A Fuzzy Correction Filtering Method Based on Innovation Sequence

Abstract

The present invention provides a fuzzy correction filtering method based on an innovation sequence, comprising: obtaining a filtered innovation sequence, calculating a Mahalanobis distance of the filtered innovation sequence; setting a starting threshold, a robust correction boundary and an adaptive correction boundary; setting a robust correction membership function, an adaptive correction membership function and a fuzzy correction criterion; performing corresponding fuzzy correction on the filter; setting a robust factor to perform robust correction on the filter; setting an adaptive correction factor to perform adaptive correction on the filter; setting an adaptive correction factor and a robust factor to perform robust adaptive correction on the filter; the fuzzy correction filtering method based on an innovation sequence provided by the present invention can take into account both the robustness and adaptability of the filter and improve the performance of the filtering algorithm.

Description

Technical Field

[0001] The present invention relates to the field of filtering, and in particular to a fuzzy correction filtering method based on an innovation sequence. Background Art

[0002] Traditional filtering algorithms are susceptible to interference from state mutations, unknown measurement noise, etc., which can lead to a decrease in algorithm accuracy and even cause the filtering algorithm to diverge in severe cases. There are two main types of filtering correction methods. For state mutations, adaptive filtering algorithms can track the actual changes in the system state in a timely manner and improve the adaptability of filtering.

[0003] For unknown measurement noise, robust filtering can effectively suppress the influence of noise and enhance the stability and anti-interference ability of filtering. However, in many practical application environments, the filtering algorithm is not only affected by state mutation, but also by complex environmental interference such as unknown measurement noise. Any single filtering correction method cannot solve this problem. Summary of the invention

[0004] Therefore, in view of the fact that the commonly used filtering algorithms in the prior art are still difficult to correct under complex interference conditions, the present invention provides a fuzzy correction filtering method based on new information sequences, which can take into account both filtering robustness and adaptability and improve the performance of the filtering algorithm.

[0005] In order to achieve the above object, the technical solution proposed by the present invention is:

[0006] A fuzzy correction filtering method based on an innovation sequence, wherein the innovation sequence includes a residual sequence between a measurement information value and a measurement prediction value obtained by a filtering measurement equation, and the filtering method includes the following steps:

[0007] S1: Obtain a filtered new information sequence according to the measurement information value and the measurement prediction value obtained by the filter measurement equation, and calculate the Mahalanobis distance of the filtered new information sequence;

[0008] S2: According to the hypothesis testing principle and the Mahalanobis distance of the filtered new information sequence, the 2 The characteristics of the distribution are used to set the fuzzy correction starting threshold, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary;

[0009] S3: setting a robust correction membership function and an adaptive correction membership function respectively according to the Mahalanobis distance of the filtered innovation sequence, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary;

[0010] S4: According to the hypothesis testing principle, compare the Mahalanobis distance of the filtered new information sequence with the fuzzy correction starting threshold;

[0011] When the Mahalanobis distance of the filtered new information sequence is less than or equal to the fuzzy correction starting threshold, no fuzzy correction is performed;

[0012] When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold, fuzzy correction is performed according to the robust correction membership function and the adaptive correction membership function;

[0013] S5: Compare the Mahalanobis distance of the filtered new information sequence, the fuzzy correction starting threshold, the second robust correction boundary and the adaptive correction boundary;

[0014] When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold and less than the second robust correction boundary, the filtering is robustly corrected by adjusting the filter measurement noise covariance matrix by setting a robust factor according to the Mahalanobis distance of the filtered new information sequence and the robust correction membership function;

[0015] When the Mahalanobis distance of the filter innovation sequence is greater than the adaptive correction boundary, the filter is adaptively corrected by setting the adaptive correction factor to adjust the filter state prediction error covariance matrix according to the Mahalanobis distance of the filter innovation sequence and the adaptive correction membership function;

[0016] When the Mahalanobis distance of the filtered new information sequence is greater than the second robust correction boundary and less than the adaptive correction boundary, a robust adaptive correction is performed, wherein the robust adaptive correction includes correcting the filtered measurement noise covariance matrix according to the robust factor and the membership of the robust correction membership function; and correcting the filtered state prediction error covariance matrix according to the adaptive factor and the membership of the adaptive correction membership function.

