Radar extended target constraint filtering method

Abstract

The invention relates to a radar extended target constraint filtering method, which comprises the steps of S1, constructing an orientation vector through sine and cosine terms of an orientation angle, and modeling the orientation vector by adopting truncated Gaussian distribution, S2, deducing OVB course constraint based on a relationship between the orientation vector and a velocity vector, S3, integrating the OVB course constraint into a VB estimation framework by constructing a pseudo measurement value, and obtaining a VB course constraint model. And S4, verifying the effectiveness of the estimation of the VB estimation framework through simulation experiment comparison by applying a projection method in the VB estimation framework and then adopting the VB estimation framework to carry out estimation. The method has the advantage of high-precision tracking.

Description

Technical Field

[0001] The invention belongs to the technical field of target tracking, and in particular relates to a radar extended target constraint filtering method. Background Art

[0002] In recent years, with the advancement of technology, the resolution of radar sensors has significantly improved. The traditional point target assumption is no longer applicable in many practical applications (such as autonomous driving) because the target scattering center may generate multiple measurements. In this case, the target must be considered an extended object (EO). The method of tracking using multiple measurements is called extended object tracking (EOT). EOT not only estimates the target's motion state but also its extended form (including orientation and size).

[0003] The tight constraint between the heading angle (i.e., the velocity direction of the target's center of mass) and the heading angle contains information about the motion state and extended form. To effectively utilize this information for estimation, modeling the heading constraint is crucial. Existing methods generally do not fully utilize the heading constraint for extended target tracking. In addition, existing methods often directly estimate the heading angle as a state or parameter. However, the heading angle has periodic characteristics and is angular data. Due to the difference in the value range of the heading angle and the heading angle, the heading constraint based on the heading angle may not hold, leading to estimation problems. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a radar extended target constraint filtering method with high-precision tracking.

[0005] The technical solutions of the present invention are as follows:

[0006] A radar extended target constraint filtering method comprises the following steps:

[0007] S1. Construct the heading vector by the sine and cosine terms of the heading angle and model it using a truncated Gaussian distribution.

[0008] S2. Based on the relationship between the heading vector and the velocity vector, derive the OVB heading constraint;

[0009] S3, integrating the pseudo measurement equation into the VB estimation framework by constructing pseudo measurement values, and estimating the state within the VB estimation framework;

[0010] S4. The effectiveness of the VB estimation framework was verified through simulation experiments.

[0011] Furthermore, the specific contents of S1 include the following steps:

[0012] S11, the EO state ξ k From the kinematic state x k 、Size X k and the orientation vector ε k Description, that is Kinematic state x k 、Size X k and the orientation vector ε k As shown below:

[0013]

[0014] in,(·) T represents the matrix transpose, is the coordinate of the center of mass position, is the Cartesian velocity vector, size X k Modeled by the inverse gamma distribution, for the ellipse EO, and represents the square of the semi-axis length, θ k Indicates the orientation angle;

[0015] S12, based on the orientation vector ε k Models a truncated Gaussian distribution vector with the following probability density function:

[0016]

[0017] Where, represents a truncated Gaussian distribution, and are the mean and covariance of the truncated Gaussian distribution, and are the mean and covariance of the "parent" Gaussian distribution, For E k The indicator function, is the corresponding normalization factor, E k Specifies the support domain of the truncated Gaussian distribution, that is, the region that satisfies the following nonlinear constraints:

[0018]

[0019] Where ||·II represents the 2-norm, ε k Each independent sample point can be regarded as a Gaussian probability density that obeys the above constraints Generated sample points.

[0020] Furthermore, the specific contents of step S2 include the following steps:

[0021] S21. Set the heading constraint equation to describe the heading angle θ kand heading angle γ k The interdependencies are as follows;

[0022]

[0023] Where, is Gaussian noise, is the noise covariance, arctan2 refers to the four-quadrant inverse tangent function, is the Cartesian velocity vector;

[0024] S22. Write the heading constraint equation equivalently in the form of a pseudo-measurement equation:

[0025]

[0026] Where, ε k =[cos(θ k ), sin(θ k )] T ; is x k Cartesian velocity vector of ; 0 m×n is an m×n zero matrix;

