Bayesian multi-model elliptic maneuvering group target tracking method based on GRU network

Abstract

The invention discloses a Bayesian multi-model elliptic maneuvering group target tracking method based on a GRU network, and relates to the technical field of target state estimation methods. The method comprises the following steps: S1, designing and training a neural network: based on a Pytorch development tool box, establishing a GRU neural network-based group target centroid motion sub-model probability estimation network, and based on a group target tracking data set, training the neural network; s2, modeling a Bayesian ellipse maneuvering group target tracking system; and S3, performing Bayesian multi-model maneuvering group target tracking based on neural network model probability estimation. According to the method, the measurement information value in the historical time window is fully grabbed through the GRU neural network, which is different from the previous method that only the current measurement value is utilized to carry out model probability estimation, and the precision is higher; and a measurement noise variance model in the group target tracking model is optimized, so that the measurement noise variance model better conforms to the actual situation, and the estimation precision is further optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of target state estimation methods, and in particular to a Bayesian multi-model elliptical maneuvering group target tracking method based on a GRU network. Background Art

[0002] With the rapid development of science and technology, the means of camouflage and stealth of formation group targets have been greatly strengthened, and sensors (radar, sonar, etc.) face huge challenges in tracking formation targets (such as aircraft formations, missiles, surface ship formations, and UUV, AUV formations). In the field of group target tracking, the relative spatial distance between targets is very small, and it is difficult or impossible for sensors to distinguish all targets. In addition, the motion states of each target are similar, resulting in overlapping of correlation gates during tracking, causing serious data association ambiguity. This difference in tracking objects requires us to examine the group target tracking problem from another perspective, that is, when the dense multi-targets that are difficult to distinguish do not meet the conditions for resolution, they are not resolved but tracked as a whole. After obtaining the overall motion state of the group, consider obtaining the approximate information of individual members in the group. On the other hand, due to the rapid development of science and technology, the mobility of formation group targets is becoming stronger and stronger, and the requirements for tracking algorithms are also getting higher and higher.

[0003] As a general mobile target tracking method, multi-model tracking technology can be applied to solve the problem of mobile group target tracking. However, due to the uncertainty of the number of formation targets and the influence of complex environmental clutter, it is more difficult to correct the probability of each sub-model through the posterior probability density function for group targets compared to particle targets. There are still great technical difficulties in directly applying multi-model tracking technology to mobile group target tracking. To this end, this method proposes a model probability estimation algorithm based on GRU neural network, and combines it with the improved multi-model tracking technology to propose a Bayesian multi-model elliptical mobile group target tracking method based on GRU network. Summary of the invention

[0004] The purpose of the present invention is to provide a Bayesian multi-model elliptical maneuvering group target tracking method to solve the maneuvering group target tracking problem.

[0005] The technical solution to achieve the purpose of the present invention is: a Bayesian multi-model elliptical maneuvering group target tracking method based on a GRU network, comprising the following steps:

[0006] Step S1, design and training of neural network: based on the Pytorch development toolbox, establish a probability estimation network of the group target centroid motion sub-model based on the GRU neural network, and train the neural network based on the group target tracking data set;

[0007] Step S2, Bayesian elliptical maneuvering group target tracking system modeling;

[0008] Step S3, Bayesian multi-model maneuvering group target tracking based on neural network model probability estimation.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) the GRU neural network is used to fully capture the value of the measurement information within the historical time window, which is different from the previous method of using only the current measurement value for model probability estimation, and has higher accuracy; (2) the method optimizes the measurement noise variance model in the group target tracking model to make it more in line with the actual situation and further optimize the estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 This is the structure diagram of the GRU neural network.

[0011] Figure 2 The flowchart for Bayesian multi-model elliptical maneuvering group target tracking settlement.

[0012] Figure 3 This is a curve diagram of the estimation accuracy of the center of mass state for group target tracking in a typical route.

