A target tracking method based on inverse gamma-gaussian inverse Wishart distribution

Abstract

The application belongs to the technical field of radar data processing, and particularly relates to a target tracking method based on inverse gamma-Gaussian inverse Wishart distribution, a hierarchical state space model of a tracking system is acquired, and a joint probability density function is constructed; measurement information and state information are input to the hierarchical state space model; a fading factor and a prior measurement noise covariance are acquired; a state estimation value of the state approximate probability density function is extracted; a fading factor approximate probability density function is acquired, an updated fading factor is extracted based on the fading factor approximate probability density function; a measurement noise covariance approximate probability density function is acquired; an updated measurement covariance estimation value is extracted; when the state estimation value converges, the state estimation value is output; the application estimates an accurate measurement statistical model, assists in calculating a fading factor to correct a motion model under inaccurate measurement, and improves the tracking precision of a maneuvering target under an inaccurate measurement environment.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar data processing, and particularly relates to a target tracking method based on inverse gamma-Gaussian inverse Wishart distribution. BACKGROUND

[0002] State estimation problems exist widely in the field of target tracking, and accurate state information can provide effective technical support for the pilot's grasp of the situation and the guidance of the fire control system. For a linear target tracking system, Kalman filter (KF) is an optimal estimation method, and this method needs an accurate state transition model and a measurement model. The state transition model is usually determined by the target maneuvering characteristics, and the measurement model is determined by the geometric relationship between the target state and the measurement information. For example, when the target moves at a constant speed, we can use the constant speed model to construct the state transition model, and if the system can obtain the target position information, the measurement matrix can be set based on the relationship between the position information and the state information. In the actual target tracking process, due to the complexity of target maneuvering, the motion model used is difficult to match the target maneuvering characteristics. Moreover, due to the external environment and the signal interference of the enemy target, the measurement information obtained is inaccurate, which causes the measurement statistical model constructed to deviate from the actual model. Using the traditional Kalman filter to estimate the state of the target in such an environment will inevitably result in poor target tracking effect. Although the strong tracking filter can solve the problem of model mismatch to some extent, this method is based on the residual orthogonal principle to realize model compensation, and needs accurate measurement data to assist in processing, so it is still not applicable in the inaccurate measurement environment. Therefore, how to realize accurate tracking of the target in the environment of inaccurate measurement and motion model mismatch is a problem that needs to be solved in current practical engineering applications. SUMMARY

[0003] In order to solve the above problems, the present application provides a target tracking method based on inverse gamma-Gaussian inverse Wishart distribution, comprising:

[0004] Step S1: obtaining a hierarchical state space model of a tracking system, and constructing a joint probability density function;

[0005] Step S2: inputting measurement information and state information to the hierarchical state space model; setting the correlation matrix parameter and the degree of freedom parameter of the hierarchical state space model, obtaining the fading factor and the prior measurement noise covariance;

[0006] Step S3: obtaining the state approximate probability density function based on the joint probability density function, the fading factor and the measurement noise covariance; extracting the state estimation value of the state approximate probability density function;

[0007] Step S4: obtaining a fading factor approximate probability density function based on the joint probability density function, the state estimation value and the measurement noise covariance, and extracting an updated fading factor based on the fading factor approximate probability density function;

[0008] Step S5: obtaining the measurement noise covariance approximate probability density function based on the joint probability density function, the updated fading factor and the state estimation value, and extracting an updated measurement covariance estimation value based on the measurement noise covariance approximate probability density function;

[0009] Step S6: outputting the state estimation value when the state estimation value converges.

[0010] Preferably, the method for obtaining the hierarchical state space model of the tracking system comprises:

[0011] Step S10: modeling the process noise and the measurement noise by using a Gaussian distribution;

[0012] Step S11: introducing a fading factor to correct the target motion model, and modeling the fading factor by using an inverse Gamma distribution;

[0013] Step S12: modeling the measurement noise covariance by using an inverse Wishart distribution, and obtaining a measurement noise covariance model;

[0014] Step S13: modeling the measurement likelihood function by using a Gaussian distribution, and obtaining a measurement likelihood function model;

[0015] Step S13: obtaining the hierarchical state space model.

[0016] Preferably, the state approximate probability density function, the fading factor approximate probability density function and the measurement noise covariance approximate probability density function are all solved by using a variational Bayesian method.

[0017] The advantages of the present application include that the present application designs a target tracking method based on an inverse Gamma-Gaussian inverse Wishart distribution under a variational Bayesian framework, estimates an accurate measurement statistical model, helps to calculate a fading factor to correct a motion model under inaccurate measurement, and improves the tracking precision of a maneuvering target under an inaccurate measurement environment. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is the root mean square error of the position and velocity of the three algorithms of the present application;

[0019] Figure 2 is the root mean square error of the velocity of the three algorithms of the present application. DETAILED DESCRIPTION

[0020] For the purpose, technical solutions and advantages of the embodiments of the present application to be clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar notations represent the same or similar elements or elements with the same or similar functions throughout. The described embodiments are part of the embodiments of the present application, rather than all the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application. The embodiments of the present application will be described in detail below with reference to the drawings.