[0017] Furthermore, the calculation formula for calculating the Mahalanobis distance of the filtered new information sequence is shown in formula (1):

[0018]

[0019] In formula (1), P ηk is the covariance of the new information sequence at the kth moment, η k The residual between the measured value predicted by the measurement equation at the kth moment and the measurement information is used to obtain the filtered new information sequence. The calculation formula is shown in formula (2):

[0020]

[0021] In formula (2), z k represents the measurement information value at the kth moment, Represents the measurement prediction value obtained according to the filtered measurement equation at the kth moment.

[0022] Furthermore, the calculation formulas of the robust modified membership function and the adaptive modified membership function are shown in formula (3) and formula (4) respectively:

[0023]

[0024]

[0025] In formula (3) and formula (4), b s represents the starting threshold of blur correction, b r1 represents the first robust correction boundary, b r2 represents the second robust correction boundary, b a Represents the adaptive correction boundary.

[0026] Among them, b s is 2 The upper quantile of the distribution, b s The value of χ 2 The upper quantile table of the distribution is determined, b r1 、b r2 、b s are all arbitrary real numbers, and n represents the state dimension of the system.

[0027] Robust modified membership function f r is a double trapezoidal membership function, and the adaptive modified membership function f a It is a semi-parabolic membership function.

[0028] Furthermore, the calculation process of the filtering measurement noise covariance matrix is ​​shown in formula (5):

[0029]

[0030] In formula (5), represents the robustly corrected filtered measurement noise covariance matrix, f r represents the membership of the robust modified membership function, μ k is the robust factor at the kth moment, R k represents the filtered measurement noise covariance matrix at the kth moment.

[0031] Furthermore, the calculation process of the filter state prediction error covariance matrix is ​​shown in formula (6):

[0032]

[0033] In formula (6), represents the filter state prediction error covariance matrix after adaptive correction, f a represents the membership of the adaptive modified membership function, λ krepresents the adaptive factor at the kth moment, Φ k-1 represents the system state matrix at the k-1th moment, P k-1 represents the state error covariance matrix at time k-1, Q k represents the system noise covariance matrix at the kth moment.

[0034] Furthermore, the calculation process of the robust factor is shown in formula (7):

[0035]

[0036] In formula (7), μ k (i) represents the robust factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after robust correction, represents the covariance of the new information sequence after robust correction;

[0037] Where Z k represents the measurement matrix at the kth moment, P k / k-1 represents the filter state prediction error covariance matrix at the kth moment;

[0038] The initial value of the iteration of the robust factor is 1, and the iteration termination condition is shown in formula (8):

[0039]

[0040] Furthermore, the calculation process of the adaptive factor is shown in formula (9):

[0041]

[0042] In formula (9), λ k (i) represents the adaptive factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after adaptive correction, represents the covariance of the new information sequence after adaptive correction;

[0043] in

[0044] The initial value of the iteration of the adaptive factor is 1, and the iteration termination condition is shown in formula (10):

[0045]

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The fuzzy correction filtering method based on the new information sequence proposed in the present invention not only takes into account the correction when the filtering system is interfered by measurement noise or model inaccuracy when setting the fuzzy correction criterion, but also takes into account the correction when the two occur at the same time. This method can take into account both the robustness and adaptability of the filtering and improve the performance of the filtering algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is an overall flow chart of the fuzzy correction filtering method based on the new information sequence described in the present invention;

[0049] Figure 2 It is the execution diagram based on new information judgment and fuzzy correction described in the present invention;

[0050] Figure 3 This is a simulation test diagram of the volumetric Kalman filter algorithm in the present invention;

[0051] Figure 4 This is the blur correction effect diagram of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with 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 in the invention, all other embodiments obtained by ordinary technicians in this field without creative work, any modifications, equivalent substitutions, improvements, etc., should be included in the protection scope of the present invention.

