Radar target tracking method based on shape correlation hybrid model

Abstract

The invention relates to a radar target tracking method based on a shape-dependent hybrid model, and the method comprises the steps: dividing the exterior of a vehicle into four rectangular sub-regions according to the edge centralized measurement characteristics, modeling each rectangular sub-region as a shape-dependent Gaussian component, describing the four rectangular sub-regions through a shape-dependent Gaussian mixture model, and meanwhile, carrying out the modeling of the four rectangular sub-regions through a shape-dependent Gaussian mixture model. A shape scaling factor is introduced, each rectangular sub-region is regarded as a result of performing one-dimensional scaling and translation on the overall shape of the vehicle through the shape scaling factor, joint estimation and measurement association is realized by adopting a variational Bayesian method in combination with hidden variables based on the four rectangular sub-regions, simulation data is generated through a simulation experiment, and the overall shape of the vehicle is subjected to one-dimensional scaling and translation. Verifying the effectiveness after the joint estimation and measurement association in the step 2; the method has the advantage that the tracking performance is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of extended target tracking, and in particular relates to a radar target tracking method based on a shape-dependent hybrid model. Background Art

[0002] As one of the core sensors in autonomous driving systems, automotive radar can achieve high-precision environmental perception at a reasonable cost even under complex weather conditions. With the improvement of automotive radar resolution, multiple measurements from the same target can be obtained within a single time step. In this case, since the physical shape of the target cannot be ignored, the target to be tracked should be treated as an extended object (EO). Similarly, vehicle tracking based on high-resolution radar should be classified as an extended object tracking (EOT) problem. Compared with traditional point target tracking methods, EOT methods can simultaneously estimate the target's motion state and its extended form (shape and orientation). This morphological information is of great significance for target recognition and classification.

[0003] In the field of EOT research, existing literature has proposed various models for characterizing the distribution of EO measurements (scattering centers). These models can be categorized into two main types: profile models and surface models. In recent years, some surface models have been combined with random matrix (RM) models to achieve joint tracking of EO orientation angles. These models parameterize the target's extended shape using semi-axis length and orientation angle, thereby imbuing it with a clear physical meaning.

[0004] In practical applications, automotive radar measurement data exhibits high complexity, with measurement points often concentrated near the edges of vehicle targets. This type of data is difficult to fully describe using traditional contour or surface models. Radar measurement data with concentrated edge distribution is more suitable for shape-dependent modeling. However, research in this area remains limited within existing technologies, presenting significant potential for development and technical optimization.

[0005] Based on the above considerations, the present invention proposes a radar target tracking method based on a shape-dependent hybrid model. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a radar target tracking method based on a shape-dependent hybrid model. By introducing a shape scaling factor, each hybrid component can correspond to a sub-region describing the target edge, thereby effectively and adaptively characterizing the complex edge measurement distribution characteristics of the vehicle target. Simulation results show that compared with the existing methods, the present invention achieves a significant improvement in tracking performance, especially in the estimation of the center of mass position, showing higher accuracy and robustness.

[0007] The technical solutions of the present invention are as follows:

[0008] A radar target tracking method based on a shape-dependent hybrid model comprises the following steps:

[0009] Step 1: Based on the measurement characteristics of the vehicle target, the vehicle exterior is divided into four rectangular sub-regions. Each rectangular sub-region is modeled as a Gaussian component that depends on the vehicle shape. The four rectangular sub-regions are described by a shape-dependent Gaussian mixture model. At the same time, a shape scaling factor is introduced, and each rectangular sub-region is regarded as the result of a one-dimensional scaling and translation of the overall vehicle shape by the shape scaling factor.

[0010] Step 2: Based on the four rectangular sub-regions in step 1, a variational Bayesian method is used in combination with latent variables to jointly estimate the vehicle's motion state, heading angle state, shape state, shape scaling factor state, and hybrid weight state, and perform measurement association.

[0011] Step 3: Generate simulation data through simulation experiments to verify the effectiveness of the joint estimation and measurement association in step 2.

[0012] Furthermore, each rectangular sub-region in the step 1 corresponds to an edge of the rectangular vehicle shape, and each rectangular sub-region is regarded as the result of scaling and translating the overall vehicle shape along the direction or perpendicular to the direction by the shape scaling factor. The shape scaling factor is modeled as a random variable and is obtained by the diagonal positive definite random matrix variable C k Characterize all shape scaling factors.