[0027] S23. At time step k, assume a set of N k Measurement value For filtering, is the rth 2-dimensional Cartesian position measurement, where and The measured coordinate values on the x-axis and y-axis are respectively. In radar sensor applications, since the r-th polar coordinate measurement includes the measured distance and direction The rth radar position measurement can be obtained by using the standard coordinate transformation, that is, and Assuming that each position measurement source is located on the surface of the elliptical object and obeys a uniform spatial distribution, the new measurement model is:

[0028]

[0029] Where H k is the measurement matrix; Gaussian noise that takes into account both dimensional uncertainty and true measurement noise; is the rotation matrix; X k is the size state; λ = 1 / 4 is the scale parameter; R k is the covariance of the actual measurement noise, for The transpose of .

[0030] Furthermore, pseudo-measurement values are constructed and integrated into the VB estimation framework, which includes the following steps:

[0031] S31. By using the matched linearization method, the measurement equation can be rewritten as:

[0032]

[0033] Where D k is the estimated value of the extended target shape, B k is the noise transformation matrix; Measuring noise for extended morphology;

[0034] S32. Get the real measurement Z k Likelihood function of :

[0035]

[0036] Where, For B k The transpose of And Z k is the real measurement set, and y0 = 0 is the pseudo measurement;

[0037] S33: Confirm the likelihood function based on step S32 It can be expressed as:

[0038]

[0039] S33, at time step k, receive Z k Previously, all available measurement information was contained in Z k-1 In order to achieve the design of recursive filters, the following general assumptions are made for this method:

[0040]

[0041] Where, is the motion state x k-1 The mean and covariance parameters of ; For size status X k-1 Two scale parameters of ; are the angle vector states ε k-1 The mean and covariance parameters of ;

[0042] For the heading constraint model, the kinematic state x can be obtained k and size status X k The predicted probability density function of :

[0043]

[0044] Where,

[0045]

[0046] in, 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 X k The forgetting factor; are the predicted values of the two scale parameters of the size state at time k;

[0047] For ε k , the predicted density is assumed to be:

[0048]

[0049] Each sample point of the truncated Gaussian distribution in the above formula can be regarded as Generate sample points that satisfy the constraints, so the above formula can be equivalently expressed as:

[0050]

[0051] Therefore, a two-stage estimation scheme is used to obtain the predicted parameters of the angle vector. In the first stage: Under the assumption of , we deduce the analytical results to obtain the parameters Phase 2: Applying the constraint ||ε k || 2 =1 determines the constraint parameters with constraints

[0052] Furthermore, based on the VB estimation framework and the measurement update of the pseudo-measurement equation, the estimated values of the motion state, size and orientation vector state are output. The specific steps include steps S31-S34, and also include the following content:

[0053] The factorized approximation of the posterior probability density is:

[0054] p(ξ k |Z k )≈q x (x k )q X (X k )q ε (ε k ) (20)

[0055] where q x (x k ) is the posterior probability density of the motion state; qx (X k ) is the posterior probability density of the shape state; q ε (ε k ) is the posterior probability density of the angle vector state; they can be expressed as:

[0056]

[0057] Where,

[0058]

[0059] in,

[0060]

[0061] in, is the contribution of other states to the covariance of the angle vector state except the angle vector state;

[0062] In addition, to satisfy the constraint ||ε k || 2 =1, the mean and covariance of the angle vector state are modified as follows:

[0063]

[0064]

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. The present invention introduces the heading vector into state space modeling and combines it with constraints based on the heading vector to establish a constraint relationship model between the heading angle and the heading angle. This not only significantly improves the performance of state estimation, but also effectively solves the common ambiguity problem in the heading angle estimation process.

[0067] 2. This paper proposes an OVB EOT model. This model introduces a heading vector as a state variable and combines it with an OVB heading constraint to describe the constraint relationship between the heading angle and the heading vector. The heading vector is modeled using a truncated Gaussian distribution.

[0068] 3. The present invention adopts the variational Bayesian (VB) method to realize state estimation, and integrates the heading-based constraint equation into the VB framework through the pseudo-measurement method.

[0069] 4. The present invention uses the projection method to perform OVB constraint estimation, so that the truncated Gaussian distribution can be naturally integrated into the VB framework.

[0070] 5. Through simulation experiments, the present invention verifies the effectiveness of the proposed model and algorithm compared with the existing orientation-based EOT algorithm.