[0013] Figure 4 This is a curve diagram of the estimation accuracy of the extended shape parameters for group target tracking in a typical route. DETAILED DESCRIPTION

[0014] The present invention proposes a Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network, which can solve the problem of accurate tracking of maneuvering group targets, and its positioning accuracy is significantly better than that of traditional multi-model maneuvering group target tracking methods.

[0015] A Bayesian multi-model elliptical maneuvering group target tracking method based on a GRU network comprises the following steps:

[0016] Step S1: Design and training of neural network:

[0017] Step S11: Based on the Pytorch development toolbox, a GRU neural network is designed. The designed neural network mainly includes two GRU neural network layers and one fully connected layer, wherein the state dimension of the hidden layer of the GRU neural network is 128. The input vector feature number is 8, the input vector length is 8, and the output is the probability of each sub-model.

[0018] Step S12: construct a mobile group target motion data set, in which the group target mass center motion model is uniform linear motion or uniform circular motion, the number of routes in the data set is 100,000, of which 50,000 are uniform linear motion routes and 50,000 are uniform circular motion routes. The group targets fly in formation with the mass center as the center, and the group target formation remains unchanged during the flight. The specific motion equation of the group target mass center is as follows:

[0019] 1) The equation of uniform linear motion is

[0020] x k+1 =F CV x k +B CV w k,CV (28)

[0021] in

[0022]

[0023] where x k is the motion state vector of the center of mass of the group target at time k, F CV is the uniform linear motion state transfer matrix, T is the sampling interval, B CV is the noise input weight matrix of uniform linear motion process, w k,CV is the noise vector of the uniform linear motion process at time k;

[0024] 2) The equation of uniform circular motion is

[0025] x k+1 =F CT x k +B CT w k,CT (30)

[0026] in

[0027]

[0028] where x k is the motion state vector of the center of mass of the group target at time k, F CT is the uniform circular motion state transfer matrix, T is the sampling interval, B CT is the noise input weight matrix of the uniform circular motion process, w k,CT is the noise vector of the uniform circular motion process at time k;

[0029] The initial motion state of the center of mass of the group target in each route data is where [x pos ,y pos ] T represents the centroid position of the group target, x pos ,y pos The value range is [-20000, -20000], which conforms to the uniform distribution. vel ,y vel ] T Represents the centroid velocity of the group target, with a value range of [-340,340], which conforms to the uniform distribution.

[0030] Step S13: GRU neural network training

[0031] Step S13a: The data set is randomly divided into a training set, a test set, and a validation set in a ratio of 8:1:1. The training set has 80,000 data items, and the test set and validation set have 10,000 data items each.

[0032] Step S13b: During training, for a piece of data in a training set, first extract the measurement data features to generate an input vector.

[0033] When the neural network input vector is generated, the input is of length N L The measured feature vector The single eigenvector is defined as follows

[0034]

[0035] in

[0036]

[0037] in is the first set of measurement data in the input time series, represents the rth measurement data in the k-time measurement set, represents the expectation of all data in the measurement set at time i, is a single feature generated by the measurement set corresponding to time i, and the sample label is the true probability of the current centroid motion model.

[0038] Step S13c: The training optimizer is selected as Adam, and the learning rate is set to 10 -3 , the epoch is set to 120, and every 2 epochs, the learning rate decreases by a multiplication factor of 0.5. Through training, the corresponding group target centroid motion model probability estimation GRU neural network model can be obtained.

[0039] Step S2: To facilitate the detailed description of the proposed method in the subsequent steps, the Bayesian elliptical maneuvering group target tracking system is modeled in this step. The specific process is: Step S21: Establish the group target center of mass motion equation and extended shape equation; Step S22: Establish the group target measurement model.