[0013] Furthermore, the step 1 also considers estimating the vehicle motion state x k , towards the vector Φ k and shape X k , and define these variables as follows:

[0014]

[0015] Where, (·) T represents the matrix transpose, and are the x-coordinate and y-coordinate of the target center of mass in the Cartesian coordinate system, is the Cartesian centroid position vector; and are the velocities of the center of mass in the x-axis and y-axis directions in the Cartesian coordinate system, is the Cartesian center of mass velocity vector; the direction angle θ k represents the angle of counterclockwise rotation from the x-axis, ω k is the yaw rate; shape X k By half-length square and half-width squared parameterization;

[0016] Based on the above variables and definitions, in addition to the state defined by formula (1), the newly defined state includes the state defined by C k The shape scaling factor of the representation and the mixing weight π k , to simplify the representation, all states to be estimated are represented as Θ k ={x k , Φ k , X k , C k ,π k}.

[0017] Furthermore, regarding the shape X k The content includes the following parts:

[0018] S101. Assuming that the scattering centers of each rectangular sub-area are uniformly distributed and using moment matching technology to approximate the uniform distribution with a Gaussian distribution, the shape-dependent GM position measurement model can be described as:

[0019]

[0020] Where, is the rth Cartesian position measurement; H k is the measurement matrix; is the Cartesian centroid position vector; is the rotation matrix; is the multiplicative noise consisting of four Gaussian components and their corresponding weights; is the actual measurement noise; represents Gaussian distribution; R k is the measurement error covariance matrix;

[0021] Multiplicative noise and position measurement The conditional probability density function is:

[0022]

[0023] Where h t and are the mean and covariance of the t-th multiplicative noise Gaussian component, both of which are related to the shape scaling factor C k Correlation; Mixed Weight for Assuming that it obeys the Dirichlet distribution, the probability density function is m k is the concentration parameter of the distribution, for The transpose of

[0024] S102, using the above multiplicative noise Modeling edge concentration measurement distribution;

[0025] Shape scaling factor model: Assuming that the edge concentration measurement distribution area has a symmetrical structure, the shape scaling factor can be expressed as:

[0026]

[0027] Where, and Half length With half width Shape scaling factor of

[0028] Given the shape scaling factor C k Middle C k，1 with c k，2 The value range is (0, 1], assuming C k Obeys truncated inverse Gamma distribution;

[0029] Gaussian components and shape scaling factor C k Relationship: If the scattering centers are evenly distributed over the entire rectangular vehicle surface, then the multiplicative noise Can be modeled as a Gaussian distribution in, is the scale factor, and I2 is the 2×2 identity matrix;

[0030] Therefore, assuming that the scattering centers are uniformly distributed in the tth region, they can also be modeled as Gaussian distributions, and their probability density function is Mean h t and covariance It is related to the shape scaling factor of the t-th region, and the specific relationship is as follows:

[0031]

[0032] Where,

[0033] Correspondingly, the covariance It can be described as:

[0034]

[0035] Where,

[0036]

[0037] in is the scale factor, and Half length With half width The shape scaling factor, and are the coefficients of the covariance components.

[0038] Furthermore, the contents of step 2 include the following:

[0039] S201, for all states Θ at time k-1 k-1 ={x k-1 , Φ k-1 , X k-1 , C k-1 ,π k-1 The posterior probability density of} makes the following assumptions:

[0040]

[0041] Where, is the motion state x k-1 The mean and covariance parameters of ; is the angle vector state Φ k-1 The mean and covariance parameters of ; is the shape state X k-1 The two scale parameters of is the shape scaling factor C k-1 Two scale parameters of ; is the weight state π k-1 Concentration parameters; is the set of all measurements up to time k, and the measurement at each moment is Defined as a set of Cartesian position measurements Doppler velocity measurement set The union of N k is the number of measurement points, is the rth Doppler velocity measurement; represents Gaussian distribution; IG(·) represents inverse Gamma distribution; represents Dirichlet distribution;

[0042] S202, Prediction

[0043] Movement state xk The state prediction is:

[0044]

[0045] Where, The state transition matrix representing the motion state; The process noise covariance matrix representing the motion state; is the predicted mean and predicted covariance parameters of the motion state at time k;

[0046] For the angle vector Φ k , we can get:

[0047]

[0048] Where, The state transition matrix representing the angle vector state; The process noise covariance matrix representing the angle vector state; is the predicted mean and predicted covariance parameters of the angle vector state at time k;

[0049] Mixing weight π k Concentration parameters Through the forgetting factor Propagate as follows:

[0050]

[0051] Where t = 1, ..., 4, the forgetting factor is the predicted value of the concentration parameter of the weight state at time k;

[0052] For shape state X k With shape scaling factor state C k , we can get:

[0053]

