A variational bayes-based interactive multi-model target tracking method and system

Abstract

The application discloses an interactive multi-model target tracking method and system based on a variational Bayes, and relates to the field of target tracking.The method comprises the following steps: establishing a target tracking model of a tracked target; the target tracking model comprises a target kinematics model and a measurement model; using multiple filters to perform state estimation on the tracked target according to corresponding target kinematics models; and fusing state estimation results of each filter based on a variational Bayes method to obtain final state estimation of the tracked target.The application improves target tracking precision and solves the problem that a traditional multi-model simplifies estimation results of multiple filters into a single Gaussian distribution, thereby losing estimation precision.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and in particular to an interactive multi-model target tracking method and system based on variational Bayes. Background Technology

[0002] In the field of mobile target tracking, the most common tracking filtering method is Kalman filtering, which uses various sensors to acquire measurement data related to the target's state, thereby estimating the target's state. It has wide applications in military, autonomous driving, and traffic control.

[0003] In tracking filters, a single-model filtering structure is typically used to track targets, assuming that there is only one motion model for the target. However, when tracking maneuvering targets, due to the diverse and constantly changing motion patterns, a single model alone cannot guarantee continuous and stable tracking. To address this issue, multi-model methods are commonly used for tracking maneuvering targets, with the interactive multi-model method being the most common. This method establishes multiple sub-filters based on different target kinematic models and interacts the estimation results of each sub-filter at input and output to achieve effective tracking of maneuvering targets. However, traditional multi-model methods simplify the mixture Gaussian distribution of the estimation results from multiple filters into a single Gaussian distribution when fusing the estimation results of each sub-filter to obtain the final state estimate of the target. This operation results in a loss of estimation accuracy. Therefore, how to fully utilize the estimation results of multiple sub-filters to achieve accurate estimation of the state of maneuvering targets is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] Therefore, the purpose of this invention is to provide an interactive multi-model target tracking method and system based on variational Bayesian, which solves the problem that traditional multi-model methods simplify the estimation results of multiple filters into a single Gaussian distribution, resulting in a loss of estimation accuracy.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] An interactive multi-model target tracking method based on variational Bayes, comprising:

[0007] Establish a target tracking model for the tracked target; the target tracking model includes a target kinematics model and a measurement model;

[0008] Multiple filters are used to estimate the state of the tracked target based on the corresponding target kinematic model;

[0009] The state estimation results of each filter are fused using the variational Bayesian method to obtain the final state estimate of the tracked target.

[0010] Optionally, the expression for the target kinematic model is as follows:

[0011]

[0012] The expression for the measurement model is as follows:

[0013] z k =h(x k )+v k

[0014] in, Let be the n-dimensional target state vector at time k. Let f(·) and h(·) be the m-dimensional measurement vector at time k, and f(·) and h(·) be the known nonlinear state equation and measurement equation, respectively. For the n-dimensional process noise at time k-1, Let m be the m-dimensional Gaussian measurement noise at time k, where the subscript k represents the discrete time series and the superscript m represents the m-dimensional Gaussian measurement noise at time k. k =1,…,r, where r is the identifier of the target kinematic model and r is the number of target kinematic models.

[0015] Optionally, multiple filters are used to estimate the state of the tracked target based on the corresponding target kinematic model, specifically including:

[0016] Calculate the interaction probability of the target kinematic model corresponding to each of the filters;

[0017] Based on the interaction probability, calculate the initial state value and covariance of the tracked target after the interaction of each target kinematic model;

[0018] The initial state value and the covariance are filtered by the target kinematic model corresponding to each filter to achieve state estimation of the tracked target.

[0019] Optionally, the formula for calculating the interaction probability is as follows:

[0020]

[0021] Where, μ i|j (k-1|k-1) represents the interaction probability between the i-th target kinematic model and the j-th target kinematic model at time k-1, p ij Let μ be the transition probability between the i-th target kinematic model and the j-th target kinematic model. i (k-1) represents the probability of the kinematic model of the i-th target at time k-1. Let be the normalization constant for the j-th objective.

[0022] Optionally, the formulas for calculating the initial state value and covariance of the tracked target after the interaction are as follows:

[0023]

[0024]

[0025] in, For time k-1, the m-th time k = the initial state values ​​of the tracked target after the kinematic models of j targets are compared. For time k-1, the m-th time k = Estimated states of i target kinematic models, For time k-1, the m-th time k = the covariance of the kinematic models of j targets after cross-variance For time k-1, the m-th time k = Covariance of i target kinematic models.

