Maneuvering Target Tracking Method Based on Variational Bayesian Multiple Model Particle Filter

Abstract

The present invention discloses a maneuvering target tracking method based on variational Bayesian multi-model particle filtering. Aiming at the problems that the multi-model particle filtering algorithm depends on the transition probability matrix and randomly discriminates the model state of particles, the model state and the transition probability matrix are priori modeled by introducing the multinomial distribution and the Dirichlet distribution respectively. Under the variational Bayesian framework, the target state, the model state and the transition probability matrix are jointly optimized by the coordinate ascent method to improve the target tracking accuracy. Compared with the existing multi-model filtering algorithms, the present invention directly selects the conjugate prior distributions of the model state and the transition probability matrix, and decouples the joint distribution of the target state, the model state and the transition probability under the variational Bayesian framework to obtain the target state estimation result. The maneuvering target tracking method based on variational Bayesian multi-model particle filtering has certain scientific value and practical engineering significance for the enrichment and development of the theory and technology of moving target tracking.

Description

Technical Field

[0001] The present invention belongs to the technical field of information processing, and particularly relates to a maneuvering target tracking method based on variational Bayesian multi-model particle filtering. Background Technique

[0002] Target tracking is a method that utilizes the motion target information obtained by detection means such as radar, sonar, and infrared, and estimates and tracks the motion state of the target, such as position, velocity, acceleration, etc. Usually, the target motion model is obtained in the Cartesian coordinate system, and the measured distance, azimuth angle, etc. of the target are obtained in the polar coordinate system. Therefore, the problem of nonlinear estimation cannot be avoided in engineering implementation. In addition, with the development of technology, the maneuvering ability of the target is increasing day by day, and the structure and parameters of the target motion mode change greatly. In this case, the single-model algorithm is difficult to meet the requirements of tracking speed and accuracy, while the multi-model algorithm can avoid the inaccuracy of the model caused by target maneuvering when using the single-model algorithm, improve the tracking performance of maneuvering targets, and thus achieve accurate tracking of highly maneuvering targets.

[0003] The particle filter algorithm realizes recursive Bayesian filtering through a non-parametric Monte Carlo simulation method, and is applicable to any nonlinear system that can be described by a state space model, and its accuracy approaches the optimal estimate. In addition, for the problem of maneuvering targets, the multi-model particle filter algorithm combined with the particle filter algorithm and the multi-model algorithm can achieve good results. However, the multi-model particle filter algorithm relies on the transition probability matrix to randomly determine the model state of the particles. Therefore, the number of particles in each model is proportional to the model probability, and randomly determining the model state of the particles will result in inaccurate approximation of the particle selection model and the posterior distribution of the target true state, leading to a decrease in target tracking accuracy. In addition, the multi-model particle filter algorithm is highly dependent on the transition probability matrix. When the information of the transition probability matrix is inaccurate or unknown, the ability of the multi-model particle filter algorithm to distinguish the model state of the particles will be weakened, and even misjudgment phenomena will occur, resulting in a sharp decrease in target tracking accuracy. Summary of the Invention

[0004] The purpose of the present invention is to provide a maneuvering target tracking method based on variational Bayesian multi-model particle filtering, which can effectively improve the target tracking accuracy in the scenario of maneuvering targets.

[0005] The technical solution adopted by the present invention is as follows: To achieve the above object, the specific steps are as follows:

[0006] S1: For the target motion model and measurement model, and set the initial state probability density function p(x0) according to the prior information and the state evolution model, where x0 represents the initial state value; based on the initial state probability density function p(x0), randomly generate N initial particles, and N is a value that measures the computational amount and estimation accuracy.

[0007] The specific steps of S1 are as follows:

[0008] S1.1 Preset the state model and measurement model of the target as follows:

[0009] x k = f k-1 (x k-1 , r k ) + w k (r k )

[0010] y k = h k (x k , r k ) + v k

[0011] Wherein, and respectively represent the state and measurement information of the target at time k, n x and n y are the dimensions of x k and y k respectively, n x > n y , and respectively represent the vector spaces of the state and measurement; f(·) and h(·) represent the state transition function and measurement transition function, r k ∈{1,..., M} represents the unknown model index of the system at time k, and M is the total number of models; w k and v k respectively represent the process noise and measurement noise of the discrete system, and w k and v k both follow Gaussian distributions with zero mean and covariances Q k (r k ) and R k respectively;

[0012] S1.2 Assume that the switching of the moving target system model follows a Markov chain, and the specific processes of Bayesian prediction and update of its target state estimation are as follows:

[0013] Prediction:

[0014]

[0015] Where p(x k , r k = j|Y 1:k-1 ) represents the prior distribution of the target state when the current model is selected as j, and Y 1:k-1 represents the set of measurements from the initial time to time k - 1;

[0016] Update:

[0017]

[0018] where \(p(y k |x k ,r k =j)\) represents the likelihood function, which is determined by the measurement equation. Since the measurement value is independent of \(r\) after obtaining the state prediction value, so \(p(y k |x k ,r k =j)=p(y k |x k |x k ). \(p(x k ,r k =j|Y 1:k )\) represents the posterior distribution of the target state when the current model is selected as \(j\), and \(Y 1:k \) represents the set of measurements from the initial time to time \(k\);

[0019] S2: Model the model state using the multinomial distribution. Considering that the true model state is unknown, at time \(k\), expand the latent variable \(r\) of the particle model state k , and define where M is the maximum number of models, is determined by the categorical distribution, so it can be represented by the multinomial distribution:

[0020]

[0021] where represents probability, and satisfies \(\delta(\cdot)\) represents the Dirac function;

[0022] S3: Model the transition probability matrix using the Dirichlet distribution. When the model transition probability matrix \(\Pi k is unknown, assume that each row is independent of each other

[0023]

[0024]

[0025]

[0026] where \(\pi k,ij represents the element of the transition probability matrix, and p(\Pi k ) represents the probability distribution of \(\Pi k , and use the Dirichlet distribution for \(\Pi kPerform prior modeling

[0027]

[0028] where α k,iM is the parameter of the distribution, C(α k,i ) is the normalization constant, Dir(π k,i ; α k,i ) represents the Dirichlet distribution of the Π k row vector; thus

[0029]

[0030] where represents the α k power of the ij-th element of Π k,ij , represents the product from j = 1 to j = M for .

[0031] S4: Based on the measurement set Y k , establish the evidence lower bound function in the variational Bayesian framework, and solve for the model state, transition probability matrix, and target state;

[0032] The specific steps of S4 are as follows:

[0033] S4.1 Use the variational distributions q(x k ), q(r k ), q(Π k ) to approximate the joint distribution of the target state posterior distribution p(x k |Y 1:k ), the model state distribution p(r k |Y 1:k ), and the transition probability matrix distribution p(Π k |Y 1:k ):

[0034] q(x k )q(r k )q(Π k ) ≈ p(x k , r k , Π k |Y 1:k )

[0035] S4.2 Judge the approximation degree by comparing the KL divergence between the variational distribution and the true distribution

[0036]

[0037] where represents q(x k )q(rk )q(Π k ) and p(x k , r k , Π k |Y 1:k ) of the KL divergence, where q(x k ) represents the variational distribution of the target state, q(r k ) represents the variational distribution of the model state, q(Π k ) represents the variational distribution of the transition probability matrix, and p(x k , r k , Π k |Y 1:k ) represents the joint distribution of the target state, model state, and model transition probability;

[0038] S4.3 Rewrite the KL divergence between q(x k )q(r k )q(Π k ) and p(x k , r k , Π k |Y 1:k ) as:

[0039]

[0040] where is defined as the evidence lower bound (ELBO)

[0041]

[0042] Since the recursive likelihood p(y k |Y 1:k-1 ) is independent of the state and can be regarded as a constant. Therefore, minimizing the KL divergence is the same as maximizing the evidence lower bound;

[0043] S4.4 Optimize each variational distribution based on the current information of other variational distributions. For ease of solution, solve for all available information from the joint distribution p(y k , x k , r k , Π k |Y 1:k-1 )

[0044] p(y k , x k , r k , Π k |Y 1:k-1 ) = p(y k |x k , r k )p(x k |Y 1:k-1)p(r k , Π k |Y 1:k-1 )p(Π k |Y 1:k-1 )

[0045] where p(y k |x k , r k ) represents the likelihood function, p(x k |Y 1:k-1 ) represents the prior distribution of the target state, p(r k , Π k |Y 1:k ) represents the joint distribution of the model state and the transition probability matrix, p(Π k |Y 1:k-1 ) represents the transition probability matrix distribution;

[0046] S4.5 Solve the variational distribution q(Π k ) of the transition probability matrix by the coordinate ascent method:

[0047]

[0048] where denotes taking the expectation with respect to · about r k and x k , and c and c1 represent normalization constants; Since the model state update is related to the transition probability matrix, the joint distribution of the model state and the transition probability matrix is written as:

[0049]

[0050] where ∝ denotes proportional to; In the conjugate distribution, for a single particle, the above formula can be written as:

[0051]

[0052] where denotes the probability that the nth particle predicts the current model state to be m; denotes the likelihood function when the current model state is m; denotes the innovation covariance when the current model state is m; After normalization, the posterior distribution form is

[0053] p(r k , Π k |Y 1:k ) = Mul(r k |μ k|k )

[0054] where Mul(r k |μ k|k)The polynomial distribution representing the model state, μ k|k ∝ μ k|k-1 · Λ(y k ), Λ(y k ) = [Λ1(y k ), Λ2(y k ),..., Λ M (y k )] represents all model likelihood functions, μ k|k-1 represents the probability prediction of all particle model states at time k, μ k|k represents the probability of all particle model states at time k; thus

[0055]

[0056] where π k-1|k-1,ij represents the value of the ij-th element of Π k-1 at time k - 1, represents the probability that the current model state of the n-th particle at time k is j;

[0057] S4.6 Solve the variational distribution q(x k ) of the target state by the coordinate ascent method:

[0058]

[0059] where represents taking the expectation of · with respect to r k and Π k , c and c2 represent normalization constants, thus

[0060] q(x k ) = p(x k | r k , Π k , Y 1:k )

[0061] The solved variational distribution is the approximately obtained posterior probability distribution of the target state, and the target estimated state value is solved by the method of weighted averaging.

[0062] The beneficial effects of the present invention are as follows: Through the above technical solutions, the present invention proposes a maneuvering target tracking method based on variational Bayesian multi-model particle filtering for existing problems.

[0063] Firstly, use variational Bayesian inference and the polynomial distribution and Dirichlet distribution to construct the variational distributions of the model state and the transition probability matrix respectively;

[0064] Secondly, based on the joint distribution constructed by the measurement set, model state, transition probability matrix and target state, use the coordinate ascent method according to the mean field theory to obtain the variational distribution approaching the true distribution;

[0065] Finally, the variational distribution is introduced into the variational Bayesian framework to obtain the approximate posterior distribution of the target state. By more accurately partitioning the state of the particle model and estimating the state transition probability matrix in real time, the target tracking accuracy is improved. Description of the Drawings

[0066] Figure 1 is the flowchart of the method of the present invention;

[0067] Figure 2 is the position RMSE curve graph in the simulation experiment of the present invention;

[0068] Figure 3 is the velocity RMSE curve graph in the simulation experiment of the present invention;

[0069] Figure 4 is the schematic diagram of the CV model probability comparison in the simulation experiment of the present invention;

[0070] Figure 5 is the schematic diagram of the CT model probability comparison in the simulation experiment of the present invention;

[0071] Figure 6 is the position ARMSE graph of each algorithm with different TPMs in the simulation experiment of the present invention;

[0072] Figure 7 is the velocity ARMSE graph of each algorithm with different TPMs in the simulation experiment of the present invention. Detailed Embodiment

[0073] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0074] As Figure 1 shown, the present invention includes the following steps:

[0075] S1: For the target motion model and measurement model, and set the initial state probability density function p(x0) according to the prior information and state evolution model, where x0 represents the initial state value; based on the initial state probability density function p(x0), randomly generate N initial particles, and N is a value for measuring the computational amount and estimation accuracy.

[0076] S2: Model the model state using the polynomial distribution. Considering that the true model state is unknown, expand the hidden variable r of the particle model state at time k k in dimension, and define where M is the maximum number of models, Determined by the categorical distribution, so it can be represented by a multinomial distribution:

[0077]

[0078] where represents the probability of, and satisfies δ(·) represents the Dirac function;

[0079] S3: Model the transition probability matrix using the Dirichlet distribution. When the model transition probability matrix Π k is unknown, assume that each row is independent of each other

[0080]

[0081]

[0082]

[0083] where π k,ij represents the elements of the transition probability matrix, and p(Π k ) represents the probability distribution of Π k , and use the Dirichlet distribution to perform prior modeling on Π k

[0084]

[0085] where α k,iM is the parameter of the distribution, C(α k,i ) is the normalization constant, Dir(π k,i ; α k,i ) represents the Dirichlet distribution of the row vectors of Π k ; thus

[0086]

[0087] where represents the α k th power of the ij-th element of Π k,ij , represents the product from j = 1 to j = M of .

