Fault-tolerant integrated navigation method based on improved multivariate accumulation and control chart

Abstract

The invention provides a fault-tolerant integrated navigation method based on an improved multivariate accumulation and control chart, which comprises the following steps: firstly, acquiring a measured value of a sensor, constructing multivariate accumulation and statistics according to information calculated in volume Kalman filtering, and acquiring a control limit through the statistics and operation time; then judging whether the sensor breaks down or not, still needing to construct multivariate accumulation and statistics, comparing the multivariate accumulation and statistics with the control limit, if the multivariate accumulation and statistics are larger than the control limit, breaking down, and if the multivariate accumulation and statistics are smaller than the control limit, performing normal filtering for navigation positioning. When a fault occurs, the degree of the fault is identified, and the fault is reduced according to the degree of the fault, so that the robustness of filtering is ensured, and high-precision navigation positioning is carried out. The fault-tolerant integrated navigation method designed by the invention can guarantee the positioning precision of the navigation system under different degrees of faults, and has good fault-tolerant performance and robustness.

Description

Technical Field

[0001] The invention relates to the technical field of fault-tolerant combined navigation, and in particular to a fault-tolerant combined navigation method based on an improved multivariate cumulative sum control diagram. Background Art

[0002] Integrated navigation technology is widely used in daily life, military, aviation and navigation. However, affected by the complex environment, the sensors used in navigation sometimes experience signal fluctuations or even failures, which leads to reduced navigation accuracy or even failure. Therefore, it is necessary to ensure that the integrated navigation system operates stably, effectively and even with high precision when a fault occurs. In addition, sensitive fault detection, effective fault identification and robust filtering methods are prerequisites for ensuring the smooth operation of the fault-tolerant navigation system. In summary, it is necessary to establish a fault-tolerant integrated navigation method to ensure the smooth operation of the navigation system when the navigation system fluctuates or fails.

[0003] Cumulative sum statistics are widely used in the field of fault detection due to their high sensitivity, and the multivariate cumulative sum control chart is an accurate and stable monitoring tool. It sets effective control limits to ensure low false alarm rates and false detection rates, thereby performing high-precision fault detection. In addition, the fault degree is analyzed through generalized canonical correlation analysis, and the fault degree is effectively identified to reduce the fault to varying degrees. Finally, the idea of ​​M estimation is used to ensure the robustness of the filter and improve the filtering accuracy of the combined navigation. By organically combining the above methods, a highly robust, highly stable, fault-tolerant combined navigation system is finally realized. Summary of the invention

[0004] In view of the relevant problems of the current fault-tolerant integrated navigation, the present invention provides a fault-tolerant integrated navigation method based on an improved multivariate cumulative sum control chart. The method is based on the organic integration of multivariate cumulative sum control chart, generalized canonical correlation analysis and M estimation, and can realize a highly robust and stable fault-tolerant integrated navigation system.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A fault-tolerant combined navigation method based on an improved multivariate cumulative sum control chart comprises the following steps:

[0006] Step 1: Obtain the measurement values ​​of the sensors used for integrated navigation in an interference-free and relatively stable environment, construct and record the multivariate cumulative sum statistics based on the new information calculated in the cubature Kalman filter, and also record the cumulative sum sequence.

[0007] Step 2: Repeat step 1 until the set deadline T, and then control the limit CL based on the multivariate cumulative and statistical quantity calculated within time T.

[0008] Step 3: Initialize and perform fault-tolerant integrated navigation to obtain the measurement value Z of the sensor used for integrated navigation.k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k .

[0009] Step 4: If the constructed MC k >CL, go to step 5, otherwise go to step 6.

[0010] Step 5: Construct a weight matrix based on the cumulative sum sequence recorded in step 1 and construct a fault degree function.

[0011] Step 6: Reconstruct the Kalman gain according to the fault degree, correct and filter, obtain the state matrix and covariance matrix, complete the filtering process and then proceed to step 3.