[0054] Where n = 1, 2, and X k and C k The forgetting factor; are the predicted values of the two scale parameters of the shape state at time k; are the predicted values of the two scale parameters of the shape scaling factor state at time k;

[0055] S203. Measurement update based on variational Bayesian method;

[0056] Based on the variational Bayesian method, the posterior probability density of all states to be estimated is Can be approached as:

[0057]

[0058] where q x (x k ) is the posterior probability density of the motion state; q X (X k ) is the posterior probability density of the shape state; q C (C k ) is the posterior probability density of the shape scaling factor state; q Φ Φ k ) is the posterior probability density of the angle vector state; q π (π k ) is the posterior probability density of the weight state;

[0059] In order to obtain an analytical solution, the noise-free measurement Z is introduced k and the correlation vector L k , the posterior probability density q Z (Z k ) and q L (L k ) is approximately:

[0060]

[0061] in, is the rth noise-free position measurement; is the mean of the rth noise-free position measurement in the previous iteration; is the covariance of the rth noise-free position measurement in the previous iteration; l r，t is the association vector corresponding to the rth measurement point associated with the tth sub-rectangle; is the probability density of association between the rth measurement point and the tth sub-rectangle; through the variational Bayesian iterative method, the above parameters can be obtained by the following formula:

[0062]

[0063] in, is the covariance contribution of the Doppler measurement to the noise-free measurement state; is the mean contribution of the Doppler measurement to the noise-free measurement state; is the rth true position measurement; is the estimated value of the motion state; is the inverse of the measurement error covariance; is the estimated value of the shape corresponding to the t-th sub-rectangle; is the unnormalized association probability density parameter; is the distance from the centroid of the t-th sub-rectangle to the target centroid;

[0064] x k , Φ k and π k The posterior probability density of is approximately:

[0065]

[0066] Where,

[0067]

[0068] Where, G3=[0,1]; G4=[1,0]; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the position measurement to the heading angle; is the mean contribution of position measurement to the heading angle; is the predicted value of the motion state; is the predicted value of the heading vector; is the predicted covariance matrix of the motion state; is the predicted covariance matrix of the orientation vector; is the predicted value of the concentration parameter;

[0069] X k The posterior probability density of is approximately:

[0070]

[0071] In the formula, the estimated parameters are:

[0072]

[0073] in, are the predicted values of the two scale parameters of the shape state at time k; is the probability density of association when the rth measurement point is associated with the tth sub-rectangle; γ k is the contribution of other estimated states except the shape state to the shape scale parameter;

[0074] For the shape scaling factor state C k , we can get:

[0075]

[0076] The estimated parameters are:

[0077]

[0078] Where, are the predicted values of the two scale parameters of the shape scaling factor state at time k; is the association probability density when the rth measurement point is associated with the tth sub-rectangle; is the contribution of other estimated states except the shape scaling factor state to the scale parameter of the shape scaling factor when the rth measurement point is input.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] 1. This paper proposes a shape-dependent GM position measurement model for automotive radar EOT. By integrating prior shape information with an adaptive SSF, this model effectively characterizes the edge-focused measurement characteristics of a vehicle. Even when the target is partially observable, the shape-dependent modeling mechanism allows the model to flexibly infer the invisible portion of the target through a rectangular subregion represented by four Gaussian components. Furthermore, the SSF dynamically adjusts based on the diffusion of the measurement value along the corresponding edge, thereby constructing a time-varying measurement model that adapts to the dynamic evolution of the measurement distribution.

[0081] 2. This paper derives a VB estimation framework. This method supports recursive analytical estimation of the vehicle's motion state, shape parameters, heading angle, and yaw rate, and simultaneously estimates the SSF of each Gaussian component. The effectiveness of the proposed model and method is verified using simulation data. The evaluation results include a detailed comparative analysis and discussion, particularly highlighting the significant advantages of the proposed method in estimating the center of mass position.

[0082] In summary, the present invention has the advantage of significantly improving tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 is a visualization diagram of rectangular sub-areas 1-4 of the method of the present invention;

[0084] Figure 2 This is a comparison chart of the estimated values of the trajectory of the S1 scenario in a specific time step in the method of the present invention;

[0085] Figure 3 This is a graph showing the average GWD and RMSE estimation results using the existing method in the S1 scenario of the method of the present invention;

[0086] Figure 4 This is a comparison chart of the estimated values of the trajectory of the S2 scenario in a specific time step in the method of the present invention;

[0087] Figure 5 This is a graph showing the average GWD and RMSE estimation results using the existing method in the S2 scenario of the method of the present invention. DETAILED DESCRIPTION