[0071] In summary, the present invention has the advantage of high-precision tracking of extended targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 A diagram showing the relationship between the heading angle and the course angle in the method of the present invention;

[0073] Figure 2 is the truncated Gaussian distribution graph in the method of the present invention;

[0074] Figure 3 is the trajectory and shape estimation graph of S1 at the selected time step in the method of the present invention;

[0075] Figure 4 Figure 1 shows the EO estimation results of S1 in the method of the present invention, including (a) average GWD; (b) RMSE of center of mass position; (c) RMSE of center of mass velocity; (d) RMSE of heading angle; (e) true value and estimated result of semi-axis length 1; (f) true value and estimated result of semi-axis length 2.

[0076] Figure 5 Figure 1 shows the EO estimation results of S2 in the method of the present invention, including (a) average GWD; (b) RMSE of center of mass position; (c) RMSE of center of mass velocity; (d) RMSE of heading angle; (e) true value and estimated result of semi-axis length 1; (f) true value and estimated result of semi-axis length 2.

[0077] Figure 6 It is the trajectory and shape estimation diagram of S2 at the selected time step in the method of the present invention. DETAILED DESCRIPTION

[0078] 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.

[0079] like Figures 1 to 6 As shown, a radar extended target constraint filtering method includes the following steps:

[0080] Step 1: Model the orientation vector based on the truncated Gaussian distribution:

[0081] A.EO status

[0082] This paper mainly studies the single ellipse EOT problem. k From the kinematic state x k 、Size X kand the orientation vector ε k Description, that is Kinematic state x k 、Size X k and the orientation vector ε k As shown below:

[0083]

[0084] in,(·) T represents the matrix transpose, is the coordinate of the center of mass position, is the Cartesian velocity vector, size X k Modeled by the inverse gamma distribution, for the ellipse EO, and represents the square of the semi-axis length, θ k Indicates the orientation angle.

[0085] B. State Modeling

[0086] 1) Probability distribution of orientation vector and rotation matrix

[0087] Towards vector ε k can be modeled as a truncated Gaussian distribution vector with the following probability density function:

[0088]

[0089] Where, represents a truncated Gaussian distribution, and are the mean and covariance of the truncated Gaussian distribution, and are the mean and covariance of the "parent" Gaussian distribution, For E k The indicator function, is the corresponding normalization factor, E k Specifies the support domain of the truncated Gaussian distribution, that is, the region that satisfies the following nonlinear constraints:

[0090]

[0091] In the formula, ||·|| represents the 2-norm, ε k Each independent sample point can be regarded as a Gaussian probability density that obeys the above constraints Generated sample points;

[0092] Shaped by Given, and X k The predetermined density is given by:

[0093]

[0094] In the formula, IG(δ;a,b)=b a δ -a-1 exp(-bδ -1 )Γ -1 (a) indicates The inverse Gamma distribution has a shape parameter of The scale parameter is For the ellipse EO, and represents the square of the semi-axis length, assuming For X k The parameters at the k-1th time step are and Predictable and For the forgetting factor;

[0095] The diagram of the truncated Gaussian distribution is as follows Figure 2 As shown. Among them, ε k Each independent sample point can be regarded as a Gaussian probability density that obeys the above constraints Generated sample points.

[0096] Step 2: Derivation of OVB heading constraint based on the relationship between heading vector and velocity vector:

[0097] A. Derivation of Heading Constraints

[0098] Set the heading constraint equation to describe the heading angle θ k and heading angle γ k The interdependencies are as follows;

[0099]

[0100] Where, is Gaussian noise, is the noise covariance, arctan2 refers to the four-quadrant inverse tangent function, is the Cartesian velocity vector;

[0101] The heading constraint equation is equivalently written as a pseudo-measurement equation:

[0102]

[0103] Where, ε k =[cos(θ k ), sin(θ k )] T ; is x kThe Cartesian velocity vector of ; Om×n is the m×n zero matrix;

[0104] B. New measurement model

[0105] At time step k, suppose a set of N k Measurement value For filtering, is the rth 2-dimensional Cartesian position measurement, where and The measured coordinate values on the x-axis and y-axis are respectively. In radar sensor applications, since the r-th polar coordinate measurement includes the measured distance and direction The rth radar position measurement can be obtained by using the standard coordinate transformation, that is, and Assuming that each position measurement source is located on the surface of the elliptical object and obeys a uniform spatial distribution, the new measurement model is:

[0106]

[0107] Where H k is the measurement matrix; Gaussian noise that takes into account both dimensional uncertainty and true measurement noise; is the rotation matrix; X k is the size state; λ = 1 / 4 is the scale parameter; R k is the covariance of the actual measurement noise, for The transpose of .