[0021] A variational Bayesian target tracking method based on inverse gamma-Gaussian inverse Wishart distribution, the specific scheme of the algorithm includes the following steps:

[0022] 1. Hierarchical state space model modeling

[0023] Assume that the linear system target state space model is composed of the following two formulas (motion model).

[0024] X k+1 =F k X k +W k (1)

[0025] Z k+1 =H k+1 X k+1 +V k+1 (2)

[0026] In the formula: X k is the target state vector; F k is the state transition matrix; W k is the process noise; Z k+1 is the measurement vector; H k+1 is the measurement matrix; V k+1 represents the measurement noise; the process noise is subject to a Gaussian distribution with a mean of 0 n and a covariance of Q k ; the measurement noise is modeled as a Gaussian distribution with a mean of 0 m and a covariance of R k+1 . Wherein, n and m are the state dimension and the measurement dimension, respectively.

[0027]

[0028]

[0029] Since the problem of model mismatch often occurs in the process of maneuvering target tracking, the fading factor λ k is introduced to modify the model, and the fading factor λ

[0030]

[0031] where Γ(·) is the gamma function, and a and b are the degree of freedom parameters of inverse gamma distribution. There are two advantages of modeling the fading factor λ

[0032] with inverse gamma distribution: 1) the distribution can guarantee the conjugacy of the fading factor λ

[0033]

[0034] where X k+1k is the state vector, F k is the state transition matrix, and Q kk is the process noise covariance. Since the statistical uncertainty of the measurement noise exists, the measurement noise covariance is modeled as inverse Wishart distribution.

[0035]

[0036] where μ k+1 is the degree of freedom parameter of pseudo-Wishart distribution, Σ k+1 is the scale matrix of inverse Wishart distribution, and Γ m (·) is the m-variable gamma function. Based on the measurement equation and the measurement noise model, the expression of the measurement likelihood function is as follows.

[0037]

[0038] The hierarchical state space model constructed in this paper consists of equations (3)-(8).

[0039] 3. Variational Bayesian solution

[0040] From the hierarchical state space model constructed, it can be found that the set of parameters to be estimated Ψ can be set as

[0041] Ψ = {λ k , X k+1 , R k+1} (9)

[0042] Consider solving each of the parameters to be estimated independently. First, construct the joint probability density function p (λ k ,X k+1 ,R k+1 ,Z 1:k+1 ) based on the set of parameters to be estimated and the set of observations.

[0043]

[0044] Subsequently, set the initial probability density function for each parameter, and the initial probability density function for each parameter to be estimated is expressed as follows.

[0045] q 0 (R k+1 )=p(R k+1 ) (11)

[0046] q 0 (λ k )=p(λ k ) (12)

[0047] Finally, solve each of the parameters to be estimated. The approximate probability density function of the target state is expressed as follows.

[0048]

[0049] The expressions of the related variables are as follows.

[0050]

[0051]

[0052]

[0053]

[0054] where E j [·] represents the mathematical expectation of the variable obtained in the jth iteration. The mathematical expectation of the variable corresponding to the 0th iteration can be obtained based on equations (11) and (12). The approximate probability density function of λ k is expressed as follows.

[0055] q j (λ k )=IG(λ k ;a j ,b j ) (18)

[0056] The expressions of the related variables are as follows.

[0057]

[0058]

[0059]

[0060] According to formula (18)-(21), The expression of

[0061]

[0062] It is worth noting that when , it means that the filter considers that the system has no motion model mismatch problem, at this time can be forcibly set to 1.

[0063] The measurement noise covariance R k+1 The approximate probability density function expression of

[0064]

[0065] Wherein, The expression of

[0066]

[0067] According to formula (23) and (24), The expression of

[0068]

[0069] 4、State information extraction

[0070] When the state information reaches convergence in the variational Bayesian iteration process, the iteration process is terminated at this time, and the corresponding state information is extracted.

[0071]

[0072]

[0073] In the formula, N VB is the iteration step number when the filter iteration is terminated, X k+1|k+1 is the state information output by the filter, and P k+1|k+1 is the state covariance information output by the filter.

[0074] 5、Parameter setting

[0075] Since the role of λ k is the same as that of the conventional fading factor of the strong tracking filter, in the setting process of the degrees of freedom parameters a and b, the initial estimated value of the fading factor should satisfy

[0076]

[0077] The expressions of the relevant variables are as follows.

[0078] N k,STF = V k -R k+1 (28)

[0079]

[0080]

[0081] ε k = Z k+1 -H k+1 X k+1k (31)

[0082] The forgetting factor p is in the range of 0.95-1. In order to satisfy equation (27), the degrees of freedom parameters a and b are set to satisfy

[0083]

[0084] When μ k+1 and Σ k+1 are set, it is also necessary to ensure that is the covariance information estimated at the initial time. Since the filter has updated the filter measurement noise covariance at the previous time, the relevant matrix parameters and the degrees of freedom parameters can be set based on the covariance information estimated at the previous time. In summary, μ k+1 and Σ k+1 should satisfy the following equations.

