A method for integrated estimation of radar cluster target shape, size and centroid state

Abstract

The application discloses a radar cluster target shape scale and centroid state integrated estimation method, first sets algorithm parameters and initial intensity, carries out signal processing on radar echo to obtain measurement with amplitude information at k time, then after all Gaussian Gamma components in the posterior intensity at k-1 time are predicted, the prior intensity at k time is obtained, then the intensity is updated by using the combined measurement with amplitude to obtain the posterior intensity at k time, finally the centroid state, shape contour and contained individual number of the cluster target at k time are extracted according to the weight in the posterior intensity at k time, integrated estimation of the radar cluster target shape scale and centroid state is realized. The method of the application regards the cluster target as a whole, and the contained individual number and shape parameters are included in the state, integrated estimation is carried out under the Bayesian filtering framework, and the integrated estimation problem of the centroid state, contained individual number and arbitrary and time-varying shape of the indistinguishable cluster target is solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar multi-target tracking, and particularly relates to a method for integrated estimation of the shape and size of a radar cluster target and the centroid state. BACKGROUND

[0002] In various urban and natural environments, cluster targets have arbitrary and time-varying shapes, involving many individuals that are close in distance (relative to radar resolution), consistent in size, and similar in motion. Such targets include biological groups (such as birds, fish), crowds of people, and groups of unmanned aerial vehicles, etc. The indistinguishable, arbitrary, and time-varying shape caused by the density of the cluster target makes cluster target tracking challenging. In addition, biological cluster detection is of great significance to facility collision avoidance, agricultural disaster warning, and biological research; the tracking of unmanned aerial vehicle groups with clustering, autonomy, and intelligence is also crucial in multi-agent systems, distributed control, and information fusion. In order to evaluate the situation of various cluster targets, we usually need to estimate their centroid state, density, shape, cardinality (i.e. the number of individuals included), etc. Therefore, cluster target tracking has important significance and application in civil use.

[0003] Existing group target tracking algorithms usually focus on two types of targets: resolvable group targets and non-resolvable group targets. In resolvable group target tracking, most methods model the group structure by focusing on the interaction between individuals in the cluster; in non-resolvable group target tracking, individuals are usually treated as a whole, similar to extended target tracking, which usually focuses on estimating the cluster shape and centroid state rather than individual target state. The literature "Liu W, Zhu S, Wen C, et al. Structure modeling and estimation of multiple resolvable group targets via graph theory and multi-Bernoulli filter. Automatica, 2018, 89: 274-289." proposes a motion model for group targets, derives the relationship between individuals based on graph theory, and uses this relationship to correct the cooperative noise and estimate the target state, but this method cannot estimate the cluster shape. The literature "Wang Y, Hu G, Zhou H. Group targets tracking using multiple models GGIW-CPHD based on best-fitting Gaussian approximation and strong tracking filter. Journal of Sensors, 2016, 2016." considers modeling the cluster shape as an ellipse and filtering estimation, and proposes a multiple model best-fitting Gaussian approximation method to solve target maneuvering, but this method is difficult to handle the case where individuals cannot be distinguished. CN 114740467 A discloses a group target tracking and number, outline dynamic estimation method based on radar amplitude track points, which assumes that the cluster shape is an ellipse and uses post-processing to extract, but the ellipse assumption is relatively limited, the calculation is large and depends on the performance of the clustering algorithm. Therefore, the above methods can only estimate part of the information of the group target, and cannot integrally estimate all the information of the group target. SUMMARY

[0004] To solve the above technical problems, the present application provides a radar group target shape and size integrated estimation method, which can solve the problem that existing group target tracking algorithms cannot integrally estimate the centroid state (including position, velocity, etc.), shape and size of the group target, and thus fully perceive the situation of the group target.

[0005] The technical scheme adopted by the present application is: a radar group target shape and size integrated estimation method, the specific steps are as follows:

[0006] S1, set algorithm parameters, initialize initial intensity;

[0007] S2, signal processing is carried out on the radar echo to obtain the measurement of the band amplitude information at time k;

[0008] Firstly, the radar observes the cluster target and obtains the radar echo data at time k. Then, after the echo data is processed through the radar signal processing procedures including data correction, pulse compression, MTD processing, constant false alarm detection, and DOA estimation, the measurement of the band amplitude information at time k is obtained. Finally, the polar coordinate measurement is converted to the rectangular coordinate system, and the measurement is divided.

[0009] S3, based on the target survival probability, the motion process and the shape change process of the cluster target, and the exponential forgetting factor of the Gamma distribution, a joint state Markov transition equation of the cluster target is obtained, the weight of the Gaussian Gamma component, the Gaussian part and the Gamma part are predicted respectively, and after all the Gaussian Gamma components contained in the posterior intensity function at time k-1 are predicted, the prior intensity function at time k is obtained;

[0010] Wherein, the weight represents the expectation of the number of targets, the Gaussian part includes the centroid state and the shape contour information of the cluster target, and the Gamma part includes the target number information contained in the cluster target.