[0026] Optionally, the state estimation results of each filter are fused based on the variational Bayesian method to obtain the final state estimate of the tracked target, specifically including:

[0027] Calculate the joint probability density based on the variational Bayesian method;

[0028] Based on the joint probability density, the weights of the state estimation results of each filter are calculated according to the measurement model;

[0029] The state estimation results of each filter are fused based on the weights to obtain the final state estimate of the tracked target.

[0030] This invention also provides an interactive multi-model target tracking system based on variational Bayes, comprising:

[0031] The model building module is used to build a target tracking model for the tracked target; the target tracking model includes a target kinematics model and a measurement model.

[0032] The state estimation module is used to estimate the state of the tracked target using multiple filters based on the corresponding target kinematic model.

[0033] The fusion module is used to fuse the state estimation results of each filter based on the variational Bayesian method to obtain the final state estimate of the tracked target.

[0034] Optionally, the state estimation module specifically includes:

[0035] An interaction probability calculation unit is used to calculate the interaction probability of the target kinematic model corresponding to each of the filters;

[0036] The initial state value and covariance calculation unit is used to calculate the initial state value and covariance of the tracked target after the interaction of each of the target kinematic models based on the interaction probability.

[0037] The state estimation unit is used to filter the initial state value and the covariance through the target kinematic model corresponding to each of the filters, so as to realize the state estimation of the tracked target.

[0038] Optionally, the fusion module specifically includes:

[0039] The joint probability calculation unit is used to calculate the joint probability density based on the variational Bayesian method.

[0040] The weight calculation unit is used to calculate the weights of the state estimation results of each filter based on the joint probability density and the measurement model.

[0041] The fusion unit is used to fuse the state estimation results of each filter based on the weights to obtain the final state estimate of the tracked target.

[0042] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0043] This invention employs multiple filters to estimate the state of the tracked target based on the corresponding target kinematic model. The state estimation results from each filter are then fused using a variational Bayesian method to obtain the final state estimate of the tracked target. This invention approximates the joint probability density of the state and the model through Bayesian inference, solving the problem of traditional multi-model approaches that simplify the estimation results of multiple filters to a single Gaussian distribution, thus sacrificing estimation accuracy, without increasing computational cost. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart of the interactive multi-model target tracking method based on variational Bayes provided by the present invention;

[0046] Figure 2 A simulation diagram for tracking the scene;

[0047] Figure 3 This is a diagram illustrating the comparison of position estimation errors.

[0048] Figure 4 This is a diagram illustrating the comparison of speed errors. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] The purpose of this invention is to provide an interactive multi-model target tracking method and system based on variational Bayesian methods. The main idea of ​​Interactive Multi-Model (IMM) is to utilize multiple filters to effectively track maneuvering targets. Each filter uses a different target kinematic model to estimate the target in parallel, obtaining estimation results based on its respective target model. The weights of each sub-filter's estimation results in the fusion estimation are calculated based on measurement data, and weighted fusion is used to achieve effective estimation of the maneuvering target. Traditional multi-model methods simplify the mixture of Gaussian distributions of multiple filter estimation results into a single Gaussian distribution during fusion, resulting in a loss of estimation accuracy. Therefore, this invention, based on the variational Bayesian method, improves estimation accuracy without increasing computational load by using Bayesian inference of the approximate state and the joint probability density of the model.

[0051] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Example 1

[0053] like Figure 1 As shown, the interactive multi-model target tracking method based on variational Bayes provided by this invention includes the following steps:

[0054] S1: Establish a target tracking model for the tracked target; the target tracking model includes a target kinematics model and a measurement model.

[0055] Considering the motion of the tracked target, establish a target kinematic model and a measurement model:

[0056]

[0057] z k =h(x k )+v k (2)

[0058] In the formula, Let be an n-dimensional target state vector. Let f(·) and h(·) be m-dimensional measurement vectors, and f(·) and h(·) be the known nonlinear state equation and measurement equation, respectively. With a mean of 0 and a variance of n-dimensional process noise, The mean is 0 and the variance is R. k m-dimensional Gaussian measurement noise, where the subscript k represents the discrete time series and the superscript m k =1,…,r are the identifiers for the target kinematic model, indicating that at time k, the target is moving according to m. k The corresponding target kinematic model motion, where r is the number of target kinematic models in the model set.

