Robust method based on fault cutting

Abstract

The present invention discloses a robust method based on fault cutting, which is applied to a GNSS / SINS integrated navigation system with dual navigation sensors, and includes: improving and optimizing on the basis of the residual chi-square test method and the fading sequential probability ratio detection method; identifying the fault type according to the two optimized detection methods, setting a processing factor according to the fault type, and realizing the cutting process of the fault by alternately responding with the reset processing factor and the robust processing factor; the present invention effectively improves the robust effect of the traditional robust method.

Description

Technical Field

[0001] The present invention relates to the technical field of fault cutting, and particularly to a robust method based on fault cutting. Background Art

[0002] In the process of a combined navigation system, timely fault detection and fault handling of measurement information have become a common method to ensure the stability of the combined navigation system. In terms of fault detection, common fault detection methods include the χ 2 method and the sequential probability ratio test (SPRT), where the χ 2 method includes the state χ 2 method and the residual χ 2 method. The residual χ 2 test has become a commonly used detection method due to its simple calculation and sensitivity to sudden change faults. However, for small amounts of slowly varying faults, it is slow to respond. The state χ 2 and the double-state χ 2 can produce good detection effects on slowly varying faults. However, over time, the recursive filter is vulnerable to contamination by cumulative errors; the SPRT method, as a residual-based test method, is independent of the statistical changes of the state and has become a commonly used software fault detection method in combined navigation systems. However, the traditional SPRT method has problems such as detection time delay, negative statistical values, and delayed detection of fault termination. Further improvement and optimization are still needed. Some scholars reset the statistical quantity of the SPRT method by combining the fault termination time of the residual χ 2 test to eliminate the time delay problem after fault termination. In the actual combined navigation process, due to the mutual coupling relationship between system states, a single moment of fault will cause a fault tailing phenomenon in the combined positioning result. This method can only detect the fault size that meets the residual χ 2 test as the fault termination time and cannot detect the termination time of slowly varying faults during the tailing process. There are also methods that enhance the influence of new epochs on the change rate and statistical quantity of the test statistic by introducing a fading factor, improving the detection rate of the traditional SPRT algorithm and overcoming the defect that the traditional SPRT method cannot detect the termination moment of slowly varying faults.

[0003] When a system measurement failure is detected, corresponding measures need to be taken to handle the failure to ensure the stability of the system. Some scholars isolate the faulty sensor in a multi-navigation sensor system and do not use the measurement information of the faulty sensor in the federated filter, which has become a common method to ensure the robustness of the system during multi-sensor integrated navigation. In a dual-navigation sensor system, some scholars adopt the method of setting the faulty measurement information to zero to eliminate the influence of the faulty measurement information on the positioning result. However, with the continuous application of the fault over a long time, the inertial navigation state is not corrected in time by the measurement information, resulting in a positioning divergence phenomenon. Most scholars use the robust method to handle the fault. By assigning a weight of 0-1 to the covariance of the fault, the weight of the faulty measurement information in the state update is reduced to achieve the isolation effect. However, this method is only effective for single-step mutation faults and will produce trailing and insignificant processing phenomena for continuous mutation faults or slow-varying faults respectively. Summary of the Invention

[0004] To solve the problems existing in the prior art, the purpose of the present invention is to provide a robust method based on fault cutting, which effectively improves the robustness of the traditional robust method.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a robust method based on fault cutting, which is applied to a GNSS / SINS dual-navigation sensor integrated navigation system, and specifically includes the following steps:

[0006] Step 1: Improve and optimize based on the residual chi-square test method and the fading sequential probability ratio test method;

[0007] Step 2: Identify the fault type according to the two optimized detection methods, set the processing factor according to the fault type, and achieve the cutting process of the fault by alternately responding with the reset processing factor and the robust processing factor.