[0040] The specific process of establishing the group target center of mass motion equation and the extended shape equation in step S21 is as follows:

[0041] Step S211: The motion equation of the mass center of the group target is as follows:

[0042]

[0043] where x k is the motion state vector of the group target center of mass, is the state transfer matrix, Id is a d-dimensional unit matrix, where d is the spatial dimension; F k is the state transfer matrix in a single dimension; is the Kronecker product between matrices; D k is the process noise covariance coefficient matrix; X k is a parametric symmetric positive definite random matrix representing the shape of the ellipse;

[0044] Step S212: The group target extended shape equation is

[0045]

[0046] Where y represents the point vector on the contour of the group target ellipse. is the measurement matrix, X k is a parametric symmetric positive definite random matrix representing the shape of the ellipse; x k is the motion state vector of the center of mass of the group target at time k;

[0047] Extended shape parameter matrix X k The dynamic equation is:

[0048]

[0049] where δ k >d-1 is the degree of freedom parameter, matrix A k is the transfer matrix of the parameter matrix of the specific extended shape; W(Y; a, C) represents the symmetric positive definite random matrix Y satisfying the Wishart distribution with a degree of freedom and C parameter matrix.

[0050] The specific process of establishing a group target measurement model in step S22 is as follows:

[0051] Assume that the set of group target measurement values ​​at time k is n k is the total number of measurements at time k; the measurement equation is

[0052]

[0053] in H k is the measurement matrix in one-dimensional space, is the rth measurement vector at time k, is Gaussian white noise, indicating measurement noise, satisfying Among them B k is the process noise input matrix, X k is a parametric symmetric positive definite random matrix representing the shape of an ellipse, R k is the sensor measurement variance matrix.

[0054] Step S3: Bayesian multi-model maneuvering group target tracking based on neural network model probability estimation. The specific process is: Step S31: Setting the initial state of the tracking method; Step S32: Performing filtering operations to calculate key parameters representing the state estimation of the maneuvering extended group target.

[0055] The initial state setting of the tracking method in step S31 is as follows: at time k=0, the initial state of the tracking method is set

[0056]

[0057] in is the initialization parameter, is the initialization parameter of the i-th sub-model.

[0058] Step S2 calculates the key parameters for the state estimation of the maneuverable extended group target. The specific process is: k = 1, 2, ... T s At this moment, the following steps are executed cyclically, T s is the total filtering time;

[0059] a) reinitializing the uniform linear motion sub-model filter and the uniform circular motion sub-model filter based on the moment matching method;

[0060] Group target centroid state reinitialization:

[0061]

[0062] Where N r is the number of sub-filters, is the state estimate of the i-th sub-filter at time k-1 about the centroid of the group target, is the switching probability from model j to model i at time k, p m,n ,q l,h To calculate the intermediate parameters, is the state estimation covariance matrix of the ith subfilter at time k-1 about the center of mass of the group target, d is the dimension of the target motion state, is the parameter matrix of the i-th sub-filter at time k-1 regarding the group target shape contour estimation, is the covariance matrix for multi-model interaction centroid estimation, is the k-1 moment dimension related optimization parameter, It is the intermediate calculation variable of the distribution parameter matrix of the i-th sub-filter at time k-1 about the group target shape contour estimation parameter matrix;

[0063] Group target extended shape parameters reinitialization:

[0064]

[0065] in is the distribution parameter matrix of the i-th sub-filter about the group target shape contour estimation parameter at time k-1, is the parameter matrix of the i-th sub-filter at time k-1 regarding the group target shape contour estimation, is k-1 moment N r The weighted expectation of the parameter matrix of the model about the group target shape contour estimation, is the expectation of the parameter matrix of the j-th sub-filter at time k-1 about the group target contour estimation, is k-1 moment N r The weighted expectation of the cross-covariance of the model's parameter matrix estimates about the group target shape profile, To calculate the intermediate parameter matrix;

[0066] b) Perform the time update step in the Bayesian estimation in each sub-filter. The specific steps and related formulas are as follows:

[0067] Group target centroid time update steps:

[0068] From the group center of mass motion equation, we can get the group center of mass motion state x k The predicted probability density function is:

[0069]

[0070] where p[·|·] represents the conditional probability density function, represents a Gaussian distribution with expectation a and variance A. k-1 is the cumulative measurement set from time 0 to time k-1, It is calculated by the following formula;

[0071] The group target center of mass motion state time update:

[0072]

[0073] in is the group target centroid state transfer matrix corresponding to the sub-filter. Correspondingly, the state estimation prediction covariance matrix is:

[0074]

[0075] in is the process noise variance corresponding to the sub-filter;

[0076] For the extended shape time update part, the extended shape parameter matrix prediction probability density function is:

[0077]

[0078] in is the generalized type II Beta distribution function, δ k is the preset parameter, A k is the group target profile transformation matrix at time k, where the relevant parameter calculation formula is as follows:

[0079] Extended shape parameter matrix time update:

[0080]

[0081] Where d is the target motion dimension, λ k-1 Intermediate calculation variables.

[0082]

[0083] c) Perform the measurement update step in the Bayesian estimation in each sub-filter. The specific steps and related formulas are as follows:

[0084] The probability density function of the center of mass motion state measurement update is:

[0085]

[0086] in And other related parameter matrices are calculated by the following formula:

[0087]

[0088] Among them B k is the noise shape weighting matrix, n k is the number of measurements at time k, is the expected measurement at time k;

[0089] The extended state measurement update probability density function is:

[0090]

[0091] Where IW(·) is the inverse Wishart distribution function, and the calculation formula of related parameters is as follows:

[0092]

[0093] in is the intermediate calculation matrix, All of them can be calculated from the above.

[0094] d) The GRU neural network calculates the probability of the current group target center of mass motion mode. The specific steps are as follows:

[0095] The GRU neural network input vector I is calculated by formula (33) k, input the trained GRU neural network, and then obtain the output vector is the probability of each sub-model;

[0096] e) Based on the probabilities of each sub-filter obtained in step d), the outputs of each sub-filter are fused, and a final fused estimate is obtained based on moment matching;

[0097] Group target centroid state fusion estimation:

[0098]

[0099] Fusion estimation of group target extended shape parameters:

[0100]

[0101] in and is the estimated value of the state of the group target center of mass at time k, is the weight coefficient of sub-model j at time k, is the estimated value of the state of sub-model j at time k about the centroid of the group target, P k|k is the state estimation covariance matrix about the center of mass of the group target at time k, p i,j ,q l,h is the intermediate variable, s is the dimension of the state vector of each dimension, d is the dimension of the target motion, is the cross-covariance weighting matrix for group target centroid estimation, is the estimated error covariance matrix of sub-model j at time k about the centroid of the group target, is the k-time dimension-related optimization parameter, It is the intermediate calculation variable of the distribution parameters of the parameter matrix of the group target shape profile estimation at time k. is the distribution parameter matrix of the estimated parameter matrix of the group target shape contour at time k, is the parameter matrix for estimating the contour of the group target at time k, N is the kth moment r The weighted expectation of the parameter matrix of the model about the group target shape contour estimation, is the expectation of the parameter matrix of the j-th sub-filter at time k about the group target contour estimation, N is the kth moment r The weighted expectation of the cross-covariance of the model's parameter matrix estimates about the group target shape profile, To calculate the intermediate parameter matrix; get the key parameters representing the state estimation of the maneuvering extended group target at time k

[0102] Example

[0103] In this experimental scenario, the group of targets moves in formation at 300 sampling moments, alternating between uniform linear motion and uniform turning motion in 5 time periods. The sampling time T in uniform turning motion and uniform linear motion is 1.0s. The process noise is Gaussian white noise with a mean of 0 and a variance of 4, and the measurement noise is Gaussian white noise with a mean of 0 and a variance of 3. The initial state of the target motion is x0=[x pos ,y pos ,x vel ,y vel ] T =[100,200,-50,60] T Tracking the real trajectory of group targets and the measurement set Figure 1 shown.