[0088] S4: Based on the measurement set Y k , establish the evidence lower bound function in the variational Bayesian framework, and solve for the model state, transition probability matrix, and target state;

[0089] The specific steps of the said S1 include the following:

[0090] S1.1 Preset the target state model and measurement model as follows:

[0091] x k = f k-1 (x k-1 , r k ) + w k (r k )

[0092] y k = h k (x k , r k ) + v k

[0093] Wherein, and respectively represent the state and measurement information of the target at time k, n x and n y are the dimensions of x k and y k respectively, n x > n y , and respectively represent the vector spaces of the state and measurement; f(·) and h(·) represent the state transition function and measurement transition function, r k ∈ {1,..., M} represents the unknown model index of the system at time k, and M is the total number of models; w k and v k respectively represent the process noise and measurement noise of the discrete system, and w k and v k both follow Gaussian distributions with zero mean and covariances Q k (r k ) and R k respectively;

[0094] S1.2 Assume that the system model switching follows a Markov chain. The specific process of the nonlinear Bayesian filtering is as follows:

[0095] Prediction:

[0096]

[0097] where p(x k , r k = j|Y 1:k-1 ) represents the prior distribution of the target state when the current model is selected as j, and Y 1:k-1 represents the set of measurements from the initial time to time k - 1;

[0098] Update:

[0099]

[0100] where p(y k |x k ,r k = j) represents the likelihood function, which is determined by the measurement equation. Since the measurement value is independent of r after obtaining the state prediction value, so p(y k |x k ,r k ,r k = j) = p(y k |x k ). p(x k ,r k = j|Y 1:k ) represents the posterior distribution of the target state when the current model is selected as j, and Y 1:k represents the set of measurements from the initial time to time k;

[0101] The specific steps of S4 are as follows:

[0102] S4.1 Use the variational distributions q(x k ), q(r k ), q(Π k ) to approximate the joint distribution of the target state distribution p(x k |Y 1:k ), the model state distribution p(r k |Y 1:k ) and the transition probability matrix distribution p(Π k |Y 1:k ):

[0103] q(x k )q(r k )q(Π k ) ≈ p(x k ,r k ,Π k |Y 1:k )

[0104] S4.2 Determine the approximation degree by comparing the KL divergence between the variational distribution and the true distribution

[0105]

[0106] where represents the KL divergence between q(x k )q(r k )q(Π k ) and p(x k ,r k ,Π k |Y 1:k ), q(x k) represents the variational distribution of the target state, q(r k ) represents the variational distribution of the model state, q(Π k ) represents the variational distribution of the transition probability matrix, p(x k ,r k ,Π k |Y 1:k ) represents the joint distribution of the target state, the model state, and the model transition probability;

[0107] S4.3 Rewrite the KL divergence between q(x k )q(r k )q(Π k ) and p(x k ,r k ,Π k |Y 1:k ) as follows:

[0108]

[0109] where is defined as the evidence lower bound (ELBO)

[0110]

[0111] Since the recursive likelihood p(y k |Y 1:k-1 ) is independent of the state, it can be regarded as a constant. Therefore, minimizing the KL divergence is the same as maximizing the evidence lower bound;

[0112] S4.4 Each variational distribution is optimized based on the current information of other variational distributions. For ease of solution, solve for all available information from the joint distribution p(y k ,x k ,r k ,Π k |Y 1:k-1 )

[0113] p(y k ,x k ,r k ,Π k |Y 1:k-1 ) = p(y k |x k ,r k )p(x k |Y 1:k-1 )p(r k ,Π k |Y 1:k-1 )p(Π k |Y 1:k-1 )

[0114] where p(yk |x k ,r k ) represents the likelihood function, p(x k |Y 1:k-1 ) represents the prior distribution of the target state, p(r k ,Π k |Y 1:k ) represents the joint distribution of the model state and the transition probability matrix, p(Π k |Y 1:k-1 ) represents the distribution of the transition probability matrix;

[0115] S4.5 solves the variational distribution q(Π k ) of the transition probability matrix by the coordinate ascent method:

[0116]

[0117] where represents taking the expectation with respect to · over r k and x k ; c and c1 represent normalization constants; since the model state update is related to the transition probability matrix, the joint distribution of the model state and the transition probability matrix is written as:

[0118]

[0119] where ∝ means proportional to; in the conjugate distribution, for a single particle the above equation can be written as:

[0120]

[0121] where represents the probability that the nth particle predicts the current model state to be m; represents the likelihood function of the current model state being m; represents the innovation covariance of the current model state being m; after normalization, the posterior distribution form is