[0053] A fuzzy correction filtering method based on an innovation sequence, wherein the innovation sequence includes a residual sequence between a measurement information value and a measurement prediction value obtained by a filtering measurement equation, such as Figure 1 As shown, the filtering method comprises the following steps:

[0054] S1: Obtain a filtered new information sequence according to the measurement information value and the measurement prediction value obtained by the filter measurement equation, and calculate the Mahalanobis distance of the filtered new information sequence;

[0055] S2: According to the hypothesis testing principle and the Mahalanobis distance of the filtered new information sequence, the 2 The characteristics of the distribution are used to set the fuzzy correction starting threshold, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary;

[0056] S3: setting a robust correction membership function and an adaptive correction membership function respectively according to the Mahalanobis distance of the filtered innovation sequence, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary;

[0057] S4: Figure 2As shown, according to the hypothesis testing principle, the Mahalanobis distance of the filtered new information sequence is compared with the fuzzy correction starting threshold;

[0058] When the Mahalanobis distance of the filtered new information sequence is less than or equal to the fuzzy correction starting threshold, no fuzzy correction is performed;

[0059] When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold, fuzzy correction is performed according to the robust correction membership function and the adaptive correction membership function;

[0060] S5: Figure 2 As shown, the Mahalanobis distance of the filter innovation sequence, the fuzzy correction starting threshold, the second robust correction boundary and the adaptive correction boundary are compared;

[0061] When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold and less than the second robust correction boundary, the filtering is robustly corrected by adjusting the filter measurement noise covariance matrix by setting a robust factor according to the Mahalanobis distance of the filtered new information sequence and the robust correction membership function;

[0062] When the Mahalanobis distance of the filter innovation sequence is greater than the adaptive correction boundary, the filter is adaptively corrected by setting the adaptive correction factor to adjust the filter state prediction error covariance matrix according to the Mahalanobis distance of the filter innovation sequence and the adaptive correction membership function;

[0063] When the Mahalanobis distance of the filtered new information sequence is greater than the second robust correction boundary and less than the adaptive correction boundary, a robust adaptive correction is performed, wherein the robust adaptive correction includes correcting the filtered measurement noise covariance matrix according to the robust factor and the membership of the robust correction membership function; and correcting the filtered state prediction error covariance matrix according to the adaptive factor and the membership of the adaptive correction membership function.

[0064] The calculation formula for calculating the Mahalanobis distance of the filtered new information sequence is shown in formula (1):

[0065]

[0066] In formula (1), is the covariance of the new information sequence at the kth moment, η k The residual between the measured value predicted by the measurement equation at the kth moment and the measurement information is used to obtain the filtered new information sequence. The calculation formula is shown in formula (2):

[0067]

[0068] In formula (2), z k represents the measurement information value at the kth moment, Represents the measurement prediction value obtained according to the filtered measurement equation at the kth moment.

[0069] The calculation formulas of the robust modified membership function and the adaptive modified membership function are shown in formula (3) and formula (4) respectively:

[0070]

[0071]

[0072] In formula (3) and formula (4), b s represents the starting threshold of blur correction, b r1 represents the first robust correction boundary, b r2 represents the second robust correction boundary, b a Represents the adaptive correction boundary.

[0073] Among them, b s is 2 The upper quantile of the distribution, b s The value of χ 2 The upper quantile table of the distribution is determined, b r1 、b r2 、b s are all arbitrary real numbers, and n represents the state dimension of the system.

[0074] Robust modified membership function f r is a double trapezoidal membership function, and the adaptive modified membership function f a It is a semi-parabolic membership function.

[0075] The calculation process of the filtering measurement noise covariance matrix is ​​shown in formula (5):

[0076]

[0077] In formula (5), represents the robustly corrected filtered measurement noise covariance matrix, f r represents the membership of the robust modified membership function, μ k is the robust factor at the kth moment, R k represents the filtered measurement noise covariance matrix at the kth moment.

[0078] The calculation process of the filter state prediction error covariance matrix is ​​shown in formula (6):

[0079]

[0080] In formula (6), represents the filter state prediction error covariance matrix after adaptive correction, f arepresents the membership of the adaptive modified membership function, λ k represents the adaptive factor at the kth moment, Φ k-1 represents the system state matrix at the k-1th moment, P k-1 represents the state error covariance matrix at time k-1, Q k represents the system noise covariance matrix at the kth moment.