[0059] S2: Multiple filters are used to estimate the state of the tracked target based on the corresponding target kinematic model.

[0060] S21: Perform interactive fusion of the tracking results of each sub-filter at the previous time step, including interactive probability, initial value of interactive state, and covariance.

[0061] Calculate the interaction probability μ i|j (k-1|k-1):

[0062]

[0063] In the formula, p ij It is the probability transition matrix of the target kinematic model. The element in the i-th row and j-th column represents the target kinematic model m. k =j to target kinematic model m k =Transition probability of i, μ i (k-1) represents the target kinematic model probability at the previous time step. This is the normalization constant.

[0064] Calculate the initial state values ​​after the interaction of each sub-model. Covariance j = 1, 2, ..., r:

[0065]

[0066]

[0067] In the formula, and The mth time in the previous moment k = Estimated state and covariance of i target kinematic models.

[0068] S22: Parallel filtering. After obtaining the initial state values ​​after the interaction of each sub-model, each sub-model uses its own target kinematic model to perform filtering in parallel to obtain its own filtering results.

[0069] For each sub-filter, the following operations are performed in parallel:

[0070] State prediction in one step:

[0071]

[0072] In the formula, To utilize m k = the one-step predicted value of the target state obtained by the target kinematic model corresponding to i, F (i) For the nonlinear target motion equation f (i The result after linearization is (·). To find the sign of the partial derivative.

[0073] State covariance One step in the prediction:

[0074]

[0075] In the formula, the superscript T indicates transpose.

[0076] Calculate the gain matrix

[0077]

[0078] In the formula, This is the linearized result of the nonlinear measurement equation.

[0079] Calculate the posterior estimate and covariance of the state:

[0080]

[0081]

[0082] In the formula, For a one-step prediction of the measurement, I is an n-dimensional identity matrix.

[0083] S3: The state estimation results of each filter are fused based on the variational Bayesian method to obtain the final state estimate of the tracked target.

[0084] This invention is based on the variational Bayesian method, which uses Bayesian inference to obtain the joint probability density of the approximate state and the target kinematic model.

[0085] Introducing random variables Denotes the target kinematic model that takes effect at time k, where And satisfy That is, when time k, the target follows m k =i model can be represented as the motion of the model. And j≠i, therefore the random variable M k It conforms to a multinomial distribution with the probability μ of the target kinematic model as a parameter.

[0086]

[0087] In the formula, μ=[μ1(k),μ2(k),K,μ r (k)].

[0088] Then consider random variable M k One-step prediction probability density and likelihood function p(z) k |x k M k This can be represented as:

[0089]

[0090]

[0091] In the formula, This represents the posterior estimate of the state at time k-1, where N(·) represents a Gaussian distribution. This is used to obtain the joint posterior probability p(x) of the target state and the model. k M k |z 1:k The variational Bayesian method estimates unknown parameters by minimizing the following index function.

[0092] J = KL(q(x) k )q(M k )||p(x k M k |z 1:k (14)

[0093] Wherein KL(q(x) k )q(M k )||p(x k M k |z 1:k )) represents the calculation of q(x) k )q(M k ) and p(x k M k |z 1:k The KL divergence between the two distributions is q(·), which is an approximation of the distribution of the parameter to be estimated.

[0094] Minimizing the above index yields the solution for the substituted parameters:

[0095]

[0096] In the formula, E[·] represents the expected operation, and Θ k ={x k M k} represents the parameter to be estimated. For Θ k One of the elements in Indicates that the set contains, except for Other elements, Indicates and The relevant constants; Θ k Substituting the elements in the table into the index function in sequence yields the variational Bayesian update of the corresponding parameters to be estimated.

[0097] Substituting equations (11), (12), and (13) into equation (15), we get:

[0098]

[0099] After parallel filtering by each sub-filter, different weights are assigned to the results of each sub-filter using the measured values ​​to obtain the model probability μ at that moment. i (k), i = 1, ..., r.

[0100] Will Substituting into the equation, the updated model probability is:

[0101]

[0102] Where, the likelihood function This is the normalization factor.