[0012] Further, the new information calculated in the integrated navigation and volumetric Kalman filtering described in step 1 constructs a multivariate cumulative sum statistic and a cumulative sum sequence, specifically:

[0013] Integrated navigation can be simplified into a nonlinear optimal filtering problem, and a complex system model can be constructed:

[0014] X k =F(X k-1 )+W k-1

[0015] Z k =H(X k )+V k

[0016] Where F(·) and H(·) are the nonlinear state and measurement transfer matrices, respectively, and X k is the state matrix, Z k is the measurement matrix, W k The mean is zero and the variance is Q k The process noise matrix, V k The mean is zero and the variance is R k The measurement noise matrix. According to this model, cubature Kalman filtering is performed and its innovation is calculated, specifically:

[0017]

[0018] Where P represents the error covariance matrix, the subscript k / k-1 represents one-step prediction, and L = 2n,ω i =1 / (2n), n represents the number of volume points, ξ i,K Represents a volume point set, specifically:

[0019]

[0020] In the formula, New information can be obtained through measurement and one-step prediction measurement, specifically:

[0021]

[0022] Next, we construct the multivariate cumulative sum statistic MC k Sum cumulative sum sequence B k , specifically:

[0023]

[0024] MC k =max{0,(B′ k ∑ -1 B k ) 1 / 2 -ml k}

[0025] Where m>0 can be set manually to control the growth rate of multivariate cumulative sum statistics, l1=1 and l k = l k-1 +1, when MC k-1 >0, then make l k =1.

[0026] Furthermore, the multivariate cumulative sum statistic control limits described in step 2 are specifically:

[0027] CL=F(x) -1 (1-α)

[0028] In the formula, α represents the significance level, F(x) represents the cumulative distribution function, and the probability density function of f(x) is:

[0029]

[0030] In the formula, δ represents the smoothing parameter, represents the Gaussian kernel function.

[0031] Further, the initialization described in step 3 is performed and the fault-tolerant integrated navigation is performed to obtain the measurement value Z of the sensor used for the integrated navigation. k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k , specifically:

[0032] Get the measurement value Z according to the sensor used in the integrated navigation k , and calculate the multivariate cumulative sum statistic MC according to the formula k Used for fault detection, where k is the current time.

[0033] Further, the MC described in step 4 k>CL, proceed to step 5, otherwise proceed to step 6. Specifically:

[0034] According to the multivariate cumulative sum statistic MC k Compare the size with the calculated control limit CL. If the former is greater than the latter, a fault occurs and proceed to step 5 to identify and reduce the fault; otherwise, proceed to step 6 for conventional filtering.

[0035] Furthermore, in step 5, a weight matrix is ​​constructed based on the cumulative sum sequence recorded in step 1 to construct a fault degree function. Specifically:

[0036]

[0037] Where U k A typical correlation matrix k-time sequence, where v = 1,...,d v . and N = 1, ..., T + 1. The calculation of obtaining the typical correlation matrix U is as follows:

[0038]

[0039] In the formula, B v =[B1,…,B T ,B k ] represents the matrix used to calculate the correlation. Λ represents the diagonal matrix including r largest eigenvalues, Represents the regularization term.

[0040] The fault degree function is constructed according to the weight matrix, which is:

[0041]

[0042] Furthermore, the Kalman gain is reconstructed according to the fault degree in step 6, and the correction and filtering are performed to obtain the state matrix and the covariance matrix, which are specifically:

[0043]

[0044] In the formula, K k represents the Kalman gain, With P k Represent the obtained state matrix and covariance matrix respectively. XZ,k / k-1 and P ZZ,k / k-1 They represent the covariance matrix between state prediction and measurement prediction and the measurement prediction mean square error matrix, respectively, which are:

[0045]

[0046] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0047] 1) The use of multivariate cumulative and control chart technology is more sensitive to the detection of minor faults, and can more effectively judge faults, ensuring a lower false alarm rate and false alarm rate, thereby making the system's early warning more reliable and ensuring subsequent fault identification and mitigation.