[0085]

[0086] At the initial time, is set based on the calibration error of the measuring device.

[0087] In the actual processing process, the one-step state updating process of the present application is realized by the following steps:

[0088] 1. Parameter setting

[0089] The target state information is initialized, and the relevant matrix parameters and the degrees of freedom parameters are set based on equations (27)-(33) and the calibration error of the measuring device.

[0090] 2. Initial value calculation of the parameters to be estimated

[0091] The initial information of each parameter to be estimated is calculated based on equations (11), (12) and (33).

[0092] 3. Variational Bayesian iteration process

[0093] Based on equations (13)-(27), update the approximate probability density function of each parameter to be estimated, and calculate the expected value of each parameter to be estimated to assist in the next iteration update.

[0094] 4. Iteration Termination Judgment

[0095] Set a relevant threshold and compare the difference between the state estimate obtained in the current iteration and the state estimate obtained in the previous iteration. If the difference is less than the threshold, the iteration terminates and proceeds to step 5; otherwise, proceed to step 3 and continue updating the parameters to be estimated.

[0096] 5. Status information output

[0097] Based on the latest state approximation probability density function, the corresponding state information and covariance information are recorded and output.

[0098] Implementation Case:

[0099] The target initially moves at a constant speed in a two-dimensional plane, and the tracking system uses a constant speed model to track it. The target measurement information consists of the target's position information. Suddenly, the target accelerates, but the system does not consider this maneuver and continues to track it using the constant speed model. This leads to a comparison of the tracking performance of traditional algorithms and the algorithm of this invention when using the constant speed model to track the target during its maneuvering motion.

[0100] When the target performs a maneuver, its initial true state is X0 = [10000m, 10000m, 50m / s, 100m / s]. T The target's actual acceleration in both axes is 5m. 2 The initial covariance of the algorithm is set to P. 0|0 =diag([10000m 2 10000m 2 10000m 2 / s 2 10000m 2 / s 2 The initial position X of the algorithm 0|0 Based on Gaussian distribution Randomly generated. The target process noise covariance is... Sampling time t = 1s; total duration 100s. The measurement noise covariance calibrated by the measuring equipment is... The actual measurement noise covariance under interference conditions is

[0101] We compare the proposed algorithm (VB-STF) with the strong tracking filter (STF) and the Kalman filter (KF). The relevant parameters are set as follows: in STF, the forgetting factor is set as ρ = 0.995; in VB-STF, the relevant parameters are set as follows: ρ = 0.995, μ k+1 = 4, N VB = 4.

[0102] Figure 1 and Figure 2 The root mean square errors (RMSE) of position and velocity of the three algorithms are shown in Table 1, and the time average root mean square errors (TRMSE) of position and velocity of the three algorithms are shown in Table 1. It can be found that the proposed algorithm has better state estimation accuracy than the KF and the STF, which also means that the application has better tracking accuracy under the mismatch and inaccurate measurement of the motion model.

[0103] Table 1

[0104]

[0105] The above merely illustrates the specific implementation of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A target tracking method based on inverse gamma-Gaussian inverse Wissaud distribution, characterized in that, include: Step S1: Obtain the hierarchical state-space model of the tracking system and construct the joint probability density function; Step S2: Input measurement information and state information into the hierarchical state space model; set the correlation matrix parameters and degree of freedom parameters of the hierarchical state space model to obtain the fading factor and prior measurement noise covariance; Step S3: Obtain the approximate state probability density function based on the joint probability density function, the fading factor, and the measurement noise covariance; extract the state estimate value of the approximate state probability density function; Step S4: Obtain the approximate probability density function of the fading factor based on the joint probability density function, the state estimate, and the measurement noise covariance; and extract the updated fading factor based on the approximate probability density function of the fading factor. Step S5: Obtain the approximate probability density function of the measurement noise covariance based on the joint probability density function, the updated fading factor, and the state estimate; extract the updated measurement covariance estimate based on the approximate probability density function of the measurement noise covariance. Step S6: When the state estimate converges, output the state estimate; Methods for obtaining a hierarchical state-space model of a tracking system include: Step S10: Model the process noise and measurement noise using a Gaussian distribution; Step S11: Introduce a fading factor to correct the target motion model; model the fading factor using an inverse gamma distribution; Step S12: Model the measurement noise covariance using the inverse Wittsch distribution to obtain the measurement noise covariance model; Step S13: Model the measurement likelihood function using a Gaussian distribution to obtain the measurement likelihood function model; Step S13: Obtain the hierarchical state space model.

2. The target tracking method based on the inverse gamma-Gaussian inverse Wissaud distribution as described in claim 1, characterized in that, The approximate probability density function of the state, the approximate probability density function of the fading factor, and the approximate probability density function of the measurement noise covariance are all solved using variational Bayesian methods.

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