[0108] Step 3: Heading constraint integration based on VB:

[0109] A. Likelihood Function

[0110] By using the matched linearization method, the measurement equation can be rewritten as:

[0111]

[0112] Where D k is the estimated value of the extended target shape; and are the one-step prediction values of the orientation vector and size at time step k, respectively, B k is the noise transformation matrix; Measuring noise for extended morphology;

[0113] In this way, the actual measurement Z k The likelihood function is:

[0114]

[0115] Where, For B k The transpose of And Z k is the true measurement set, and y0=0 is the pseudo measurement; therefore, the likelihood function It can be expressed as:

[0116]

[0117] The above equation can provide information about the motion state x k and the orientation vector ε k constraint information.

[0118] B. Prediction

[0119] At time step k, we receive Z k Previously, all available measurement information was contained in Z k-1 In order to achieve the design of recursive filters, the following general assumptions are made for this method:

[0120]

[0121] Where, is the motion state x k-1 The mean and covariance parameters of ; For size status X k-1 Two scale parameters of ; are the angle vector states ε k-1 The mean and covariance parameters of .

[0122] For the heading constraint model, the kinematic state x can be obtained k and size status X k The predicted probability density function of :

[0123]

[0124] Where,

[0125]

[0126] in, 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 X k The forgetting factor; are the predicted values of the two scale parameters of the size state at time k;

[0127] For ε k , the predicted density is assumed to be:

[0128]

[0129] Each sample point of the truncated Gaussian distribution in the above formula can be regarded as Generate sample points that satisfy the constraints, so the above formula can be equivalently expressed as:

[0130]

[0131] Therefore, a two-stage estimation scheme is adopted to obtain the predicted parameters of the angle vector. The first stage: Under the assumption of , we deduce the analytical results to obtain the parameters Phase 2: Applying the constraint ||ε k |‖ 2 =1 determines the constraint parameters with constraints

[0132] C. Measurement Update Based on Variational Bayesian Method

[0133] EOT aims to estimate the state ξ of the target k The traditional method assumes that the semi-axis length follows a Gaussian distribution and uses the extended Kalman filter (EKF) to solve the posterior density. However, in this paper, the square of the semi-axis length (given by X k (denoted) is modeled as an inverse Gamma distribution, and there is a constraint relationship between the state parameters, resulting in the posterior density p(ξ k |Z k ) is difficult to calculate. Since the VB framework has significant advantages in dealing with complex posterior densities, the VB method can be used to seek an approximate analytical solution.

[0134] The factorized approximation of the posterior probability density of all states to be estimated is:

[0135] p(ξ k |Z k )≈q x (x k )q x (X k )q ε (ε k ) (twenty one)

[0136] 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 ε (εk ) is the posterior probability density of the angle vector state; they can be expressed as:

[0137]

[0138] Where,

[0139]

[0140] in,

[0141]

[0142] in, is the contribution of other states to the covariance of the angle vector state except the angle vector state.

[0143] In addition, to satisfy the constraint ||ε k || 2 =1, the mean and covariance of the angle vector state are modified as follows:

[0144]

[0145] The algorithm in this paper that uses pseudo-measurements is called "EOT-OV." For comparison, the algorithm that does not use pseudo-measurements is called "EOT-OV0." The proposed algorithm recursively outputs estimates of the motion state, size, and orientation vector state through multiple iterations. Due to the universal nature of the VB method, the iterative process converges.

[0146] Step 4: Simulation experiment verification and algorithm performance comparison analysis:

[0147] The proposed algorithms (EOT-OV and EOT-OV0) will be compared with the most advanced orientation-based EOT algorithms EOT-OA and MEM-EKF*. m The root-mean-square errors (RMSEs) of the target's centroid position and orientation angle in Monte Carlo (MC) and the average Gaussian-Wasserstein distances (GWDs) between the joint centroid position and the extended shape estimate are included.