[0088] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0089] like Figures 1 to 5 As shown, a radar target tracking method based on a shape-dependent hybrid model comprises the following steps:

[0090] Step 1: Multi-region Gaussian component modeling and shape scaling factor (SSF) characterization based on edge concentration measurement characteristics:

[0091] Figure 1 The edge-focused radar measurements shown can be described by four rectangular sub-regions, each corresponding to an edge of the rectangular vehicle shape. Regions 1-4 are as follows Figure 1 As shown, in addition, each region can be regarded as the result of scaling and translation of the overall vehicle shape along the direction or vertical direction by SSF. Since the SSF of each region is unknown, difficult to preset, and may change over time, this embodiment models it as a random variable and uses the diagonal positive definite random matrix variable C k Characterize all SSFs.

[0092] Except C k In addition, the present invention also considers estimating the vehicle motion state x k , towards the vector Φ k and shape X k . These variables are defined as follows:

[0093]

[0094] Where (·)T represents the matrix transpose, and are the x-coordinate and y-coordinate of the target center of mass in the Cartesian coordinate system, ( Figure 1 (marked with ★ in the middle) is the Cartesian center of mass position vector; and are the velocities of the center of mass in the x-axis and y-axis directions in the Cartesian coordinate system, is the Cartesian center of mass velocity vector; the direction angle θ k represents the angle of counterclockwise rotation from the x-axis, ω k is the yaw rate; shape Xk By half-length square and half-width squared Parameterization, such as Figure 1 shown.

[0095] A. Shape-dependent GM position measurement model

[0096] Assumptions Figure 1 The scattering centers in each region are evenly distributed, and the moment matching technique is used to approximate the uniform distribution with a Gaussian distribution. Therefore, the shape-dependent GM position measurement model can be described as:

[0097]

[0098] Where, is the rth Cartesian position measurement; H k is the measurement matrix; is the Cartesian centroid position vector; is the rotation matrix; is the multiplicative noise consisting of four Gaussian components and their corresponding weights; is the actual measurement noise; represents Gaussian distribution; R k is the measurement error covariance matrix.

[0099] Multiplicative noise and position measurement The conditional probability density function is:

[0100]

[0101] Where h t and are the mean and covariance of the t-th multiplicative noise Gaussian component, both of which are related to the shape scaling factor C k Correlation; Mixed Weight for Assuming that it obeys the Dirichlet distribution, the probability density function is m k is the concentration parameter of the distribution, for The transpose of .

[0102] Using the above multiplicative noise Modeling edge concentration measurement distribution:

[0103] 1) Shape Scaling Factor Model: To obtain the statistical characteristics of the t-th sub-rectangular component, the key lies in the t-th SSF, which is used to describe the offset of the measurement value relative to the centroid position and the degree of diffusion along the corresponding edge. To simplify the calculation, it is assumed that the edge-concentrated measurement distribution area has a symmetrical structure:

[0104]

[0105] Where, and Half length With half width The shape scaling factor.

[0106] Formula (5) is used when θ = 0 and The visualization results are as follows Figure 1 shown.

[0107] Given that C k Middle C k，1 with C k，2 The value range is (0, 1], assuming C k Obeys the truncated inverse Gamma distribution.

[0108] like Figure 1 As shown, the half length and half width of each area can be obtained by X k with C k For example, the half-length of region 1 is equal to the half-width of the overall vehicle shape The half-width of region 1 is In addition, it is assumed that the scattering centers in different regions have uniform distributions with different densities. This modeling method can effectively characterize the edge concentration measurement characteristics and establish a close connection between each region and the overall vehicle shape. k For vehicles, the proposed model only needs to change C k The different measurement diffusion degrees can be described ( Figure 1 middle or )'s edge concentration measurement distribution.

[0109] 2) Gaussian component and C k Relationship: If the scattering centers are evenly distributed over the entire rectangular vehicle surface, then the multiplicative noise Can be modeled as a Gaussian distribution (in, And I n is the n×n identity matrix). Therefore, assuming that the scattering centers uniformly distributed in the tth region can also be modeled as a Gaussian distribution, its probability density function is Mean h t and covariance It is related to the SSF of the t-th region. The specific relationship is as follows:

[0110]

[0111] Where,

[0112] Correspondingly, the covariance It can be described as:

[0113]

[0114] Where,

[0115]

[0116] in is the scale factor, and Half length With half width The shape scaling factor, and are the coefficients of the covariance components.