[0103] Target state fusion estimation, will Substituting into the formula, the updated target state is:

[0104]

[0105]

[0106] To verify the effectiveness of the method of this invention, a tracking scenario was first constructed for simulation. A ground target performs the following motions: uniform linear motion from 0 to 10 s, uniform turning motion with an angular velocity of 12° / s from 10 to 20 s, and uniform turning motion with an angular velocity of -12° / s from 20 to 30 s. The initial position of the target is x0 = 0 m, y0 = 0 m, and the initial velocity is V. x0 =50m / s, V y0 =0m / s, the radar is located at the origin, and the simulation scenario is as follows: Figure 2 As shown.

[0107] Tracking simulations were performed using a single model based on Extended Kalman Array (EKF), an Interactive Multiple Model (IMM), and the proposed filter method. The target kinematics model selected for EKF was a two-dimensional constant acceleration (CA) model, as follows:

[0108]

[0109] Among them, the state variables are selected as two-dimensional position and velocity, x t =[xy V x V y The simulation step size is T = 0.1 s.

[0110] IMM and the method of this invention select CV and CT models. The CT model is as follows:

[0111]

[0112] If the tracking filter can obtain the target's position information, then the measurement equation can be expressed as:

[0113]

[0114] Among them, v t It follows a Gaussian distribution with variance R. k =diag[10 2 10 2 The initial state error covariance is P0 = diag[(100m)]. 2 (100m) 2 (50m / s) 2 (50m / s) 2 ].

[0115] Comparison of tracking results of the three algorithms Figure 3 and Figure 4 As shown, the single-model EKF significantly increases its error when the target is maneuvering due to the inaccuracy of the target kinematic model. While the traditional interactive multi-model approach covers the target's motion with multiple models when the motion changes, resulting in lower position tracking error, it suffers from approximation error because it simplifies the estimation results of multiple sub-filters to a single Gaussian distribution. The interactive multi-model method based on variational Bayesian inference proposed in this paper obtains the target's state update through variational Bayesian inference, reducing approximation error and achieving higher position tracking accuracy than the traditional single model without increasing the computational load of the algorithm.

[0116] Example 2

[0117] In order to implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, an interactive multi-model target tracking system based on variational Bayes is provided below.

[0118] The system includes:

[0119] The model building module is used to build a target tracking model for the tracked target; the target tracking model includes a target kinematic model and a measurement model.

[0120] The state estimation module is used to estimate the state of the tracked target using multiple filters based on the corresponding target kinematic model.

[0121] The fusion module is used to fuse the state estimation results of each filter based on the variational Bayesian method to obtain the final state estimate of the tracked target.

[0122] Furthermore, the state estimation module specifically includes:

[0123] An interaction probability calculation unit is used to calculate the interaction probability of the target kinematic model corresponding to each of the filters.

[0124] The initial state value and covariance calculation unit is used to calculate the initial state value and covariance of the tracked target after the interaction of each target kinematic model based on the interaction probability.

[0125] The state estimation unit is used to filter the initial state value and the covariance through the target kinematic model corresponding to each of the filters, so as to realize the state estimation of the tracked target.

[0126] Furthermore, the fusion module specifically includes:

[0127] The joint probability calculation unit is used to calculate the joint probability density based on the variational Bayesian method.

[0128] The weight calculation unit is used to calculate the weights of the state estimation results of each filter based on the joint probability density and the measurement model.

[0129] The fusion unit is used to fuse the state estimation results of each filter based on the weights to obtain the final state estimate of the tracked target.

[0130] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0131] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An interactive multi-model target tracking method based on variational Bayes, characterized in that, include: Establish a target tracking model for the tracked target; The target tracking model includes a target kinematics model and a measurement model; Multiple filters are used to estimate the state of the tracked target based on the corresponding target kinematic model; The state estimation results of each filter are fused based on the variational Bayes method to obtain the final state estimate of the tracked target. Specifically, the state estimation results of each filter are fused based on the variational Bayesian method to obtain the final state estimate of the tracked target, which includes: Introducing random variables Denotes the target kinematic model that takes effect at time k, where And satisfy ,random variable Consistent with the probability of the target kinematic model Multinomial distribution with parameters: （11） In the formula, ; Consider random variables One-step prediction probability density and likelihood function Represented as: （12） （13） In the formula, This represents the posterior estimate of the state at time k-1. Representing a Gaussian distribution, the variational Bayesian method estimates the unknown parameters by minimizing the following index function: （14） in, Indicates calculation and KL divergence between two distributions This is an approximation of the distribution of the parameter to be estimated; Minimizing the above index yields the solution for the parameters: （15） In the formula, To achieve the desired operation, For the parameters to be estimated, for One of the elements in Indicates that the set contains, except for Other elements, Indicates and Relevant constants; will Substituting the elements in the index function in sequence, we obtain the variational Bayes update of the corresponding parameters to be estimated. Substituting equations (11), (12), and (13) into equation (15), we get: （16） After parallel filtering by each sub-filter, different weights are assigned to the results of each sub-filter using the measured values ​​to obtain the model probability at that moment. ; Will Substituting into equation (15), the updated model probability is: （17） Where, the likelihood function , Normalization factor; Target state fusion estimation will Substituting into equation (15), the updated target state is: （18） （19）。 2. The interactive multi-model target tracking method based on variational Bayes as described in claim 1, characterized in that, The expression for the target kinematic model is as follows: The expression for the measurement model is as follows: in, For time k A dimensional target state vector. For time k dimensional measurement vector, and These are the known nonlinear state equations and measurement equations, respectively. For time k-1 Dimensional process noise, For time k Vigaussian measurement noise, subscript Represents discrete time series, superscript , which serves as the identifier for the target kinematic model. The number of target kinematic models.