[0081] The calculation process of the robust factor is shown in formula (7):

[0082]

[0083] In formula (7), μ k (i) represents the robust factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after robust correction, represents the covariance of the new information sequence after robust correction;

[0084] Where Z k represents the measurement matrix at the kth moment, P k / k-1 represents the filter state prediction error covariance matrix at the kth moment;

[0085] The initial value of the iteration of the robust factor is 1, and the iteration termination condition is shown in formula (8):

[0086]

[0087] The calculation process of the adaptive factor is shown in formula (9):

[0088]

[0089] In formula (9), λ k (i) represents the adaptive factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after adaptive correction, represents the covariance of the new information sequence after adaptive correction;

[0090] in

[0091] The initial value of the iteration of the adaptive factor is 1, and the iteration termination condition is shown in formula (10):

[0092]

[0093] The present invention adopts Matlab_2018a software and conducts a correction simulation test with the volumetric Kalman filter algorithm as the object. The state equation and measurement equation of the volumetric Kalman filter algorithm are shown in formula (11);

[0094]

[0095] In formula (11), k represents the number of filtering iterations, rand(4,1) represents a four-dimensional vector, each element in the vector is (0,1), x represents a four-dimensional filtering state vector, and the initial value is x(0) = [0 0 0 0], Φ represents the system state matrix, which is a fourth-order matrix with the main diagonal elements being 1 and the remaining elements being 0.01, Z represents the fourth-order identity matrix, and Q represents the system noise covariance matrix, Q = 10 -4 Z, R represents the measurement noise covariance matrix, R = 10 -1 ·Z.

[0096] The parameter settings of the present invention are shown in Table 1;

[0097] Table 1 Parameter settings

[0098]

[0099] Assume that the measurement dimension n = 4 and select the fuzzy correction starting threshold By checking 2 The upper quantile table of the distribution is available: According to χ 2 Test principle, the new information sequence obeys χ 2 The probability that the Mahalanobis distance of the new information sequence is within the initial correction boundary is 99%, and the probability that it exceeds the initial correction boundary is 1%. Therefore, as shown in Table 1, the fuzzy correction starting threshold is set.

[0100] When the system state does not change and is subject to a small range of disturbance, robust correction is performed, so the robust correction boundary b r1 and b r2 Set to and e.b s ; When the system state changes, the new information sequence will change to a large extent, so the boundary b will be adaptively modified a Set to e 2 b s , where e is a natural constant.

[0101] like Figure 3 As shown in Figure 1, it describes the impact of non-Gaussian noise on the simulation system when it runs in different environments and occasions. It can be seen that the measurement noise doubles exponentially from the 40th iteration and then remains unchanged.

[0102] like Figure 3 As shown, when the iteration reaches the 40th and 41st times, a positive step signal with a strength of 50 is applied to the system state, when the iteration reaches the 80th and 81st times, a reverse step signal with a strength of 150 is applied to the system state, and when the iteration reaches the 120th to 125th times, a reverse signal with a strength of 20 is continuously applied to the system. It can be seen that when the state of the simulation system undergoes a discontinuous jump, the model value deviates from the actual value, resulting in model inaccuracy.

[0103] like Figure 4 As shown in the figure, the correction results of the filtering in the simulation system under the above interference are described. It can be seen that when it is only affected by noise and no jump occurs, robust correction can be performed to weaken the influence of measurement noise; when the system state jumps, reasonable adaptive correction can be made to accurately track the system state and improve the adaptability of the filtering algorithm.

[0104] By adopting the fuzzy correction filtering method based on the new information sequence provided by the present invention, the filtering estimation value can effectively track the actual situation of the system and has good stability, which can effectively improve the filtering performance.