[0104] Set the group target tracking sub-model information as follows:

[0105] Model 1: CV motion model;

[0106] Model 2: CT motion model;

[0107] The method proposed in the present invention estimates the above group target as follows: Figure 2 As shown. Figure 2 It can be concluded that the method proposed in this paper can achieve accurate tracking of the center and contour of the maneuvering group target.

[0108] To further illustrate the superiority of the GRU neural network proposed in this paper in the calculation of sub-model probabilities in group target tracking, the model probability given by the GRU network is compared with the model probability given by the classic interactive multi-model algorithm, as shown in Figure 2. Figure 3 As shown. Figure 3 It can be clearly concluded that the GRU network proposed in the present invention is more accurate in estimating the probability of the model motion model, which lays a good foundation for the subsequent more accurate estimation of the motion trajectory and morphology of the group targets.

[0109] The root mean square error RMSE of the group target motion center position estimation and velocity estimation is as follows: Figure 4 shown. Figure 4 Where GRU-EGTT represents the mobile group target tracking method proposed by the present invention, and IMM represents the classic interactive multi-model mobile group target tracking method. Figure 4 It can be seen that the method proposed in the present invention has better estimation errors for the center position and motion speed of the group targets than the classic IMM method, and has higher tracking accuracy.

Claims

1. A Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network, characterized in that: The following steps are involved: Step S1, design and training of neural network: based on the Pytorch development toolbox, establish a probability estimation network of the group target centroid motion sub-model based on the GRU neural network, and train the neural network based on the group target tracking data set; Step S2, Bayesian elliptical maneuvering group target tracking system modeling; Step S3, Bayesian multi-model maneuvering group target tracking based on neural network model probability estimation.

2. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 1 is characterized in that: The specific process of the above step S1 is: Step S11: Based on the Pytorch development toolbox, a GRU neural network is designed, wherein the GRU neural network includes two GRU neural network layers and one fully connected layer, wherein the state dimension of the GRU neural network layer is 128; the input vector feature number is 8, the input vector length is 8, and the output is the probability of each sub-model; Step S12: constructing a motion data set of maneuverable group targets, in which the mass center motion model of the group targets is uniform linear motion or uniform circular motion, the number of routes in the data set is 100,000, of which 50,000 are uniform linear motion routes and 50,000 are uniform circular motion routes. The group targets fly in formation with the mass center as the center, and the group target formation remains unchanged during the flight; Step S13: GRU neural network training Step S13a: randomly divide the data set into a training set, a test set, and a validation set in a ratio of 8:1:1; the training set has 80,000 data items, and the test set and validation set have 10,000 data items each; Step S13b: During training, for a piece of data in a training set, first extract the measurement data features to generate an input vector; Step S13c: The training optimizer is selected as Adam, and the learning rate is set to 10 -3 , the epoch is set to 120, and every 2 epochs, the learning rate decreases by a multiplication factor of 0.5; through training, the corresponding group target center of mass motion model probability estimation GRU neural network model is obtained.

3. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 2 is characterized in that: When constructing the mobile group target motion data set in the above step S12, the group target centroid motion model is specifically: 1) The equation of uniform linear motion is x k+1 =F CV x k +B CV w k,CV (28) in where x k is the motion state vector of the center of mass of the group target at time k, F CV is the uniform linear motion state transfer matrix, T is the sampling interval, B CV is the noise input weight matrix of uniform linear motion process, w k,CV is the noise vector of the uniform linear motion process at time k; 2) The equation of uniform circular motion is x k+1 =F CT x k +B CT w k,CT (30) in where x k is the motion state vector of the center of mass of the group target at time k, F CT is the uniform circular motion state transfer matrix, T is the sampling interval, B CT is the noise input weight matrix of the uniform circular motion process, w k,CT is the noise vector of the uniform circular motion process at time k; The initial motion state of the center of mass of the group target in each route data is: where [x pos ,y pos ] T represents the centroid position of the group target, x pos ,y pos The value range is [-20000, -20000], which conforms to the uniform distribution. vel ,y vel ] T Represents the centroid velocity of the group target, with a value range of [-340,340], which conforms to the uniform distribution.

4. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 2 is characterized in that: When the above neural network input vector is generated, the input is of length N L The measured feature vector The single eigenvector is defined as follows in in is the first set of measurement data in the input time series, represents the rth measurement data in the k-time measurement set, represents the expectation of all data in the measurement set at time i, is a single feature generated by the measurement set corresponding to time i, and the sample label is the true probability of the current centroid motion model.

5. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 1 is characterized in that: The specific process of the above step S2 is: Step S21: Establishing the group target center of mass motion equation and extended shape equation; Step S22: Establishing a group target measurement model.

6. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 5 is characterized in that: The specific process of establishing the group target center of mass motion equation and the extended shape equation in step S21 is as follows: Step S211: The motion equation of the mass center of the group target is as follows: where x k is the motion state vector of the group target center of mass, is the state transfer matrix, I d is a d-dimensional unit matrix, where d is the spatial dimension; F k is the state transfer matrix in a single dimension; is the Kronecker product between matrices; D k is the process noise covariance coefficient matrix; X k is a parametric symmetric positive definite random matrix representing the shape of the ellipse; Step S212: The group target extended shape equation is: Where y represents the point vector on the contour of the group target ellipse. is the measurement matrix, X k is a parametric symmetric positive definite random matrix representing the shape of the ellipse; x k is the motion state vector of the center of mass of the group target at time k; Extended shape parameter matrix X k The dynamic equation is: where δ k >d-1 is the degree of freedom parameter, matrix A k is the transfer matrix of the parameter matrix of the specific extended shape; W(Y; a, C) represents the symmetric positive definite random matrix Y satisfying the Wishart distribution with a degree of freedom and C parameter matrix.

7. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 5 is characterized in that: The specific process of establishing the group target measurement model in step S22 is as follows: Assume that the set of group target measurement values ​​at time k is n k is the total number of measurements at time k; the measurement equation is in H k is the measurement matrix in one-dimensional space, is the rth measurement vector at time k, is Gaussian white noise, indicating measurement noise, satisfying Among them B k is the process noise input matrix, X k is a parametric symmetric positive definite random matrix representing the shape of an ellipse, R k is the sensor measurement variance matrix.

8. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 1 is characterized in that: The specific process of the above step S3 is: Step S31: Setting the initial state of the tracking method; Step S32: Execute filtering operation to calculate key parameters characterizing the maneuverable extended group target state estimation.

9. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 8 is characterized in that: The initial state setting of the tracking method in step S31 is as follows: at time k=0, the initial state of the tracking method is set in is the initialization parameter, is the initialization parameter of the i-th sub-model.