[0117] B. Doppler velocity measurement model

[0118] In order to integrate Doppler velocity into the Bayesian filtering framework, it is necessary to parameterize the Doppler velocity using the introduced variables. This problem can be solved by introducing latent variables, and the following Doppler velocity measurement model is obtained:

[0119]

[0120] Where, It is a noisy Doppler velocity measurement; It is a noise-free Doppler measurement; the measurement noise satisfy is the measurement noise variance; the rth measurement direction vector (MDV) (The radar position at time step k is ), G1=[02×2,I2] T , And G3 = [0, 1].

[0121] Step 2: Joint estimation and measurement based on VB method:

[0122] For all states θ at time k-1 k-1 ={x k-1 , Φ k-1 , X k-1 , C k-1 ,π k-1 The posterior probability density of} makes the following assumptions:

[0123]

[0124] Where, is the motion state x k-1 The mean and covariance parameters of ; is the angle vector state Φ k-1 The mean and covariance parameters of ; is the shape state X k-1 The two scale parameters of is the shape scaling factor C k-1 Two scale parameters of ; is the weight state π k-1 Concentration parameters; is the set of all measurements up to the kth moment, and the measurement at each moment is Defined as a set of Cartesian position measurements Doppler velocity measurement set The union of N k is the number of measurement points, is the rth Doppler velocity measurement; represents Gaussian distribution; IG(·) represents inverse Gamma distribution; represents Dirichlet distribution.

[0125] A. Forecast

[0126] Movement state x k The state prediction is:

[0127]

[0128] Where, The state transition matrix representing the motion state; The process noise covariance matrix representing the motion state; are the predicted mean and predicted covariance parameters of the motion state at time k.

[0129] For the angle vector Φ k , we can get:

[0130]

[0131] Where, The state transition matrix representing the angle vector state; The process noise covariance matrix representing the angle vector state; are the predicted mean and predicted covariance parameters of the angle vector state at time k.

[0132] Mixing weight π k Concentration parameters Through the forgetting factor Propagate as follows:

[0133]

[0134] Where t = 1, ..., 4, the forgetting factor is the predicted value of the concentration parameter of the weight state at time k.

[0135] For shape state X k With shape scaling factor state C k , we can get:

[0136]

[0137] Where n = 1, 2, and X k and C k The forgetting factor; are the predicted values of the two scale parameters of the shape state at time k; are the predicted values of the two scale parameters of the shape scaling factor state at time k.

[0138] B. Measurement Update Based on Variational Bayesian Method

[0139] Based on the variational Bayesian method, the posterior probability density of all states to be estimated is Can be approached as:

[0140]

[0141] where q x (x k ) is the posterior probability density of the motion state; q X (X k ) is the posterior probability density of the shape state; q C (C k ) is the posterior probability density of the shape scaling factor state; q Φ (Φ k ) is the posterior probability density of the angle vector state, q π (π k ) is the posterior probability density of the weight state. is the set of all measurements up to the kth moment, and the measurement at each moment is Defined as a set of Cartesian position measurements Doppler velocity measurement set The union of N k is the number of measurement points, is the rth Doppler velocity measurement.

[0142] 1) Hidden variable Z k and Lk Calculation: To obtain an analytical solution, a noise-free measurement Z is introduced. k and the correlation vector L k , their posterior probability density q Z (Z k ) and q L (L k ) is approximately:

[0143]

[0144] in, is the rth noise-free position measurement; is the mean of the rth noise-free position measurement in the previous iteration; is the covariance of the rth noise-free position measurement in the previous iteration; l r，t is the association vector corresponding to the rth measurement point associated with the tth sub-rectangle; is the probability density of association between the rth measurement point and the tth sub-rectangle; through the variational Bayesian iterative method, the above parameters can be obtained by the following formula:

[0145]

[0146] in, is the covariance contribution of the Doppler measurement to the noise-free measurement state; is the mean contribution of the Doppler measurement to the noise-free measurement state; is the rth true position measurement; is the estimated value of the motion state; is the inverse of the measurement error covariance; is the estimated value of the shape corresponding to the t-th sub-rectangle; is the unnormalized association probability density parameter; is the distance from the centroid of the t-th sub-rectangle to the target centroid.

[0147] 2)x k , Φ k and π k The posterior probability density of is approximately:

[0148]

[0149] Where,

[0150]

[0151] Where, G3=[0,1]; G4=[1,0]; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the position measurement to the heading angle; is the mean contribution of position measurement to the heading angle; is the predicted value of the motion state; is the predicted value of the heading vector; is the predicted covariance matrix of the motion state; is the predicted covariance matrix of the orientation vector; is the predicted value of the concentration parameter.