Claims

1. A fuzzy correction filtering method based on an innovation sequence, characterized in that: The innovation sequence includes a residual sequence between a measurement information value and a measurement prediction value obtained by filtering the measurement equation, and the filtering method includes the following steps: S1: Obtain a filtered new information sequence according to the measurement information value and the measurement prediction value obtained by the filter measurement equation, and calculate the Mahalanobis distance of the filtered new information sequence; S2: According to the hypothesis testing principle and the Mahalanobis distance of the filtered new information sequence, the 2 The characteristics of the distribution are used to set the fuzzy correction starting threshold, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary; S3: setting a robust correction membership function and an adaptive correction membership function respectively according to the Mahalanobis distance of the filtered innovation sequence, the first robust correction boundary, the second robust correction boundary and the adaptive correction boundary; S4: According to the hypothesis testing principle, compare the Mahalanobis distance of the filtered new information sequence with the fuzzy correction starting threshold; When the Mahalanobis distance of the filtered new information sequence is less than or equal to the fuzzy correction starting threshold, no fuzzy correction is performed; When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold, fuzzy correction is performed according to the robust correction membership function and the adaptive correction membership function; S5: Compare the Mahalanobis distance of the filtered new information sequence, the fuzzy correction starting threshold, the second robust correction boundary and the adaptive correction boundary; When the Mahalanobis distance of the filtered new information sequence is greater than the fuzzy correction starting threshold and less than the second robust correction boundary, the filtering is robustly corrected by adjusting the filter measurement noise covariance matrix by setting a robust factor according to the Mahalanobis distance of the filtered new information sequence and the robust correction membership function; When the Mahalanobis distance of the filter innovation sequence is greater than the adaptive correction boundary, the filter is adaptively corrected by setting the adaptive correction factor to adjust the filter state prediction error covariance matrix according to the Mahalanobis distance of the filter innovation sequence and the adaptive correction membership function; When the Mahalanobis distance of the filtered new information sequence is greater than the second robust correction boundary and less than the adaptive correction boundary, performing robust adaptive correction, the robust adaptive correction comprising correcting the filtered measurement noise covariance matrix according to the robust factor and the membership of the robust correction membership function; According to the adaptive factor, the filter state prediction error covariance matrix is ​​modified according to the membership of the adaptive modified membership function.

2. The fuzzy correction filtering method based on the innovation sequence according to claim 1 is characterized in that: The calculation formula for calculating the Mahalanobis distance of the filtered new information sequence is shown in formula (1): In formula (1), is the covariance of the new information sequence at the kth moment, η k The residual between the measured value predicted by the measurement equation at the kth moment and the measurement information is used to obtain the filtered new information sequence. The calculation formula is shown in formula (2): In formula (2), z k represents the measurement information value at the kth moment, Represents the measurement prediction value obtained according to the filtered measurement equation at the kth moment.

3. The fuzzy correction filtering method based on the innovation sequence according to claim 2 is characterized in that: The calculation formulas of the robust modified membership function and the adaptive modified membership function are shown in formula (3) and formula (4) respectively: In formula (3) and formula (4), b s represents the starting threshold of blur correction, b r1 represents the first robust correction boundary, b r2 represents the second robust correction boundary, b a represents the adaptive correction boundary, and n represents the measurement dimension.

4. The fuzzy correction filtering method based on the innovation sequence according to claim 3 is characterized in that: The calculation process of the filtering measurement noise covariance matrix is ​​shown in formula (5): In formula (5), represents the robustly corrected filtered measurement noise covariance matrix, f r represents the membership of the robust modified membership function, μ k is the robust factor at the current moment, R k represents the filtered measurement noise covariance matrix at the kth moment.

5. The fuzzy correction filtering method based on the innovation sequence according to claim 4 is characterized in that: The calculation process of the filter state prediction error covariance matrix is ​​shown in formula (6): In formula (6), represents the filter state prediction error covariance matrix after adaptive correction, f a represents the membership of the adaptive modified membership function, λ k represents the adaptive factor at the kth moment, Φ k-1 represents the system state matrix at the k-1th moment, P k-1 represents the state error covariance matrix at time k-1, Q k represents the system noise covariance matrix at the kth moment.

6. The fuzzy correction filtering method based on the innovation sequence according to claim 5 is characterized in that: The calculation process of the robust factor is shown in formula (7): In formula (7), μ k (i) represents the robust factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after robust correction, represents the covariance of the new information sequence after robust correction; Where Z k represents the measurement matrix at the kth moment, P k / k-1 represents the filter state prediction error covariance matrix at the kth moment; The initial value of the iteration of the robust factor is 1, and the iteration termination condition is shown in formula (8):

7. The fuzzy correction filtering method based on the innovation sequence according to claim 6 is characterized in that: The calculation process of the adaptive factor is shown in formula (9): In formula (9), λ k (i) represents the adaptive factor at the i-th iteration at the k-th time, represents the Mahalanobis distance of the new information sequence after adaptive correction, represents the covariance of the new information sequence after adaptive correction; in The initial value of the iteration of the adaptive factor is 1, and the iteration termination condition is shown in formula (10):

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