[0011] S4, based on the joint likelihood function, the position information of the measurement and the Gaussian process regression, the amplitude information of the measurement and the Gamma distribution, the weight of the Gaussian Gamma component, the Gaussian part and the Gamma part are updated respectively, and after all the Gaussian Gamma components contained in the prior intensity function at time k are updated, the posterior intensity function at time k is obtained;

[0012] Wherein, the shape contour of the cluster is modeled as a star-convex shape, the radial distance at a preset angle is taken as the shape parameter to describe the contour, the measurement is taken as the training set, and the update of the shape parameter is recursively estimated by using the Gaussian process regression in the field of machine learning; the individuals contained in the cluster are equivalent to the measurement sources, and the number of individuals is recursively estimated by using the conjugate property of the Poisson distribution and the Gamma distribution.

[0013] S5, the cluster target state and the shape size at time k, i.e., the joint state of the cluster target, are extracted according to the weight of the Gaussian Gamma component in the posterior intensity function at time k, so as to realize the integrated joint estimation of the shape size and the centroid state of the radar cluster target;

[0014] S6. Use the posterior intensity function at time k as the input at time k+1 for the next iteration, and repeat steps S2 to S5 until the tracking process ends.

[0015] Furthermore, step S1 is specifically as follows:

[0016] S11. Set the algorithm parameters according to the scenario, and then set the expansion state of the cluster target at time k as follows:

[0017]

[0018] Among them, superscript Indicates matrix transpose; This represents the concatenated vector of the cluster target centroid state and the radial distance vector. Indicates the centroid state of the cluster target. This indicates the position of the centroid, i.e., the x and y coordinates. ψ represents the velocity of the center of mass. k Indicates the orientation angle. Indicates the yaw rate. Indicates the radial distance at a preset angle. Represents the radial distance vectors at L preset angles. This represents the i-th preset angle. This represents the corresponding radial distance, i.e., the distance from the outer contour to the center position, γ. k This indicates the number of individuals included.

[0019] S12. The initial intensity function is initialized as follows:

[0020]

[0021] Where ξ represents the cluster target state. This represents a Gaussian distribution with parameters m and P. This represents a Gamma distribution with parameters α and β. J represents a Gaussian Gamma component. 0|0 This represents the initial number of Gaussian Gamma components. J 0|0 , It can be obtained from the number of cluster targets and the initial state.

[0022] Furthermore, step S2 is specifically as follows:

[0023] S21. Set the individual target position at time k as... The location measurement space is divided into a set of disjoint, resolvable units. After mapping the positions of each volume to the position measurement space through the position measurement function h(y), the position of the volume falling into the resolving cell c at time k is obtained. i The set of individuals Tk,i The expression is as follows:

[0024] T k,i = {y k | y k ∈ Y k , h(y k ) ∈ c i} (2)

[0025]

[0026] where p k,x , p k,y represent the x, y axis coordinates respectively; N c represents the number of resolution cells, Y k represents the individual set at time k.

[0027] S22, each resolution cell generates a measurement with amplitude information according to T k,i with detection probability p D (T k,i ), and the expression is as follows:

[0028]

[0029] where the superscript P represents polar coordinates, ρ k,i , φ k,i , a k,i represent the distance, azimuth angle and amplitude of the measurement respectively, and the measurement position expression is as follows:

[0030]

[0031] where the measurement noise represents a Gaussian distribution with mean 0 and covariance ; the measurement amplitude a k,i is a positive random variable, and its distribution is represents the hypothesis that there are |T k,i | individuals in the resolution cell c i .

[0032] S23, set the clutter position to be uniformly distributed in the position measurement space, the number of clutters to be subject to a Poisson distribution, the clutter amplitude distribution to be p(a k |H0), and the clutters not to fall into the same resolution cell as the real target. Finally, the measurement set with amplitude information obtained by the radar at time k is

[0033] where the clutter RFSK k represents the clutter set at time k.

[0034] S24, polar coordinate measurement set Convert to Cartesian coordinate measurement set

[0035] where N denotes the number of measurements, superscript C denotes the Cartesian coordinates. Then measurement partitioning is performed, denotes the partitioning of into a series of non-empty subsets W.

[0036] Further, the step S3 is specifically as follows:

[0037] S31, based on steps S1-S2, the posterior intensity function D k-1|k-1 (ξ k-1 ) is expressed as follows:

[0038]

[0039] where J k-1|k-1 denotes the number of Gaussian Gamma components at time k-1, respectively denote the weight, mean, covariance and Gamma distribution parameters of the jth component.