3. The interactive multi-model target tracking method based on variational Bayes as described in claim 1, characterized in that, The state estimation of the tracked target is performed using multiple filters based on the corresponding target kinematic model, specifically including: Calculate the interaction probability of the target kinematic model corresponding to each of the filters; Based on the interaction probability, calculate the initial state value and covariance of the tracked target after the interaction of each target kinematic model; The initial state value and the covariance are filtered by the target kinematic model corresponding to each filter to achieve state estimation of the tracked target.

4. The interactive multi-model target tracking method based on variational Bayes as described in claim 3, characterized in that, The formula for calculating the interaction probability is as follows: in, Let be the interaction probability between the kinematic model of the i-th target and the kinematic model of the j-th target at time k-1. Let be the transition probability between the i-th target kinematic model and the j-th target kinematic model. Let be the probability of the kinematic model of the i-th target at time k-1. Let be the normalization constant for the j-th objective.

5. The interactive multi-model target tracking method based on variational Bayes as described in claim 4, characterized in that, The formulas for calculating the initial state value and covariance of the tracked target after the interaction are as follows: in, For time k-1, the first... The initial state values ​​of the tracked target after the kinematic model of each target are compared. For time k-1, the first... The estimated state of a target kinematic model. For time k-1, the first... The covariance of the kinematic models of each target For time k-1, the first... The covariance of a target kinematic model.

6. The interactive multi-model target tracking method based on variational Bayes as described in claim 1, characterized in that, The state estimation results of each filter are fused using the variational Bayesian method to obtain the final state estimate of the tracked target, specifically including: Calculate the joint probability density based on the variational Bayesian method; Based on the joint probability density, the weights of the state estimation results of each filter are calculated according to the measurement model; The state estimation results of each filter are fused based on the weights to obtain the final state estimate of the tracked target.

7. An interactive multi-model target tracking system based on variational Bayes, characterized in that, The system is used to execute the interactive multi-model target tracking method based on variational Bayes as described in any one of claims 1-6, and the system comprises: The model building module is used to build a target tracking model for the tracked target; the target tracking model includes a target kinematics model and a measurement model. The state estimation module is used to estimate the state of the tracked target using multiple filters based on the corresponding target kinematic model. The fusion module is used to fuse the state estimation results of each filter based on the variational Bayesian method to obtain the final state estimate of the tracked target.

8. The interactive multi-model target tracking system based on variational Bayes as described in claim 7, characterized in that, The state estimation module specifically includes: An interaction probability calculation unit is used to calculate the interaction probability of the target kinematic model corresponding to each of the filters; The initial state value and covariance calculation unit is used to calculate the initial state value and covariance of the tracked target after the interaction of each of the target kinematic models based on the interaction probability. The state estimation unit is used to filter the initial state value and the covariance through the target kinematic model corresponding to each of the filters, so as to realize the state estimation of the tracked target.

9. The interactive multi-model target tracking system based on variational Bayes as described in claim 7, characterized in that, The fusion module specifically includes: The joint probability calculation unit is used to calculate the joint probability density based on the variational Bayesian method. The weight calculation unit is used to calculate the weights of the state estimation results of each filter based on the joint probability density and the measurement model. The fusion unit is used to fuse the state estimation results of each filter based on the weights to obtain the final state estimate of the tracked target.

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