[0148] Implementation Cases

[0149] The effects of the present invention can be illustrated by the following experiments.

[0150] In the simulation, an ellipse EO with a semi-axis length of 2m and 1m is considered to move at a constant speed of 8.3m / s.

[0151] The measurement values for each time step are generated from a uniform distribution. The number of measurement values follows a Poisson distribution with a mean of 10 and the time interval T is set to 0.1s. The comparison results are based on N m = 100 Monte Carlo experiments. The noise covariance in all measurement models is set to Rk = 0.1 2 I2. The initial motion state is Covariance These parameter settings apply to all algorithms.

[0152] Scenario 1 (S1): This scenario considers a direction angle of The ellipse EO moves along a straight line. All trackers provide the same motion parameters.

[0153] Figure 3 The estimated trajectory and expanded morphology of the selected time step in scenario 1 (S1) are shown. The comparison results of S1 are as follows Figure 4 As shown, it includes average GWDs, center of mass position RMSEs, center of mass velocity RMSEs, orientation angle RMSEs, semi-axis length 1 and semi-axis length 2. Figure 4 As shown in Figure 2, the proposed method (EOT-OV) has significant tracking advantages. EOT-OV using constraint (17) can effectively estimate the motion state and extended form of the target and shows the best overall performance in terms of average GWDs. EOT-OV solves the initial parameter mismatch problem caused by highly uncertain scenarios, thereby enhancing its adaptability and practicality. In contrast, algorithms that do not consider this constraint (such as MEM-EKF*, EOT-OV0 and EOT-OA) may produce poor results, with their major and minor axis estimates interchanged (such as Figure 4 e and Figure 4 f), and the estimated value of the direction angle deviates from the true value (like Figure 4 d).

[0154] Scenario 2 (S2): In Scenario 2 (S2), it is assumed that the target has high maneuverability. EO starts from the coordinate origin and faces an angle of The entire trajectory contains three turns, and their yaw rates are (Time steps 12-26), (time steps 38-62) and (Time steps 74-103). When the target moves in a straight line, the velocity direction and heading angle are consistent. During the three turns, the angles between the velocity direction and heading are set to 0.0678 rad, 0.0813 rad, and 0.0678 rad, respectively.

[0155] Figure 5The estimated results of the average GWD, center of mass position RMSE, center of mass velocity RMSE, orientation angle RMSE, semi-axis length 1 and semi-axis length 2 of each algorithm are shown. Figure 6 The true value and ellipse shape estimation of all algorithms are shown. Figure 5 As shown, all algorithms achieve similar performance in estimating center of mass position and center of mass velocity. EOT-OV and EOT-OV0 outperform EOT-OA and MEM-EKF* in estimating heading angle and extended shape (measured by the GWD metric). EOT-OV also outperforms EOT-OV0 because it considers the OVB heading constraint in its filtering, while the latter does not. These results demonstrate that EOT-OV effectively utilizes the constraint for estimation, validating the effectiveness of the proposed EOT modeling and estimation method based on the OVB heading constraint.

[0156] This paper proposes a constrained filtering method for radar extended targets. By incorporating a heading vector into state-space modeling and combining it with OVB constraints, this method establishes a constrained relationship model between heading angles and heading angles. Compared with existing methods, the proposed method not only significantly improves estimation performance but also effectively resolves common ambiguities in heading angle estimation, providing a reliable solution for high-precision tracking of extended targets.

[0157] 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 extended target constraint filtering method, characterized by: The steps include: S1. Construct the heading vector by the sine and cosine terms of the heading angle and model it using a truncated Gaussian distribution. S2. Based on the relationship between the heading vector and the velocity vector, derive the OVB heading constraint; S3, integrating the pseudo measurement equation into the VB estimation framework by constructing pseudo measurement values, and estimating the state within the VB estimation framework; S4. The effectiveness of the VB estimation framework was verified through simulation experiments.