[0048] 2) Through generalized typical correlation analysis for fault identification, different degrees of faults can be effectively adjusted. Considering the idea of ​​M estimation, different degrees of fault reduction according to the degree of fault identified by generalized typical analysis can effectively reduce the impact of faults on the system and ensure high-precision filtering. Ensure that the system has relatively good stability and robustness, while improving the reliability of fault-tolerant integrated navigation and ensuring the navigation accuracy of the carrier during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a fault-tolerant combined navigation method based on an improved multivariate cumulative sum control chart of the present invention;

[0050] Figure 2 is the multivariate cumulative sum control chart in Example 1;

[0051] Figure 3 is the fault degree diagram generated by the generalized typical analysis in Example 1;

[0052] Figure 4 is the positioning error of the conventional volumetric Kalman filter in Example 1;

[0053] Figure 5 is the positioning error of the present invention in Example 1.

[0054] Figure 6 is the running track of the sports car in Example 2

[0055] Figure 7 It is the multivariate cumulative sum control chart in Example 2

[0056] Figure 8 is the fault degree diagram generated by the generalized typical analysis in Example 2;

[0057] Fig. 9 is the positioning error of longitude under different methods in Example 2

[0058] Fig.10 is the positioning error of the dimension under different methods in Example 2

[0059] Fig.11 is the height positioning error of different methods in Example 2 DETAILED DESCRIPTION

[0060] The following will take the inertial / GPS fault-tolerant combined navigation as an example, and combine the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Example 1: Figure 1 As shown, a fault-tolerant combined navigation method based on an improved multivariate cumulative sum control chart comprises the following steps:

[0062] Step 1: Obtain the measurement values ​​of the sensors used for integrated navigation in a relatively stable environment without interference, construct and record the multivariate cumulative sum statistics based on the new information calculated in the cubature Kalman filter, and record the cumulative sum sequence.

[0063] Step 2: Repeat step 1 until the set deadline T, and then, according to the multivariate cumulative and statistical control limits CL calculated within time T,

[0064] Step 3: Initialize and perform fault-tolerant integrated navigation to obtain the measurement value Z of the sensor used for integrated navigation. k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k ,

[0065] Step 4: If the constructed MC k >CL, then proceed to step 5, otherwise proceed to step 6.

[0066] Step 5: Construct a weight matrix based on the cumulative sum sequence recorded in step 1 and construct a fault degree function.

[0067] Step 6: Reconstruct the Kalman gain according to the fault degree, correct and filter, obtain the state matrix and covariance matrix, complete the filtering process and then proceed to step 3.

[0068] The new information calculated in the integrated navigation and volumetric Kalman filtering described in step 1 constructs multivariate cumulative sum statistics and cumulative sum sequences, specifically:

[0069] The complex system model of the inertial / GPS fault-tolerant integrated navigation system is:

[0070] X k =F(X k-1 )+W k-1

[0071] Z k =H(X k )+V k

[0072] Where F(·) and H(·) are the nonlinear state and measurement transfer matrices, respectively, and X k is the state matrix, Z k is the measurement matrix, W k The mean is zero and the variance is Q k The process noise matrix, V k The mean is zero and the variance is R k In the inertial / GPS fault-tolerant integrated navigation, is a 15-dimensional matrix, v,p,∈, They represent attitude angle, velocity, position, gyroscope drift, and accelerometer bias error respectively, and the superscript represents the n / b coordinate system. is a 3D matrix, Indicates the current location information, and the subscript indicates the inertial / GPS information. In addition, Q k With R k The specific parameters of the GPS receiver can be set according to the inertial device used. In the embodiment, the parameters selected by the sensor are simulated as follows: the random constant drift of the gyroscope is 0.03° / h, and the random walk is The accelerometer has a random constant drift of 100 μg and a random walk of The receiver's position error is 1m. Therefore, R k =diag([1I 1×3 (m)]) 2 .