[0008] As a further improvement of the present invention, the specific content of the step 1 is as follows:

[0009] Optimize the residual chi-square test by using the sequential idea. Assume that only the three-dimensional position information of latitude, longitude and altitude of the integrated navigation is observed. Let ε i,k be the position measurement residual at the kth moment, where i = 1, 2, 3; at this time, the chi-square statistic λ i,k corresponding to the residual of the ith dimension is:

[0010]

[0011] In the formula, P (i,i),k / k-1 is the diagonal element of the ith row and ith column of P k,k-1 , R (i,i),k is the diagonal element of the ith row and ith column of R k ;

[0012] In the fading sequential probability ratio detection method, the covariance P of the measurement dimension corresponding to the residual statistical result exceeding the detection threshold during the calculation of the statistic is (i,i)k,k-1 replaced with the P of the previous moment (i,i)k-1 , to prevent the P used in the calculation from (i,i)k,k-1 continuously increasing as the fault is continuously applied, thereby weakening the growth trend of the detection statistic; at the same time, to ensure that the statistic is non - negative and affect the growth rate of the statistical result, the statistic

[0013] As a further improvement of the present invention, in step 2, the specific method for identifying the fault type according to the two optimized and improved detection methods is as follows:

[0014] Calculate the measurement residual ε at the current moment k , and statistically analyze the residual at each moment to obtain the residual group vector Let the residual chi - square test statistic be The corresponding residual chi - square test threshold is The test statistic of the fading sequential probability ratio detection method The corresponding test threshold is Adopt a sequential method to simultaneously perform two tests on the residual of the i - th dimension at the k - th moment. The test situations include:

[0015] (1) When and At this time, the test result is no fault;

[0016] 2) When and , at this time, the test result is a slow - changing fault;

[0017] 3) When there must be At this time, the test result is a sudden - change fault;

[0018] Define the detection situation corresponding to the i - th dimension at the k - th moment as FT i,k .

[0019] As a further improvement of the present invention, in step 2, the processing factor is set according to the fault type as follows:

[0020] Update the processing factor through the obtained different detection situations FT i,k , different processing factors correspond to different processing methods, NT i,k is the robust processing factor, NR i,k is the reset processing factor; the value of the processing factor being 1 means this kind of processing is performed, and the value of the processing factor being 0 means this kind of processing is not performed.

[0021] As a further improvement of the present invention, in step 2, the specific manner of the alternating response of the reset processing factor and the robust processing factor is as follows:

[0022] The corresponding relationship between the three obtained processing factor combination modes and the processing methods is as follows:

[0023]

[0024] Robust processing: Use the IGGⅢ method to obtain the robust weight factor t i,k , and replace R i,k in the chi-square statistic λ (i,i),k with R (i,i),k / t i,k to achieve the robust processing of the current latitude;

[0025] Reset processing: First, replace and reset the residual statistic at the previous moment with the median of the residuals at the previous k - 1 moments to process the residual statistic at the previous moment to prevent the influence of the faulty residuals in the previous robust processing on the calculation of the median of the residuals at the current moment; at the same time, replace and reset the residual vector ε i,k that needs to be reset processed at the current moment with the median of the residuals.

[0026] The beneficial effects of the present invention are:

[0027] The present invention proposes a robust method of fault cutting for the continuous mutation faults and slow - change faults of the measurement information in the navigation system; first, introduce the sequential idea to improve the residual chi - square test to achieve the accurate positioning of mutation faults, and optimize the covariance and statistic of the fading SPRT to improve the detection sensitivity of the fading SPRT method for slow - change faults. Divide the fault types through the improved double - test method, update the processing factors for the fault types, allocate the response states of reset and robustness, and achieve the cutting of continuous faults; through the analysis of the simulation results, it shows that the algorithm of the present invention performs robust processing of fault cutting on the faults that reach the threshold of the residual chi - square test, and performs reset processing on the faults that reach the SPRT threshold but do not reach the threshold of the residual chi - square test. It effectively improves the robustness of the traditional robust method and has certain engineering reference significance. Description of the Drawings

[0028] Figure 1 Schematic diagram of the changes of each parameter of IGGⅢ in the case of slow - change faults;

[0029] Figure 2 Schematic diagram of the changes of each parameter of IGGⅢ in the case of continuous mutation faults;

[0030] Figure 3 Flowchart of the double - test method detection in the embodiment of the present invention;

[0031] Figure 4 It is the flowchart for updating the processing factor in Case 3 of the embodiments of the present invention;

[0032] Figure 5 It is the schematic diagram of the flight trajectory in the embodiments of the present invention;

[0033] Figure 6 It is the change of the GNSS position measurement error in the embodiments of the present invention;

[0034] Figure 7 It is the schematic diagram of the change of the integrated navigation positioning error without robust processing in the embodiments of the present invention;

[0035] Figure 8 It is the schematic diagram for comparing the detection results of traditional chi-square and the through chi-square in the embodiments of the present invention;