[0152] 3)X k with C k Calculation of: X k The posterior probability density of is approximately:

[0153]

[0154] In the formula, the estimated parameters are:

[0155]

[0156] in, are the predicted values of the two scale parameters of the shape state at time k; is the probability density of association when the rth measurement point is associated with the tth sub-rectangle; γ k is the contribution of other estimated states except the shape state to the shape scale parameter.

[0157] For the shape scaling factor state C k , we can get:

[0158]

[0159] Among them, the estimated parameters are:

[0160]

[0161] Where, are the predicted values of the two scale parameters of the shape scaling factor state at time k; is the association probability density when the rth measurement point is associated with the tth sub-rectangle; is the contribution of other estimated states except the shape scaling factor state to the scale parameter of the shape scaling factor when the rth measurement point is input.

[0162] The proposed method is called "EOT-SD-V". The proposed method recursively outputs estimated values for all states through a small number of iterations.

[0163] Step 3: Simulation experiment verification and model performance evaluation:

[0164] The performance of the proposed method, its variants, and other advanced methods proposed by other researchers is evaluated using simulation data. The proposed method is denoted as the EOT-SD-V method. Comparison methods include an EOT-SD-V-based method without Doppler velocity measurements (denoted as "EOT-SD"), a heading-based EOT method (denoted as "EOT-VB"), a GM method (denoted as "EOT-GM"), an adaptive GM method (denoted as "VB-EOT-GM"), and a keypoint method (denoted as "KPA").

[0165] The simulation experiments compared the root mean square error (RMSE) of the centroid position and orientation, as well as the joint centroid position and extended shape estimation in N s = the average Gaussian-Wasserstein distance (GWD) over 100 Monte Carlo runs. GWD compares two rectangles according to the following formula:

[0166]

[0167] Where,

[0168] The common parameters of all methods are set to consistent values and the same set of measurements are provided for fair comparison.

[0169] Implementation Cases

[0170] The effects of the present invention can be illustrated by the following experiments.

[0171] In all simulation scenarios, the radar installed on the ego vehicle is located at the coordinate origin (0m, 0 m). For simplicity, it is assumed that the speed of the ego vehicle is 0m / s and the radar is facing The radar is set to ensure that the main beam is always pointed at the center of the target vehicle. Tracking a 5m×2m rectangular turning target vehicle. The initial motion state of the target vehicle is x0 = [-10, 0, -5, 0] T .

[0172] Scenario 1 (S1): In S1, the target car moves in a straight line with an approximate constant velocity (CV) motion during time steps 1-10. During time steps 11-73, it moves with a yaw rate ω k= 0.25rad / s for approximate CT motion. The measurement values are generated as follows: Regions 1-4 are Figure 1 Marked in the middle. During time steps 1-10, measurements are concentrated in regions 2, 3, and 4. During time steps 11-73, measurements are concentrated only in regions 2 and 3. The measurement values follow a uniform distribution over the surfaces of these regions, and the number of measurement values per time step follows a Poisson distribution with means 5, 7, 5, and 7 in regions 1-4, respectively. The length and width of region 1 (or region 3) are 2m and 1.5m, respectively, while the shape of region 2 (or region 4) is 5m x 0.7m.

[0173] For all compared methods, the prior mean and covariance of the motion state are set as and The initial yaw rate parameter is set to and The heading angle parameter is initialized to and

[0174] Figure 2 The trajectory estimation and shape estimation at selected time steps are shown. The sub-figures from the upper right to the lower left show the true value and expanded shape of different methods at time steps 15, 30, 45 and 60, respectively.

[0175] Figure 3 Results are presented for average GWD, center of mass position RMSE, and heading angle RMSE, averaged over 100 Monte Carlo simulations. These results demonstrate the effectiveness of EOT-SD-V in tracking vehicles with edge-concentrated measurement data. The proposed method (EOT-SD-V) provides accurate state estimates, outperforming other methods at the vast majority of time steps.

[0176] Scenario 2 (S2): S2 considers tracking a target vehicle whose trajectory is a straight line with a heading of -πrad. Assume that measurements are only generated around region 3 (the rear of the vehicle). Throughout the trajectory, the number of measurements of the rear of the vehicle follows a Poisson distribution with an average of 10 at each time step. The total number of time steps is 40, and the initial yaw rate parameter is set to and The yaw rate process noise variance is set to Other parameters and initial conditions are the same as those of S1.

[0177] Figure 4 The trajectory estimation and shape estimation at selected time steps are shown. The sub-figures from the upper right to the lower left show the true value and expanded shape estimation of different methods at time steps 13, 26 and 39, respectively.