[0122] p(r k ,Π k |Y 1:k ) = Mul(r k |μ k|k )

[0123] where Mul(r k |μ k|k ) represents the multinomial distribution of the model state, μ k|k ∝ μ k|k-1 · Λ(y k ), Λ(y k ) = [Λ1(y k), Λ2(y k ),..., Λ M (y k )] represents all model likelihood functions, μ k|k-1 represents the predicted probability of the state of all particle models at time k, μ k|k represents the probability of the state of all particle models at time k; thus

[0124]

[0125] where π k-1|k-1,ij represents the value of the ij-th element of Π k-1 at time k - 1, represents the probability that the current model state of the n-th particle at time k is j;

[0126] S4.6 Solve the variational distribution q(x k ) of the target state by the coordinate ascent method:

[0127]

[0128] where represents taking the expectation with respect to · over r k and Π k and c and c2 represent normalization constants, so

[0129] q(x k ) = p(x k |r k , Π k , Y 1:k )

[0130] The solved variational distribution is the posterior probability distribution of the target state, and the target estimated state value is solved by the method of weighted mean.

[0131] The effects of the present invention can be further illustrated by the following experimental simulations:

[0132] 1. Simulation conditions and parameters

[0133] Consider a maneuvering target tracking model in the Cartesian two-dimensional coordinate system plane. The system state a1(k) and b1(k) respectively represent the position components of the target in the X-axis and Y-axis directions, and a2(k) and b2(k) are its velocity components; the state transition matrix of the constant velocity (CV) model and the state transition matrix of the constant turn (CT) model The measurement transfer matrix h k (x k ): where the process noise variance is and q1 = 0.04, q2 = 0.08, The measurement noise variance is The sampling interval T = 1 s; the initial state is x0 = [10 km, 0.3 km / s, 15 km, 0.1 km / s] T , and the movement starts at 1 s and ends at 80 s. The target performs CV movement from time 1 to 20 s, CT movement with a turning rate of ω k-1 = 8° from time 21 to 50 s, and CV movement from time 51 to 80 s. Set the TPM as: where t = 0.9, which is the initial setting of TPM. The simulation results are as follows:

[0134] 1) Figure 2 and Figure 3 are the comparisons of RMSE in position and velocity between the variational Bayesian multi-model particle filter (VBMMPF) that uses the multi-model particle filter as the kernel and jointly estimates the target state, model state, and transition probability matrix using the variational Bayesian method, and IMMUKF, IMMCKF, IMMPF, and MMPF. It can be seen from the figure that VBMMPF has the lowest RMSE curve.

[0135] 2) Figure 4 and Figure 5 give the determination results of each algorithm for the true model. It can be seen from the figure that each algorithm has a certain ability to judge the true model, but VBMMPF has the strongest ability to judge the true model, which is reflected in the fact that the VBMMPF curve is the closest to the true curve. It proves that the estimation of the model state by VBMMPF is relatively accurate.

[0136] 3) Figure 6 and Figure 7 are the comparisons of ARMSE in position and velocity of each algorithm under different model transition probabilities. It can be seen from the figure that whether in position or velocity, the ARMSE index of VBMMPF is lower than that of other algorithms. Moreover, with the change of TPM, the ARMSE indexes of other algorithms all change to a certain extent, but VBMMPF can always remain stable, proving that the estimation of the model transition probability matrix by VBMMPF is accurate.

[0137] The beneficial effects of the present invention are as follows: Through the above technical solutions, the present invention proposes a maneuvering target tracking method based on the variational Bayesian multi-model particle filter for existing problems.

[0138] First, use variational Bayesian inference and the polynomial distribution and Dirichlet distribution to construct the variational distributions of the model state and the transition probability matrix respectively;

[0139] Secondly, the joint distribution constructed based on the measurement set, model state, transition probability matrix, and target state uses the mean field theory and the coordinate ascent method to obtain a variational distribution that approximates the true distribution.