[0036] Figure 9 It is the schematic diagram of the detection result of applying a slow-varying fault to the latitude in the embodiments of the present invention;

[0037] Figure 10 It is the schematic diagram of the latitude statistical result during fault cutting in the embodiments of the present invention;

[0038] Figure 11 It is the schematic diagram of the longitude statistic during fault cutting in the embodiments of the present invention;

[0039] Figure 12 It is the global change diagram of the processing factor in the embodiments of the present invention;

[0040] Figure 13 It is the schematic diagram of the change of the robust weight factor in the embodiments of the present invention;

[0041] Figure 14 It is the change diagram of the positioning error in the embodiments of the present invention. Detailed implementation manners

[0042] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0043] Embodiment

[0044] A robust method based on fault cutting specifically includes:

[0045] 1. SINS / GPS integrated navigation system:

[0046] In this embodiment, based on the SINS / GPS integrated navigation system, the standard Kalman filter is used as the data fusion algorithm to carry out the simulation and verification of the fault cutting algorithm.

[0047] 1.1 State equation:

[0048] The system state equation of SINS / GNSS is described as follows:

[0049] X k = F k,k-1 X k-1 + Γ k W k (1)

[0050] In Equation (1): X k is the error state at time k, F k / k-1 is the state transition matrix from time k - 1 to k, X k-1 is the error state at the previous time, Γ k1 is the noise driving matrix, W k is the system noise.

[0051] The state of the system consists of the misalignment angle, velocity error, position error, gyroscope error, and accelerometer error of the SINS. The error state of the SINS is selected to be 15 - dimensional, as follows:

[0052]

[0053] In Equation (2): Φ, δv n , δp respectively represent the misalignment angle, velocity error, and position error of the SINS in the navigation coordinate system (N - system), ε b is the projection of the gyroscope zero - bias in the body coordinate system (b - system), ▽ b is the projection of the accelerometer zero - bias in the body coordinate system (b - system).

[0054] Among them, the state transition matrix F k / k-1 can be expressed as shown in Equation (3):

[0055]

[0056] 1.2. Measurement equation:

[0057] In the GNSS / SINS integrated navigation mode, the positioning information output by the SINS is corrected by the high - precision GNSS positioning information to suppress the accumulation of inertial errors over time. The measurement equation of the system can be expressed as follows:

[0058] Z k = H k X k + V k (4)

[0059] In the formula, Z k is the measured value; H k is the measurement matrix; V k is the measurement noise; in this embodiment, H k can be expressed by Equation (5).

[0060]

[0061] 1.3. Standard Kalman filter equation:

[0062] The standard Kalman filter algorithm mainly includes two parts: time update and measurement update. Among them, the time update includes state and its covariance update, and the measurement update includes filter gain, state estimation, and variance estimation:

[0063] X k / k-1 = F k X k-1 / k-1 (6)

[0064]

[0065]

[0066]

[0067] P k = (I - K k H k )P k / k-1 (10)

[0068] 2. Introduction to fault detection and robust methods:

[0069] 2.1. Fault model:

[0070] Faults can be divided into abrupt faults and gradual faults, and their fault models are as follows:

[0071]

[0072] In Equation (11), is the fault observation value, z k is the true observation value, δz k is the abrupt fault value, α z is the fault change rate, k is the current time, and k0 is the starting time of the fault.

[0073] 2.2. Residual chi-square test method:

[0074] The residual chi-square test is sensitive to abrupt faults, has a simple structure, and is convenient for calculation and use. Let the residual be ε k , which is expressed as follows:

[0075]

[0076] In Equation (12), Z k is the measurement value, is the one-step state prediction.

[0077] According to the orthogonality principle, the square of the residual Mahalanobis distance follows a chi-square distribution, and its chi-square test statistic is as follows:

[0078]

[0079] If the measured value is abnormal, it will make the square of the Mahalanobis distance of the residual not conform to the chi-square distribution with the degree of freedom of n, where n is the measurement latitude. The confidence level of the residual ε k can be judged by setting the significance level α of the chi-square test. Let Then the criterion method of the chi-square test statistic is obtained as:

[0080]

[0081] If λ k >T D , it is determined that the residual is abnormal, otherwise it is the opposite.

[0082] Since the chi-square test of the residual only relies on the state estimation information of the previous step, it can effectively detect abrupt faults. However, in the face of faults with slow-changing quantities the statistical characteristics of the residuals between adjacent epochs change little. The chi-square test of the residuals will show the phenomenon of detection delay and is not sensitive to the detection of slow-changing faults.