[0178] The comparison results of S2 are as follows Figure 5 As shown in Figure 2, the results include the average GWD, RMSE of the centroid position and RMSE of the orientation angle. Figure 5 As shown in Figure 3, EOT-SD-V outperforms other methods.

[0179] The present invention proposes a radar target tracking method based on a shape-dependent hybrid model. The model utilizes prior shape information and can adapt to edge-focused radar measurements of various unknown SSF vehicles.

[0180] Based on this model, a VB estimation method is derived that analytically and recursively estimates all vehicle states. This method fully exploits the adaptability of model parameters and the stability of the model's hybrid structure. The resulting tracking method also has an analytical form, making it easy to apply in practice. Simulation results demonstrate the effectiveness of the proposed method.

[0181] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A radar target tracking method based on a shape-dependent hybrid model, characterized in that: The steps include: Step 1: Based on the measurement characteristics of the vehicle target, the vehicle exterior is divided into four rectangular sub-regions. Each rectangular sub-region is modeled as a Gaussian component that depends on the vehicle shape. The four rectangular sub-regions are described by a shape-dependent Gaussian mixture model. At the same time, a shape scaling factor is introduced, and each rectangular sub-region is regarded as the result of a one-dimensional scaling and translation of the overall vehicle shape by the shape scaling factor. Step 2: Based on the four rectangular sub-regions in step 1, a variational Bayesian method is used in combination with latent variables to jointly estimate the vehicle's motion state, heading angle state, shape state, shape scaling factor state, and hybrid weight state, and perform measurement association. Step 3: Generate simulation data through simulation experiments to verify the effectiveness of the joint estimation and measurement association in step 2.

2. The radar target tracking method based on shape-dependent hybrid model according to claim 1, characterized in that: In the step 1, each rectangular sub-region corresponds to an edge of the rectangular vehicle shape. Each rectangular sub-region is regarded as the result of scaling and translating the overall vehicle shape along the direction or perpendicular to the direction by the shape scaling factor. The shape scaling factor is modeled as a random variable and is obtained by the diagonal positive definite random matrix variable C. k Characterize all shape scaling factors.

3. The radar target tracking method based on shape-dependent hybrid model according to claim 2, characterized in that: The first step also considers estimating the vehicle motion state x k , towards the vector Φ k and shape X k , and define these variables as follows: Where, (·) T represents the matrix transpose, and are the x-coordinate and y-coordinate of the target center of mass in the Cartesian coordinate system, is the Cartesian centroid position vector; and are the velocities of the center of mass in the x-axis and y-axis directions in the Cartesian coordinate system, is the Cartesian center of mass velocity vector; the direction angle θ k represents the angle of counterclockwise rotation from the x-axis, ω k is the yaw rate; shape X k By half-length square and half-width squared parameterization; Based on the above variables and definitions, in addition to the state defined by formula (1), the newly defined state includes the state defined by C k The shape scaling factor of the representation and the mixing weight π k , to simplify the representation, all states to be estimated are represented as Θ k ={x k , Φ k , X k , C k ,π k }.

4. The radar target tracking method based on shape-dependent hybrid model according to claim 3, characterized in that: About Shape X k The content includes the following parts: S101. Assuming that the scattering centers of each rectangular sub-area are uniformly distributed and using moment matching technology to approximate the uniform distribution with a Gaussian distribution, the shape-dependent GM position measurement model can be described as: Where, is the rth Cartesian position measurement; H k is the measurement matrix; is the Cartesian centroid position vector; is the rotation matrix; is the multiplicative noise consisting of four Gaussian components and their corresponding weights; is the actual measurement noise; represents Gaussian distribution; R k is the measurement error covariance matrix; Multiplicative noise and position measurement The conditional probability density function is: Where h t and are the mean and covariance of the t-th multiplicative noise Gaussian component, both of which are related to the shape scaling factor C k Correlation; Mixed Weight for Assuming that it obeys the Dirichlet distribution, the probability density function is m k is the concentration parameter of the distribution, for The transpose of S102, using the above multiplicative noise Modeling edge concentration measurement distribution; Shape scaling factor model: Assuming that the edge concentration measurement distribution area has a symmetrical structure, the shape scaling factor can be expressed as: Where, and Half length With half width Shape scaling factor of Given the shape scaling factor C k Middle C k，1 with c k，2 The value range is (0, 1], assuming C k Obeys truncated inverse Gamma distribution; Gaussian components and shape scaling factor C k Relationship: If the scattering centers are evenly distributed over the entire rectangular vehicle surface, then the multiplicative noise Can be modeled as a Gaussian distribution in, is the scale factor, and I2 is the 2×2 identity matrix; Therefore, assuming that the scattering centers are uniformly distributed in the tth region, they can also be modeled as Gaussian distributions, and their probability density function is Mean h t and covariance It is related to the shape scaling factor of the t-th region, and the specific relationship is as follows: Where, Correspondingly, the covariance It can be described as: Where, in is the scale factor, and Half length With half width The shape scaling factor, and are the coefficients of the covariance components.