[0140] Finally, the variational distribution is introduced into the variational Bayesian framework to obtain an approximate posterior distribution of the target state. By more precisely partitioning the particle model state and estimating the state transition probability matrix in real time, the target tracking accuracy can be improved.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A maneuvering target tracking method based on variational Bayesian multi-model particle filter, characterized in that: It includes the following steps: S1: For the target motion model and measurement model, set the initial state probability density function p(x0) according to the prior information and state evolution model, where x0 represents the initial state value; based on the initial state probability density function p(x0), randomly generate N initial particles, and N is a value for measuring the computational amount and estimation accuracy; S2: Model the model state using a multinomial distribution. Considering that the true model state is unknown, at time k, expand the dimensionality of the particle model state latent variable r and define k where M is the maximum number of models, determined by the categorical distribution, so it can be represented by a multinomial distribution: ​ wherein represents probability, and satisfies δ(·) represents the Dirac function; S3: Model the transition probability matrix using the Dirichlet distribution. When the model transition probability matrix Π k is unknown and assuming independence between each row, then: where π k,ij represents the elements of the transition probability matrix, and p(Π k ) represents the probability distribution of Π k , and the prior modeling of Π k is performed using the Dirichlet distribution where α k,iM is the parameter of the distribution, C(α k,i ) is the normalization constant, Dir(π k,i ; α k,i ) represents the Dirichlet distribution of the Π k row vector; thus Among them represents Π k the α-th power of the ij-th element k,ij power, represents the cumulative multiplication of from j = 1 to j = M; S4: According to the measurement set Y k , establish a lower bound of evidence function in the variational Bayesian framework, and solve for the model state, transition probability matrix, and target state.

2. The maneuvering target tracking method based on variational Bayesian multi-model particle filtering according to claim 1, characterized in that: The specific steps of S1 are as follows: S1.1 Preset the state model and measurement model of the target as follows: x k = f k-1 (x k-1 , r k ) + w k (r k ) y k = h k (x k , r k ) + v k Among them, and represent the state and measurement information of the system at time k, respectively. n x and n y are the dimensions of x k and y k respectively, and n x > n y . and represent the state and measurement vector spaces respectively, f(·) and h(·) represent the state transition function and measurement transition function, and r k ∈{1,...,M} represents the unknown model index of the system at time k, and M is the total number of models; w k and v k represent the process noise and measurement noise of the discrete system respectively. Both w k and v k follow Gaussian distributions with zero mean and covariances Q k (r k ) and R k respectively; S1.2 Assume that the switching of the motion target system model follows a Markov chain, and the specific processes of Bayesian prediction and update of its target state estimation are as follows: Prediction: where p(x k , r k = j|Y 1:k-1 ) represents the prior distribution of the target state when the current model is selected as j, and Y 1:k-1 represents the set of measurements from the initial time to time k-1; Update: where \(p(y\) k |x k , r k = j) represents the likelihood function, which is determined by the measurement equation; since after obtaining the state prediction value, the measurement value is independent of r k , so \(p(y\) k |x k , r k = j) = \(p(y\) k |x k ); \(p(x\) k , r k = j|Y 1:k ) represents the posterior distribution of the target state when the current model is selected as j, and Y 1:k represents the set of measurements from the initial time to time k.

3. The maneuvering target tracking method based on variational Bayesian multi-model particle filtering according to claim 1, characterized in that: The specific steps of S4 are as follows: S4.1 Use variational distributions q(x k ), q(r k ), q(Π k ) to approximate the joint distribution of the target state distribution p(x k |Y 1:k ), the model state distribution p(r k |Y 1:k ), and the transition probability matrix distribution p(Π k |Y 1:k ) S4.2 Judge the approximation degree by comparing the KL divergence between the variational distribution and the true distribution; S4.3 Due to the non-negativity of the KL divergence, the minimization of the KL divergence can be transformed into the problem of maximizing the evidence lower bound; S4.4 Each variational distribution is optimized based on the current information of other variational distributions. For the convenience of solution, all available information is obtained by solving the joint distribution p(y k , x k , r k , Π k |Y 1:k-1 ) p(y k ,x k ,r k ,Π k |Y 1:k-1 ) = p(y k |x k ,r k )p(x k |Y 1:k-1 )p(r k |Y 1:k-1 )p(Π k |Y 1:k-1 ) where p(y k |x k ,r k ) represents the likelihood function, p(x k |Y 1:k-1 ) represents the prior distribution of the target state, p(r k ,Π k |Y 1:k ) represents the joint distribution of the model state and the transition probability matrix, p(Π k |Y 1:k-1 ) represents the transition probability matrix distribution; S4.5 Solve the variational distribution \(q(\Pi\) k ) of the transition probability matrix by the coordinate ascent method: where denotes the expectation with respect to r k and x k and c and c1 denote normalization constants; S4.6 Solve the variational distribution q(x k ) of the target state by the coordinate ascent method: where denotes the expectation with respect to r k and Π k and c and c2 denote normalization constants.

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