[0083] 2.3, Fading SPRT Test Method:

[0084] The traditional SPRT algorithm is a detection method that is sensitive to slow-changing faults and is widely used in the detection process of slow-changing faults in integrated navigation. The following is a simple introduction to this algorithm.

[0085] A binary hypothesis is made for the measured values of the integrated navigation system: normal state H0 and abnormal state H1. When the measured value is fault-free, ε k conforms to a Gaussian distribution with a mean of zero, and the residual expectation and variance can be expressed as follows:

[0086]

[0087] When the measured value is faulty, ε k does not follow a Gaussian distribution with a mean of zero. The corresponding residual expectation and variance can be expressed as follows:

[0088]

[0089] In Equation (16), δv k is the fault noise.

[0090] The expectations of the residuals in Equations (15) and (16) can be represented by the mean value:

[0091]

[0092] The probability density of the residual samples under two assumptions is as follows:

[0093]

[0094]

[0095] According to the probability density function, the likelihood ratio of the two assumptions can be calculated as:

[0096]

[0097] Taking the logarithm of Equation (20), the statistic of the SPRT detection method is obtained

[0098]

[0099] Then, through simplification, the iterative relationship of the statistic can be obtained as:

[0100] λ k = λ k-1 + Δλ k (22)

[0101] Given the false alarm rate P f and the miss alarm rate P m the threshold of the statistic can be set by the SPRT method proposed by Wald as follows:

[0102]

[0103] Based on the relationship between the statistic and the threshold, the fault and normal states of the system are detected:

[0104]

[0105] The above is the traditional SPRT algorithm. To solve the problem that the fading SPRT algorithm cannot detect the end of a slowly changing fault, a fading factor is introduced into Equations (17) and (22) to reduce the influence of historical residuals and statistics, achieving the purpose of detecting the fault end time. The changes are as follows:

[0106]

[0107] 2.4. IGGⅢ Robust Method:

[0108] Common equivalent weight functions mainly include the Huber method, the Danish method, and the IGGⅢ method. IGGⅢ is also known as the three-segment method. This method corresponds to the weight-preserving area, weight-reducing area, and elimination area in the weight function, realizing the full utilization of effective information, the restricted utilization of suspicious information, and the exclusion of harmful information. It is a processing method suitable for processing measurement data.

[0109] When a fault is detected, a robust method can be used to isolate the faulty measurement information. System robustness is achieved by using a robustness factor to amplify the observation noise variance R k , and adjusting the gain matrix K k value, thereby reducing the weight of the observation information and weakening the influence on the optimal state estimate at the k-th moment . Equation (8) can be rewritten in the following form:

[0110]

[0111] In Equation (26), T k is the robustness factor. n is the measurement dimension.

[0112] In this embodiment, the IGGⅢ method is used to construct the robustness factor, and its functional expression is:

[0113]

[0114] In Equation (27): e k is the standardized residual; k0 and k1 are adjustment coefficients that are constant values. k0 usually takes values from 1.0 to 2.5; k1 takes values from 3.5 to 8.0, where the calculation method of e k is as follows:

[0115]

[0116] In Equation (28), ε k is the residual at the k-th moment, is the residual distance, and its calculation method is as follows:

[0117]

[0118] In Equation (29): is a set of residual vectors at the k-th moment, and med(·) is to take the median.

[0119] 3. Robust algorithm based on fault segmentation:

[0120] 3.1 Problem description:

[0121] In the actual process, it is difficult to effectively process the slow-varying noise and continuous mutation noise through the method of robust weight assignment for the noise covariance matrix R k . It can be assumed that a set of residual vectors of the i-th dimensional measurement information at the k-th moment containing slow-varying faults is Assume that the fault starts at the k0-th moment. At this time, contains a set of normal residual vectors before the start of the fault and a set of abnormal residual vectors after the start of the fault The standardized residual is calculated according to Equation (29) as

[0122]

[0123] Substituting Equation (11) into Equation (30), the relationship between the standardized residual and the slow-varying fault is obtained as follows:

[0124]

[0125] As the time instant k → ∞ gradually increases, The statistical results of no longer remain within a certain range. The residual data of the i-th dimension at the k-th time instant is obtained through Equation (28) and The relationship is:

[0126]