[0040] S32, the prior intensity function D k|k-1 (ξ k ) at time k is expressed as follows:

[0041]

[0042] where, denotes the newborn term given by the starting algorithm, denotes the surviving term, and the expression is as follows:

[0043]

[0044] Based on the target survival probability:

[0045]

[0046] where p S denotes the survival probability.

[0047] Based on the cluster target motion process and shape change process:

[0048]

[0049] where blkdiag denotes the block diagonal operation, F m , Q mis determined by the flocking motion model. The shape evolution parameter expression is as follows:

[0050]

[0051] wherein κ represents a forgetting factor, T s represents a sampling time interval, I L represents an L-order unit matrix, and K(θ f ,θ f ) is obtained according to the recursive form of the Gaussian process regression expression as follows:

[0052]

[0053] wherein θ represents a preset angle vector, represents a signal amplitude prior variance, and l represents a length scale.

[0054] An exponential forgetting factor based on a Gamma distribution is obtained as follows:

[0055]

[0056] wherein η k represents an exponential forgetting factor.

[0057] Further, the step S4 is specifically as follows:

[0058] S41, write the prior intensity function at the k moment in step S32 into a Gaussian Gamma mixed form, and the expression is as follows:

[0059]

[0060] wherein J k|k-1 represents the number of predicted Gaussian Gamma components at the k moment, respectively represent the weight, mean value, covariance and Gamma distribution parameter of the jth component.

[0061] S42, the posterior intensity function D k|k (ξ k ) at the k moment is expressed as follows:

[0062]

[0063] wherein represents the measurement set of the Cartesian coordinate system obtained in step S24. The missed detection item is the same as the prior intensity except that the weight is different, and the weight expression of D (ξ

[0064] ) is as follows:

[0065] Detection item The expression is as follows:

[0066]

[0067] Based on the measurement-based position information and Gaussian process regression, the following is obtained:

[0068]

[0069] Wherein:

[0070]

[0071] Wherein, I represents a unit matrix; represents the ith measurement in W, μ s represents the measurement distribution proportion mean, represents the direction vector, represents the mean of the jth target shape parameter, represents the ith preset angle thereof. And the radar measurement model and the Gaussian process recursion are both nonlinear models, then a first-order approximation is performed by using an extended Kalman filter, and the expression is as follows:

[0072]

[0073] Wherein, represents the measurement distribution proportion covariance.

[0074] Based on the measurement-based amplitude information and Gamma distribution, the following is obtained:

[0075]

[0076] Wherein, Ω represents the number of measurement sources of the cluster, that is, the number of individuals included, and the calculation formula is:

[0077]

[0078] Wherein, the calculation formula of Ω is given by the total probability formula, according to the conditional probability of the measurement amplitude, the possible that the merging measurement may come from r individuals is traversed; and the calculation formula of p(r|a) is obtained by the Bayes formula. R represents the maximum value of the individual targets that each resolution unit may include, which can be set according to the density of the cluster and the radar resolution.

[0079] Based on the joint likelihood function, the following is obtained:

[0080]

[0081] Wherein:

[0082]

[0083] Wherein, This represents the detection probability of the j-th target. λ represents the measurement in Cartesian coordinates. k c represents the clutter rate. k (z k ) represents the clutter distribution density at a given measurement location.

[0084] False alarms may occur when multiple dense clutter clusters in a scene are clustered into W. If:

[0085]

[0086] This can effectively eliminate this situation. When A < Ω, it is determined that W is composed of clutter, where A represents the boundary value between clutter and measurement.

[0087] Furthermore, step S5 is specifically as follows:

[0088] S51. The posterior intensity function D at time k in step S42 k|k (ξ k The expression for Gaussian Gamma mixture is as follows:

[0089]

[0090] Among them, J k|k This indicates the number of Gaussian Gamma components predicted at time k. Let represent the weight, mean, covariance, and Gamma distribution parameters of the j-th component, respectively.

[0091] S52, Extract the posterior strength D at time k k|k (ξ k The components with weights greater than a set threshold T are used to perform integrated joint estimation of the target shape and centroid state parameters of the radar cluster:

[0092]

[0093] in, In These represent the mean values ​​of the centroid state and the outline parameters of the cluster target, respectively.

[0094] S53. Extract according to the maximum a posteriori criterion. In As a centroid state estimate As a parameter for estimating the external profile. As an estimate of the number of individuals included.