[0073] According to the model, the cubature Kalman filter is performed and its new information is calculated, specifically:

[0074]

[0075] Where P represents the error covariance matrix, the subscript k / k-1 represents one-step prediction, and L = 2n,ω i =1 / (2n), n represents the number of volume points, ξ i,K Represents a volume point set, specifically:

[0076]

[0077] In the formula, New information can be obtained through measurement and one-step prediction measurement, specifically:

[0078]

[0079] Next, we construct the multivariate cumulative sum statistic MC k Sum cumulative sum sequence B k , specifically:

[0080]

[0081] MC k =max{0,(B′ k ∑ -1 B k ) 1 / 2 -ml k}

[0082] Where m>0 can be set manually to control the growth rate of multivariate cumulative sum statistics, l1=1 and l k = l k-1 +1, when MC k-1 >0, then make l k =1.

[0083] The multivariate cumulative sum statistic control limits described in step 2 are:

[0084] CL=F(x) -1 (1-α)

[0085] Wherein, α represents the significance level, which is set to 0.05 in this embodiment, F(x) represents the cumulative distribution function, and its probability density function is, specifically:

[0086]

[0087] In the formula, δ represents the smoothing parameter, represents the Gaussian kernel function.

[0088] Initialize and perform fault-tolerant integrated navigation as described in step 3 to obtain the measurement value Z of the sensor used for integrated navigation k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k , specifically:

[0089] Get the measurement value Z according to the sensor used in the integrated navigation k , and calculate the multivariate cumulative sum statistic MC according to the formula mentioned k Used for fault detection, where k is the current time.

[0090] MC as described in step 4 k >CL, proceed to step 5, otherwise proceed to step 6. Specifically:

[0091] According to the multivariate cumulative sum statistic MC k Compare the size with the calculated control limit CL. If the former is greater than the latter, a fault occurs and proceed to step 5 to identify and reduce the fault; otherwise, proceed to step 6 for conventional filtering.

[0092] In this embodiment, CL=3.878, the total navigation time is 468s, and a minor fault is set in the height direction of the GPS from 350s onwards. The fault detection result is as follows: Figure 2 As shown, it can be observed that the multivariate cumulative sum control chart has reliable fault detection results.

[0093] In step 5, a weight matrix is ​​constructed based on the cumulative sum sequence recorded in step 1, and a fault degree function is constructed. Specifically:

[0094]

[0095] Where U k A typical correlation matrix k-time sequence, where v = 1,...,d v . and N=1,...,T+1. Get the typical correlation matrix U v The calculation is as follows:

[0096]

[0097] In the formula, B v =[B1,…,B T ,B k ] represents the matrix used to calculate the correlation. Λ represents the diagonal matrix including r largest eigenvalues, Represents the regularization term.

[0098] The fault degree function is constructed according to the weight matrix, which is:

[0099]

[0100] Depend on Figure 3 The fault degree results can be observed, and the fault degree in the height direction can be identified to be the highest, so as to reduce the fault.

[0101] The Kalman gain is reconstructed according to the fault degree in step 6, and the correction and filtering are performed to obtain the state matrix and the covariance matrix, which are specifically:

[0102]

[0103] In the formula, K k represents the Kalman gain, With P k Represent the obtained state matrix and covariance matrix respectively. XZ,k / k-1 and P ZZ,k / k-1 They represent the covariance matrix between state prediction and measurement prediction and the measurement prediction mean square error matrix, respectively, which are:

[0104]

[0105] Figure 4 and Figure 5 The filtering results are shown, and the method of the present invention shows excellent filtering results, ensuring high accuracy and high reliability of fault-tolerant integrated navigation. Compared with conventional cubature Kalman filtering, its performance is improved by 43%.