[0127] To more clearly observe the influence of the slow-varying fault on each parameter in IGGⅢ, a set of residual vectors with a length of 100 are normal distribution values with a mean of 0 and a variance of 1. A slow-varying fault of 0.01*(k - 50) is inserted at the 50th second of the simulation. Taking the constant coefficients of IGGⅢ as k0 = 1 and k1 = 3.5, Equations (31) and (32) are calculated to obtain the changes in the residual standard deviation, standard deviation distance, and weight factor. Comparing the two cases of no fault and with fault, as Figure 1 shown, as time continuously changes, the residual value ε k gradually increases, and the residual standard deviation in the IGGⅢ algorithm also increases accordingly. Each and the standard deviation distance at the current time instant increase slowly, and the weight factor gradually tends to 0. In integrated navigation, as the fault time continues, the weight factor t k calculated by IGGⅢ tends to 0. From Equation (26), it can be obtained that when the weight factor t k →0, the corresponding measurement noise R k →∞. From Equation (8), the corresponding K k →0. After calculation through Equation (9), As the fault time extends, the system only performs one-step state prediction, resulting in the inertial divergence characteristic of the fault-dimensional measurement, leading to the failure of the IGGⅢ weighted robust method.

[0128] To more clearly observe the influence of the continuous mutation fault on each parameter in IGGⅢ, in the above simulation a mutation fault value of 5 is inserted from the 50th s to the 100th s and continues until the end of the simulation. Comparing the two cases of no fault and with fault in the comparison results, as Figure 2 shown, when the mutation fault is added, the residual value ε kSuddenly increase and then maintain at the same height level. For the parameters in the IGGⅢ algorithm, the residual standard deviation shows a sudden change first and then a slow decline. Each The distance from the standard deviation at the current moment increases rapidly, and the weight factor directly jumps to 0 first. After a period of time, it gradually approaches the normal factor. From the above, it can be obtained that within the time when the weight factor t k →0 Subsequently, the weight factor changes to the normal range. During the process of anti-robustness in integrated navigation, the dimension where a fault occurs will show a trailing phenomenon of divergence first and then adjustment, and rapid isolation cannot be achieved.

[0129] 3.2. Optimization of the double-check algorithm:

[0130] In the measurement vector of integrated navigation, if there is a fault in one-dimensional measurement information, due to the correlation between the observation vector residuals, it will cause an impact on several other observation residuals, thereby causing an abnormal phenomenon in the overall positioning result of integrated navigation. The fading SPRT can accurately detect the location where the fault occurs, and the result of the residual chi-square test is a numerical value, which cannot locate the specific location where the fault occurs. Therefore, it is necessary to optimize the residual chi-square test.

[0131] This embodiment proposes to optimize the residual chi-square test by using the sequential idea. Assume that only the three-dimensional position information of longitude, latitude, and altitude in integrated navigation is observed. Let ε i,k be the position measurement residual at the kth moment, where i = 1, 2, 3. At this time, the chi-square statistic λ i,k corresponding to the residual of the ith dimension is:

[0132]

[0133] In Equation (33), P (i,i),k / k-1 is the diagonal element of the ith row and ith column of P k,k-1 , and R (i,i),k is the diagonal element of the ith row and ith column of R k .

[0134] In the fading SPRT method, the covariance P (i,i)k,k-1 corresponding to the measurement dimension of the residual statistical result exceeding the detection threshold during the calculation of the statistic is replaced with the P (i,i)k-1 at the previous moment to prevent the P (i,i)k,k-1 used in the calculation from continuously increasing as the fault is continuously applied, thereby weakening the growth trend of the detection statistic

[18] . At the same time, to ensure that the statistic is non-negative and affects the growth rate of the statistical result, the statistic

[0135] 3.3. Fault cutting steps:

[0136] The main steps of fault cutting are divided into three steps: fault type inspection, processing factor update, and robust and reset processing. By using different processing methods at the previous moment and the current moment, the slow-changing faults that fail to pass the residual chi-square test are reset, and the continuous mutation faults and slow-changing faults that reach the residual chi-square test threshold are subject to fault reset and robust interval processing, achieving the effect of cutting continuous mutation faults and slow-changing faults. The main steps are as follows:

[0137] Step1 Fault type inspection:

[0138] Calculate the measurement residual ε k at the current moment, and statistically analyze the residuals at each moment to obtain the residual group vector Let the chi-square test statistic of the residual be The corresponding chi-square test threshold of the residual is The fading SPRT test statistic The corresponding test threshold is Use a sequential method to perform two tests on the residuals of the i-th dimension at the k-th moment simultaneously, and there are three test situations in total:

[0139] 1) When and The test result is no fault at this time.

