernel function, the Epanechnikov kernel is used here. For sample size, The smoothing coefficient is obtained using Silverman's rule of thumb. The significance level is used to adjust the strictness of the system, and AL is the alarm threshold. The standard deviation of the sample. Interquartile difference; In step 2, the integrated navigation system includes inertial, GPS, Beidou, and astronomical navigation systems. The inertial navigation system serves as the main filter and includes three sub-filters and corresponding fault monitoring modules. When the constructed statistic of one of the core multivariate index-weighted moving average control charts exceeds the alarm threshold, the entire integrated navigation system will receive an early warning. If the condition described in step 2 occurs, the sub-filter will perform fault isolation.

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