5. The radar target tracking method based on shape-dependent hybrid model according to claim 4, characterized in that: Step 2 includes the following: S201, for all states Θ at time k-1 k-1 ={x k-1 , Φ k-1 , X k-1 , C k-1 ,π k-1 The posterior probability density of} makes the following assumptions: Where, is the motion state x k-1 The mean and covariance parameters of ; is the angle vector state Φ k-1 The mean and covariance parameters of ; is the shape state X k-1 The two scale parameters of is the shape scaling factor C k-1 Two scale parameters of ; is the weight state π k-1 Concentration parameters; is the set of all measurements up to time k, and the measurement at each moment is Defined as a set of Cartesian position measurements Doppler velocity measurement set The union of N k is the number of measurement points, is the rth Doppler velocity measurement; represents Gaussian distribution; IG(·) represents inverse Gamma distribution; represents Dirichlet distribution; S202, Prediction Movement state x k The state prediction is: Where, The state transition matrix representing the motion state; The process noise covariance matrix representing the motion state; is the predicted mean and predicted covariance parameters of the motion state at time k; For the angle vector Φ k , we can get: Where, The state transition matrix representing the angle vector state; The process noise covariance matrix representing the angle vector state; is the predicted mean and predicted covariance parameters of the angle vector state at time k; Mixing weight π k Concentration parameters Through the forgetting factor Propagate as follows: Where t = 1, ..., 4, the forgetting factor is the predicted value of the concentration parameter of the weight state at time k; For shape state X k With shape scaling factor state C k , we can get: Where n = 1, 2, and X k and C k The forgetting factor; are the predicted values of the two scale parameters of the shape state at time k; are the predicted values of the two scale parameters of the shape scaling factor state at time k; S203. Measurement update based on variational Bayesian method; Based on the variational Bayesian method, the posterior probability density of all states to be estimated is Can be approached as: where q x (x k ) is the posterior probability density of the motion state; q X (X k ) is the posterior probability density of the shape state; q C (C k ) is the posterior probability density of the shape scaling factor state; q Φ (Φ k ) is the posterior probability density of the angle vector state; q π (π k ) is the posterior probability density of the weight state; In order to obtain an analytical solution, the noise-free measurement Z is introduced k and the correlation vector L k , the posterior probability density q Z (Z k ) and q L (L k ) is approximately: in, is the rth noise-free position measurement; is the mean of the rth noise-free position measurement in the previous iteration; is the covariance of the rth noise-free position measurement in the previous iteration; l r，t is the association vector corresponding to the rth measurement point associated with the tth sub-rectangle; is the probability density of association between the rth measurement point and the tth sub-rectangle; through the variational Bayesian iterative method, the above parameters can be obtained by the following formula: in, is the covariance contribution of the Doppler measurement to the noise-free measurement state; is the mean contribution of the Doppler measurement to the noise-free measurement state; is the rth true position measurement; is the estimated value of the motion state; is the inverse of the measurement error covariance; is the estimated value of the shape corresponding to the t-th sub-rectangle; is the unnormalized association probability density parameter; is the distance from the centroid of the t-th sub-rectangle to the target centroid; x k , Φ k and π k The posterior probability density of is approximately: Where, Where, G3=[0,1]; G4=[1,0]; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of Doppler velocity measurement to the motion state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the Doppler velocity measurement to the angular velocity state; is the covariance contribution of the position measurement to the heading angle; is the mean contribution of position measurement to the heading angle; is the predicted value of the motion state; is the predicted value of the heading vector; is the predicted covariance matrix of the motion state; is the predicted covariance matrix of the orientation vector; is the predicted value of the concentration parameter; X k The posterior probability density of is approximately: In the formula, the estimated parameters are: in, are the predicted values of the two scale parameters of the shape state at time k; is the probability density of association when the rth measurement point is associated with the tth sub-rectangle; γ k is the contribution of other estimated states except the shape state to the shape scale parameter; For the shape scaling factor state C k , we can get: The estimated parameters are: Where, are the predicted values of the two scale parameters of the shape scaling factor state at time k; is the association probability density when the rth measurement point is associated with the tth sub-rectangle; is the contribution of other estimated states except the shape scaling factor state to the scale parameter of the shape scaling factor when the rth measurement point is input.

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