[0140] 2) When and The test result is a slow-changing fault at this time.

[0141] 3) When There must be The test result is a mutation fault at this time.

[0142] Define the test situation corresponding to the i-th dimension at the k-th moment as FT i,k To sum up, the test process of the double-test method is as Figure 3 shown.

[0143] Step2 Processing factor update:

[0144] Update the processing factor through the different detection situations FT i,k obtained in Step1. Different processing factors correspond to different processing methods. NT i,k is the robust processing factor, and NR i,k is the reset processing factor. A processing factor value of 1 indicates that this processing is performed, and a processing factor value of 0 indicates that this processing is not performed. Different detection situations correspond to different processing methods and processes. When k = 0, the initial state of the processing factor corresponding to the fault type is shown in Equation (34). When k is not 0, the processing factor update processes for Situation 1 and Situation 2 are shown in Table 1, and the processing factor update process for Situation 3 is asFigure 4 as shown

[0145]

[0146] Table 1 Update Table of Treatment Factors for Case 1 and Case 2

[0147]

[0148]

[0149] Step 3 Robust and Reset Processing:

[0150] The corresponding relationship between the three treatment factor combination modes and treatment methods obtained through Step 2 is as shown in Equation (35).

[0151]

[0152] 1. Robust Processing:

[0153] Use the IGGⅢ method to obtain the robust weight factor t i,k , and replace R in Equation (33) (i,i),k with R (i,i),k / t i,k to achieve the robust processing of the current dimension.

[0154] 2. Reset Processing:

[0155] First, replace and reset the residual statistic of the previous moment with the median of the residuals of the previous k - 1 moments to process the residual statistic of the previous moment to prevent the influence of the faulty residuals in the previous robust processing on the calculation of the median of the residuals at the current moment. At the same time, replace and reset the residual vector ε i,k to be reset at the current moment with the median of the residuals.

[0156] 4. Simulation and Analysis:

[0157] 4.1. Simulation Parameter Settings:

[0158] In this embodiment, the effectiveness of the proposed algorithm is verified by simulating a flight training subject trajectory data. The initial position of the aircraft is set as N: 30°58′39″ north latitude, E: 104°16′54″ east longitude, altitude H: 0m, initial speed: 0 kt, and initial heading: 0°. The initial position errors in the northeast-down three directions are 1m, 1m, and 3m, the initial misalignment angle is 0.5°, and the initial speed error is 0.1m / s. The parameters of the inertial navigation are set as follows: gyro zero bias stability eb = 15° / h; gyro random walk web = 500° / sqrt(h); accelerometer zero bias stability db = 1ug; accelerometer measurement random walk web = 500ug / sqrt(Hz). The GNSS positioning position errors are set as: 1m eastward error, 1m northward error, and 3m upward error; the simulation trajectory includes the takeoff, climb, acceleration, turning and other motion states of the aircraft as Figure 5 shown.

[0159] In this embodiment, the effectiveness of the proposed algorithm is verified by applying persistent mutation faults and slow-varying faults to the longitude and latitude information measured by GNSS respectively. By applying the faults shown in Table 2 to the normal measurement information, the measurement error changes corresponding to each measurement dimension with and without fault addition can be obtained as Figure 6 shown. Among them, the false alarm rate and missed alarm rate of the residual chi-square test and the SPRT method are both 5%, the corresponding chi-square threshold is 12.84, and the SPRT threshold is 5.29.

[0160] Table 2 Fault settings for measurement information

[0161]

[0162] 4.2 Verification and analysis of the improved detection algorithm:

[0163] By applying corresponding faults to the GNSS position measurement information and using KF as the data fusion algorithm, the positioning error changes of the integrated navigation without robust processing are obtained as Figure 7 shown. It can be seen that during the process of applying faults, the navigation positioning results without robust processing are significantly affected by the faults. Figure 8 To compare the results of the sequential residual chi-square test and the traditional chi-square test with the introduction of the sequential idea under the influence of this fault. The results of the sequential residual chi-square test can clearly distinguish the dimension positions of the faulty measurement information, and are highly consistent with the traditional residual chi-square statistical results in terms of statistics. Figure 9When adding a slowly varying fault only in the latitude, the detection results of the improved fading SPRT method, the fading SPRT method, and the improved residual chi-square test change. In the figure, after the slowly varying fault is added starting from the 400th second, the critical moment for the improved fading SPRT method to reach the SPRT threshold is the 404th second, and the critical moment for the fading SPRT method to reach the SPRT threshold is the 408th second. The critical moment for the improved chi-square test to reach the chi-square threshold is the 419th second. This shows that the sensitivity of the improved fading SPRT method for detecting slowly varying faults is better than that of the fading SPRT method. At the same time, the critical moments of the SPRT method are all less than those of the chi-square test, indicating that the SPRT method has a better detection effect for slowly varying faults compared to the residual chi-square test. And combined with Figure 9 As shown, the improved fading SPRT method can successfully detect the fault end time, which is in line with the fault change situation during the integrated navigation process.

[0164] 4.3. Verification and analysis of the effectiveness of the processing factor:

[0165] The improved fading SPRT method and the improved chi-square test method are used as the detection algorithms in this embodiment. Figure 10 And Figure 11 This is the test result of applying a continuous mutation fault to the longitude and a slowly varying fault to the latitude during the fault cutting and robustness process of this embodiment. As can be seen from Figure 10 , the start times of the improved fading SPRT method and the improved chi-square test method are the 408th second and the 412th second respectively, while the occurrence time of the slowly varying fault is the 400th second. And from Figure 12 , the change of the processing factor in the latitude, it can be obtained that during the 408th second to the 451st second of the simulation, NR and robust NT alternate responses are reset to achieve the cutting process of the slowly varying fault and then perform robustness. Figure 13 The alternating change of the weight factor in the corresponding time period in Figure 12 also verifies the effectiveness of the cutting process and robustness. At the same time, the fault end time detected by the improved chi-square test method is the 451st second, and the fault end time detected by the improved fading SPRT method is the 480th second. Then, during the 451st second to the 480th second of the simulation, there is still a certain slowly varying fault in the latitude measurement. Combining Figure 11 , the change of the processing factor in the latitude, at this time only NR responds, and the measurement in this time period is continuously reset. Figure 12 This is the detection result of applying continuous mutation noise to the longitude measurement information from the 100th second to the 120th second of the simulation. It can be seen that the start times of the two detection algorithms for detecting the fault are the same, and the detected fault end times are distributed as the 121st second and the 124th second. During this time period,

[0166] 4.4. Analysis of the integrated navigation results:

[0167] In this embodiment, the normal KF integrated navigation result without any faults is used as Method 1, the result of only performing IGG III robust processing is used as Method 2, and the IGG III robust result after fault cutting processing is used as Method 3. The integrated navigation positioning error results are as Figure 14 shown. It can be seen that Method 2, which only performs IGG III robust processing, can effectively isolate the sudden faults in the altitude error, and has a certain effect on dealing with the slow-changing faults and continuous sudden faults in latitude and longitude, making the existing faults much smaller than the applied faults. However, it cannot achieve complete robust processing for slow-changing faults and continuous sudden faults. Method 3 is the integrated navigation result of the fault cutting and robust method proposed in this embodiment. The positioning result of this method fits well with the positioning result without faults in Method 1, proving that the processing algorithm in this embodiment is effective for the robust results of slow-changing faults and continuous sudden faults. To more clearly show the processing effect of the algorithm, in this embodiment, the RMSE values corresponding to the three directions of latitude, longitude, and altitude of several methods are calculated and compared, as shown in Table 3. It can be seen that the RMSE value of the algorithm in this embodiment is slightly smaller than that of Method 1. This is because in the process of integrated navigation in this embodiment, the slow-changing noise randomly appearing in the navigation process is detected and reset, making the positioning result of the algorithm in this embodiment slightly better than that of Method 1. Compared with Method 1, the positioning accuracies in latitude, longitude, and altitude are improved by 5.03%, 12.90%, and 19.94% respectively. Compared with Method 2, they are improved by 45.01%, 13.53%, and 1.09% respectively. The positioning accuracies in altitude and dimension between Method 2 and Method 3 are not much different because only sudden faults at a single moment are added in the altitude dimension, and the IGG III robust method can effectively remove single sudden faults.