[0106] Example 2: This example uses actual sports car experimental data, the specific trajectory is as follows Figure 6 As shown, the five-pointed star in the figure indicates the starting point of the track, and the running process of the sports car eventually forms a closed track. This embodiment is different from the first embodiment in that a volumetric Kalman filter based on chi-square detection is further added for comparison, and actual data is provided to verify the beneficial effect.

[0107] In this example, the effectiveness and superiority of the proposed method are further verified. The volumetric Kalman filter and the Kalman filter based on chi-square detection are selected as comparative experiments. The sensors involved in the sports car experimental data used are STIM-300 and Novatel OEM 615, and the benchmark data is obtained by post-processing FOG-AHRS110 and RTK Tianbao BD992. The specific error parameters are shown in Table 1 below.

[0108]

[0109]

[0110] Figure 7 It represents the fault detection result. It can be identified from the figure that the fault is most serious between 100s to 200s and 500s to 600s. Figure 8 The fault identification results based on generalized canonical correlation analysis are presented. Figures 9 to 11 The error results of the volumetric Kalman filter, the volumetric Kalman filter based on chi-square detection and the present invention in longitude, latitude and altitude are respectively shown. It can be seen that the time when the large error occurs is consistent with the fault detection result. The high errors in longitude and latitude of the fault identification are also consistent with the error situation in the figure. In addition, the present invention has the highest filtering accuracy, and the table below shows the mean square error of each method. The filtering accuracy of the present invention is improved by 45% and 33% respectively compared with the volumetric Kalman filter and the volumetric Kalman filter based on chi-square detection.

[0111] method Longitude latitude high Cubic Kalman Filter 2.0456 2.0637 1.1471 Cubic Kalman Filter Based on Chi-Square Detection 2.0456 1.7701 0.9891 The present invention 1.3084 1.4510 0.8524

[0112] In summary, the present invention is based on the fault-tolerant integrated navigation method of improving the multivariate cumulative and control diagram, and utilizes the multivariate cumulative and control diagram to effectively monitor the faults that occur in the fault-tolerant integrated navigation system, thereby ensuring that the designed fault detection module is sensitive and robust. In addition, the degree of fault can be effectively analyzed through generalized canonical correlation analysis, ensuring that it can be effectively weakened and analyzed when dealing with faults of different degrees. Ultimately, high-precision, high-reliability filtering can be provided to ensure high-quality positioning and navigation services. In the present invention, inertial and GPS are used as examples to analyze and perform high-precision fault-tolerant integrated navigation. In addition, the fault-tolerant integrated navigation system framework of the present invention can be used by adding multiple sensors and designing suitable error models.

[0113] It should be noted that the above embodiments are not intended to limit the protection scope of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions all fall within the protection scope of the claims of the present invention.

Claims

1. A fault-tolerant integrated navigation method based on an improved multivariate cumulative sum control chart, characterized in that: The method comprises the following steps: Step 1: Obtain the measurement values ​​of the sensors used for integrated navigation in a relatively stable environment without interference, construct and record the multivariate cumulative sum statistics based on the new information calculated in the cubature Kalman filter, and record the cumulative sum sequence B. k , Step 2: Repeat step 1 until the set deadline T, and then, according to the multivariate cumulative and statistical control limits CL calculated within time T, Step 3: Initialize and perform fault-tolerant integrated navigation to obtain the measurement value Z of the sensor used for integrated navigation. k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k , Step 4: If the constructed MC k >CL, then proceed to step 5, otherwise proceed to step 6. Step 5: Construct a weight matrix based on the cumulative sum sequence recorded in step 1 and construct a fault degree function. Step 6: Reconstruct the Kalman gain according to the fault degree, correct and filter, obtain the state matrix and covariance matrix, complete the filtering process and then proceed to step 3.