2. The radar extended target constraint filtering method according to claim 1, wherein: The specific contents of S1 include the following steps: S11, the EO state ξ k From the kinematic state x k 、Size X k and the orientation vector ε k Description, that is Kinematic state x k 、Size X k and the orientation vector ε k As shown below: in,(·) T represents the matrix transpose, is the coordinate of the center of mass position, is the Cartesian velocity vector, size X k Modeled by the inverse gamma distribution, for the ellipse EO, and represents the square of the semi-axis length, θ k Indicates the orientation angle; S12, based on the orientation vector ε k Models a truncated Gaussian distribution vector with the following probability density function: Where, represents a truncated Gaussian distribution, and are the mean and covariance of the truncated Gaussian distribution, and are the mean and covariance of the "parent" Gaussian distribution, For E k The indicator function, is the corresponding normalization factor, E k Specifies the support domain of the truncated Gaussian distribution, that is, the region that satisfies the following nonlinear constraints: In the formula, ||·|| represents the 2-norm, ε k Each independent sample point can be regarded as a Gaussian probability density that obeys the above constraints Generated sample points.

3. The radar extended target constraint filtering method according to claim 2, wherein: The specific contents of step S2 include the following steps: S21. Set the heading constraint equation to describe the heading angle θ k and heading angle γ k The interdependencies are as follows; Where, is Gaussian noise, is the noise covariance, arctan2 refers to the four-quadrant inverse tangent function, is the Cartesian velocity vector; S22. Write the heading constraint equation equivalently in the form of a pseudo-measurement equation: Where, ε k =[cos(θ k ), sin(θ k )] T ; is x k Cartesian velocity vector of ; 0 m×n is an m×n zero matrix; S23. At time step k, assume a set of N k Measurement value For filtering, is the rth 2-dimensional Cartesian position measurement, where and The measured coordinate values on the x-axis and y-axis are respectively. In radar sensor applications, since the r-th polar coordinate measurement includes the measured distance and direction The rth radar position measurement can be obtained by using the standard coordinate transformation, that is, and Assuming that each position measurement source is located on the surface of the elliptical object and obeys a uniform spatial distribution, the new measurement model is: Where H k is the measurement matrix; Gaussian noise that takes into account both dimensional uncertainty and true measurement noise; is the rotation matrix; X k is the size state; λ = 1 / 4 is the scale parameter; R k is the covariance of the actual measurement noise, for The transpose of .

4. The radar extended target constraint filtering method according to claim 3, wherein: Constructing pseudo-measurements and integrating them into the VB estimation framework involves the following steps: S31. By using the matched linearization method, the measurement equation can be rewritten as: Where D k is the estimated value of the extended target shape; B k is the noise transformation matrix; Measuring noise for extended morphology; S32. Get the real measurement Z k Likelihood function of : Where, B k The transpose of And Z k is the real measurement set, and y0 = 0 is the pseudo measurement; S33: Confirm the likelihood function based on step S32 It can be expressed as: S34, at time step k, receive Z k Previously, all available measurement information was contained in Z k-1 In order to achieve the design of recursive filters, the following general assumptions are made for this method: Where, is the motion state x k-1 The mean and covariance parameters of ; For size status X k-1 Two scale parameters of ; are the angle vector states ε k-1 The mean and covariance parameters of ; For the heading constraint model, the kinematic state x can be obtained k and size status X k The predicted probability density function of : Where, in, 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; n = 1, 2, For X k The forgetting factor; are the predicted values of the two scale parameters of the size state at time k; For ε k , the predicted density is assumed to be: Each sample point of the truncated Gaussian distribution in the above formula can be regarded as Generate sample points that satisfy the constraints, so the above formula can be equivalently expressed as: Therefore, a two-stage estimation scheme is used to obtain the predicted parameters of the angle vector. In the first stage: Under the assumption of , we deduce the analytical results to obtain the parameters Phase 2: Applying the constraint ||ε k || 2 =1 determines the constraint parameters with constraints 5. The radar extended target constraint filtering method according to claim 4, characterized in that: Based on the VB estimation framework and the measurement update of the pseudo-measurement equation, the estimated values of the motion state, size and orientation vector state are output. The specific steps include steps S31-S34, and also include the following content: The factorized approximation of the posterior probability density is: p(ξ k |Z k )≈q x (x k )q x (X k )q ε (ε k ) (20) 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 ε (ε k ) is the posterior probability density of the angle vector state; they can be expressed as: Where, in, in, is the contribution of other states to the covariance of the angle vector state except the angle vector state; In addition, to satisfy the constraint ||ε k || 2 = 1 to modify the mean and covariance of the angle vector state as follows:

Images