[0168] Table 3 RMSE of Algorithm Errors

[0169]

[0170] To solve the problem that traditional robust methods have poor processing effects on continuous mutation faults and slow-varying faults, this embodiment proposes a robust method of fault cutting. First, it is improved and optimized based on the traditional residual chi-square test method and the fading sequential probability ratio test (SPRT) to improve the accuracy of fault location and the sensitivity of fault detection. The fault type is identified according to the two improved detection methods, and the processing factor is set according to the fault type. The fault cutting process is realized by alternately responding with the reset processing factor and the robust processing factor. In the reset processing, the median of the residual statistics is used to reset the fault residual at the current moment. In the robust processing, the IGGⅢ method is used to perform robust processing on the cut fault. The simulation results show that the algorithm can effectively handle the influence of continuous mutation faults and slow-varying faults on integrated navigation, and the positioning accuracy improvement effect is significantly better than the traditional IGGⅢ robust method alone, and to a certain extent, it also improves the navigation positioning accuracy in the case of no faults.

[0171] The above-described embodiments only represent the specific implementation manners of the present invention, and the description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A robust method based on fault cutting, characterized in that It is applied to the GNSS / SINS integrated navigation system, and specifically includes the following steps: Step 1: Improve and optimize based on the residual chi-square test method and the fading sequential probability ratio detection method; The specific content of Step 1 is as follows: Optimize the residual chi-square test using the sequential idea. Assume that only the three-dimensional position information of longitude, latitude, and altitude in integrated navigation is observed, and let ε i,k be the position measurement residual at the k-th moment, where i = 1, 2, 3; at this time, the chi-square statistic λ i,k corresponding to the residual in the i-th dimension is as follows: where P (i,i),k / k-1 is the diagonal element in the i-th row and i-th column of P k,k-1 , and R (i,i),k is the diagonal element in the i-th row and i-th column of R k ; In the fading sequential probability ratio detection method, the covariance P of the measurement dimension corresponding to the residual statistical result exceeding the detection threshold during the calculation of the statistic (i,i)k,k-1 is replaced by the P of the previous moment (i,i)k-1 , which is used to prevent the continuously increasing P used in the calculation (i,i)k,k-1 from continuously increasing as the fault is continuously applied, thereby weakening the growth trend of the detection statistic; at the same time, to ensure that the statistic is non-negative and affects the growth rate of the statistical result, the statistic Step 2: Identify the fault type according to the two optimized and improved detection methods, set the processing factor according to the fault type, and achieve the cutting process of the fault by alternately responding with the reset processing factor and the robust processing factor.

2. The robust method based on fault cutting according to claim 1, characterized in that, In Step 2, the specific method for identifying the fault type according to the two optimized detection methods is as follows: Calculate the measurement residual ε at the current moment k , and perform statistics on the residuals at each moment to obtain the residual group vector Let the residual chi-square test statistic be The corresponding residual chi-square test threshold is The fading sequential probability ratio test method test statistic The corresponding test threshold is Adopt a sequential method to simultaneously perform two tests on the residuals of the i-th dimension at the k-th moment. The test situations include: 1) When and the test result is no fault at this time; 2) When and the test result is a slow-changing fault at this time; 3) When there must be the test result is a mutation fault at this time; Define the detection situation corresponding to the i-th dimension at the k-th moment as FT i,k 。 3. The robust method based on fault cutting according to claim 2, wherein In Step 2, the specific method for setting the processing factor according to the fault type is as follows: Based on the different obtained detection situations FT i,k Update the processing factor. Different processing factors correspond to different processing methods, NT i,k is the robust processing factor, NR i,k is the reset processing factor; a value of 1 for the processing factor indicates that this processing is to be carried out, and a value of 0 for the processing factor indicates that this processing is not to be carried out.

4. The robust method based on fault cutting according to claim 3, wherein, In Step 2, the specific method for resetting the alternating response mode of the processing factor and the robust processing factor is as follows: The corresponding relationship between the three obtained combinations of processing factors and processing methods is as follows: Robust processing: The robust weight factor t is obtained using the IGG III method i,k , and the chi-square statistic λ i,k in which the R (i,i),k is replaced by R (i,i),k / t i,k , to achieve robust processing of the current latitude; Reset processing: First, replace and reset the residual statistic at the previous moment in with the median of the residuals at the previous k - 1 moments to process the residual statistic at the previous moment to prevent the influence of the faulty residuals in the previous robust processing on the calculation of the median of the residuals at the current moment; at the same time, replace and reset the residual vector ε i,k to be reset in the current processing with the median of the residuals.

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