10. The Bayesian multi-model elliptical maneuvering group target tracking method based on GRU network according to claim 8, characterized in that: The calculation in step S2 above obtains the key parameters for the state estimation of the maneuverable extended group target. The specific process is: k = 1, 2, ... T s At this moment, the following steps are executed cyclically, T s is the total filtering time; a) reinitializing the uniform linear motion sub-model filter and the uniform circular motion sub-model filter based on the moment matching method; Group target centroid state reinitialization: Where N r is the number of sub-filters, is the state estimate of the i-th sub-filter at time k-1 about the centroid of the group target, is the switching probability from model j to model i at time k, p m,n ,q l,h To calculate the intermediate parameters, is the state estimation covariance matrix of the ith subfilter at time k-1 about the center of mass of the group target, d is the dimension of the target motion state, is the parameter matrix of the i-th sub-filter at time k-1 regarding the group target shape contour estimation, is the covariance matrix for multi-model interaction centroid estimation, is the k-1 moment dimension related optimization parameter, It is the intermediate calculation variable of the distribution parameter matrix of the i-th sub-filter at time k-1 about the group target shape contour estimation parameter matrix; Group target extended shape parameters reinitialization: in is the distribution parameter matrix of the i-th sub-filter about the group target shape contour estimation parameter at time k-1, is the parameter matrix of the i-th sub-filter at time k-1 regarding the group target shape contour estimation, is k-1 moment N r The weighted expectation of the parameter matrix of the model about the group target shape contour estimation, is the expectation of the parameter matrix of the j-th sub-filter at time k-1 about the group target contour estimation, is k-1 moment N r The weighted expectation of the cross-covariance of the model's parameter matrix estimates about the group target shape profile, To calculate the intermediate parameter matrix; b) Perform the time update step in the Bayesian estimation in each sub-filter. The specific steps and related formulas are as follows: Group target centroid time update steps: From the group center of mass motion equation, we can get the group center of mass motion state x k The predicted probability density function is: where p[·|·] represents the conditional probability density function, Expressing expectation Gaussian distribution with variance A. Z k-1 is the cumulative measurement set from time 0 to time k-1, It is calculated by the following formula; The group target center of mass motion state time update: in is the group target centroid state transfer matrix corresponding to the sub-filter. Correspondingly, the state estimation prediction covariance matrix is: in is the process noise variance corresponding to the sub-filter; For the extended shape time update part, the extended shape parameter matrix prediction probability density function is: in is the generalized type II Beta distribution function, δ k is the preset parameter, A k is the group target profile transformation matrix at time k, where the relevant parameter calculation formula is as follows: Extended shape parameter matrix time update: Where d is the target motion dimension, λ k-1 Intermediate calculation variables. c) Perform the measurement update step in the Bayesian estimation in each sub-filter. The specific steps and related formulas are as follows: The probability density function of the center of mass motion state measurement update is: in And other related parameter matrices are calculated by the following formula: Among them B k is the noise shape weighting matrix, n k is the number of measurements at time k, is the expected measurement at time k; The extended state measurement update probability density function is: Where IW(·) is the inverse Wishart distribution function, and the calculation formula of related parameters is as follows: in is the intermediate calculation matrix, All of them can be calculated from the above. d) The GRU neural network calculates the probability of the current group target center of mass motion mode. The specific steps are as follows: The GRU neural network input vector I is calculated by formula (33) k , input the trained GRU neural network, and then obtain the output vector is the probability of each sub-model; e) Based on the probabilities of each sub-filter obtained in step d), the outputs of each sub-filter are fused, and a final fused estimate is obtained based on moment matching; Group target centroid state fusion estimation: Fusion estimation of group target extended shape parameters: in and is the estimated value of the state of the group target center of mass at time k, is the weight coefficient of sub-model j at time k, is the estimated value of the state of sub-model j at time k about the centroid of the group target, P k|k is the state estimation covariance matrix about the center of mass of the group target at time k, p i,j ,q l,h is the intermediate variable, s is the dimension of the state vector of each dimension, d is the dimension of the target motion, is the cross-covariance weighting matrix for group target centroid estimation, is the estimated error covariance matrix of sub-model j at time k about the centroid of the group target, is the k-time dimension-related optimization parameter, It is the intermediate calculation variable of the distribution parameters of the parameter matrix of the group target shape profile estimation at time k. is the distribution parameter matrix of the estimated parameter matrix of the group target shape contour at time k, is the parameter matrix for estimating the contour of the group target at time k, N is the kth moment r The weighted expectation of the parameter matrix of the model about the group target shape contour estimation, is the expectation of the parameter matrix of the j-th sub-filter at time k about the group target contour estimation, N is the kth moment r The weighted expectation of the cross-covariance of the model's parameter matrix estimates about the group target shape profile, To calculate the intermediate parameter matrix; The key parameters characterizing the state estimation of the maneuvering extended group target at time k are obtained

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