2. The fault-tolerant integrated navigation method based on the improved multivariate cumulative sum control chart according to claim 1, characterized in that: In step 1, the new information calculated in the integrated navigation and volumetric Kalman filtering constructs multivariate cumulative sum statistics and cumulative sum sequences, specifically: Integrated navigation can be simplified into a nonlinear optimal filtering problem, and a complex system model can be constructed: X k =F(X k-1 )+W k-1 Z k =H(X k )+Vk Where F(·) and H(·) are the nonlinear state and measurement transfer matrices, respectively, and X k is the state matrix, Z k is the measurement matrix, W k The mean is zero and the variance is Q k The process noise matrix, V k The mean is zero and the variance is R k The measurement noise matrix is ​​used to perform volumetric Kalman filtering and calculate its new information according to the model, which is specifically: Where P represents the error covariance matrix, the subscript k / k-1 represents one-step prediction, and L = 2n, ω i =1 / (2n), n represents the number of volume points, ξ i，K Represents a volume point set, specifically: In the formula, k / k-1, the new information γ k It can be obtained through measurement and one-step prediction measurement, specifically: Next, we construct the multivariate cumulative sum statistic MC k Sum cumulative sum sequence B k , specifically: MC k =max{0,(B′ k ∑ -1 B k ) 1 / 2 -ml k } Where m>0 can be set manually to control the growth rate of multivariate cumulative sum statistics, l1=1 and l k = l k-1 +1, when MC k-1 > 0, then make l k =1.

3. The fault-tolerant integrated navigation method based on improved multivariate cumulative sum control chart according to claim 1, characterized in that: The multivariate cumulative sum statistic control limits described in step 2 are: CL=F(x) -1 (1-α) In the formula, α represents the significance level, F(x) represents the cumulative distribution function, and f(x) represents the probability density function, which is specifically: In the formula, δ represents the smoothing parameter, κ(·) represents the Gaussian kernel function, In the claim, k=1, ..., T, and the above steps are referred to as the first stage.

4. The fault-tolerant integrated navigation method based on improved multivariate cumulative sum control chart according to claim 1, characterized in that: In step 3, initialize and perform fault-tolerant integrated navigation to obtain the measurement value Z of the sensor used for integrated navigation. k , constructing the multivariate cumulative sum statistic MC based on the new information calculated in the cubature Kalman filter k , specifically: Get the measurement value Z according to the sensor used in the integrated navigation k , and calculate the multivariate cumulative sum statistic MC according to the formula k Used for fault detection, where k is the current time.

5. The fault-tolerant integrated navigation method based on improved multivariate cumulative sum control chart according to claim 1, characterized in that: MC as described in step 4 k >CL, then proceed to step 5, otherwise proceed to step 6, specifically: According to the multivariate cumulative sum statistic MC k Compare the size with the calculated control limit CL. If the former is greater than the latter, a fault has occurred, and proceed to step 5 to identify and reduce the fault; Otherwise, proceed to step 6 for conventional filtering.

6. The fault-tolerant integrated navigation method based on improved multivariate cumulative sum control chart according to claim 1, characterized in that: In step 5, a weight matrix is ​​constructed based on the cumulative sum sequence recorded in step 1, and a fault degree function is constructed, specifically: Where U k A typical correlation matrix k-time sequence, where v = 1, ..., d v . and N = 1, ..., T + 1, obtain the typical correlation matrix U v The calculation is as follows: In the formula, B v =[B1,…,B T , B k ] represents the matrix used to calculate the correlation, Λ represents the diagonal matrix including r largest eigenvalues, represents the regularization term, The fault degree function is constructed according to the weight matrix, which is:

7. The fault-tolerant integrated navigation method based on improved multivariate cumulative sum control chart according to claim 1, characterized in that: The Kalman gain is reconstructed according to the fault degree in step 6, and the correction and filtering are performed to obtain the state matrix and the covariance matrix, which are specifically: In the formula, K k represents the Kalman gain, With P k Represent the obtained state matrix and covariance matrix respectively, P XZ，k / k-1 and P ZZ，k / k-1 They represent the covariance matrix between state prediction and measurement prediction and the measurement prediction mean square error matrix, respectively, which are: Wherein, k represents the current moment of navigation, and the above steps are called the second stage.

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