[0095] The method of the present application firstly sets algorithm parameters, initializes initial intensity, obtains the measurement of the band amplitude information at the k moment through signal processing of the radar echo, then obtains the prior intensity function at the k moment after predicting all Gaussian Gamma components contained in the posterior intensity function at the k-1 moment, updates the intensity function by using the combined measurement with amplitude, obtains the posterior intensity function at the k moment, finally extracts the centroid state, shape contour and contained individual number of the cluster target at the k moment according to the weight in the posterior intensity function at the k moment, and realizes integrated joint estimation of the shape and size and centroid state of the radar cluster target. The method of the present application regards the cluster target as a whole, integrates the contained individual number and shape parameters into the state, and realizes integrated joint estimation under the Bayesian filtering framework, thereby solving the integrated estimation problem of the centroid state, contained individual number and arbitrary and time-varying shape of the indistinguishable cluster target.

[0096] The method of the present application can simultaneously realize integrated joint estimation of the centroid state, arbitrary shape contour and contained target number of the cluster target under the Bayesian filtering framework by using the amplitude information and Gaussian process regression in the scene where the cluster target is indistinguishable, thereby improving the accuracy of state estimation and having lower algorithm complexity. The method of the present application can be applied to the fields of biological cluster tracking, cluster unmanned aerial vehicle tracking and crowd tracking. BRIEF DESCRIPTION OF DRAWINGS

[0097] Figure 1 The figure is a flowchart of the integrated estimation method of the shape and size and centroid state of the radar cluster target of the present application.

[0098] Figure 2 The figure is a schematic diagram of the measurement of the cluster target with amplitude information in the method of the present application in the embodiment of the present application.

[0099] Figure 3 The figure is a schematic diagram of the shape contour modeling of the cluster target in the method of the present application in the embodiment of the present application.

[0100] Figure 4 The figure is the radar view in the two-dimensional plane, the real track of the cluster target, the distribution of the individual targets and the shape contour graph (the shape contour is drawn every 5s) in the embodiment of the present application.

[0101] Figure 5 The figure is the position measurement distribution graph and the position estimation of the cluster target in the embodiment of the present application after processing by the method of the present application and the comparative method. Figure 4 The figure is the comparison between the position estimation and the true value of the cluster target in the embodiment of the present application after processing by the method of the present application and the comparative method.

[0102] Figure 6 The figure is the comparison between the position estimation and the true value of the cluster target in the embodiment of the present application after processing by the method of the present application and the comparative method. Figure 4The comparison image of the estimated outline of the clustered target processed by the method of this invention and the comparison method with the actual outline (the outline is drawn every 5 seconds).

[0103] Figure 7 For the purposes of this embodiment of the invention Figure 6 A comparison of the contour estimation results of the two algorithms and the intersection-union ratio (IoU) calculated from the actual shape over time.

[0104] Figure 8 For the purposes of this embodiment of the invention Figure 4 The cluster target in the image is compared with the true value after being processed by the method of this invention and the comparison method. Detailed Implementation

[0105] This invention primarily employs simulation experiments for verification and evaluation. All steps and results have been verified as correct using Matlab 2021b. The method of this invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0106] like Figure 1 The flowchart shown below illustrates an integrated estimation method for the external shape and centroid state of a radar cluster target according to the present invention. The specific steps are as follows:

[0107] S1. Set algorithm parameters and initialize initial intensity;

[0108] S2. Perform signal processing on the radar echo to obtain a measurement with amplitude information at time k;

[0109] First, the radar observes the cluster target and acquires radar echo data at time k. Then, the echo data undergoes a radar signal processing procedure including data correction, pulse compression, MTD processing, constant false alarm rate detection, and DOA estimation to obtain the measurement with amplitude information at time k. Finally, the obtained polar coordinate measurement is converted to a rectangular coordinate system and the measurement is divided.

[0110] S3. Based on the target survival probability, the movement process and shape change process of the cluster targets and the exponential forgetting factor of the Gamma distribution, the joint state Markov transition equation of the cluster targets is obtained. The weights, Gaussian parts and Gamma parts of the Gaussian Gamma components are predicted respectively. After predicting all Gaussian Gamma components contained in the posterior intensity function at time k-1, the prior intensity function at time k is obtained.

[0111] Among them, the weight represents the expected number of targets, the Gaussian part includes the centroid state and shape contour information of the cluster targets, and the Gamma part includes the number of targets contained in the cluster targets.

[0112] S4, using the measurement set divided in step S2, based on the joint likelihood function, the position information of the measurement and the Gaussian process regression, the amplitude information of the measurement and the Gamma distribution, the weight of the Gaussian Gamma component, the Gaussian part and the Gamma part are updated respectively, after updating all Gaussian Gamma components contained in the prior intensity function at k moment, the posterior intensity function at k moment is obtained;

[0113] Wherein, the shape contour of the cluster is modeled as star convex, the radial distance at the preset angle is taken as the shape parameter to describe the contour, the measurement is taken as the training set, the update of the shape parameter uses the Gaussian process regression in the field of machine learning for recursive estimation; the individuals contained in the cluster are equivalent to the measurement source, and the conjugate property of Poisson distribution and Gamma distribution is used to recursively estimate the number of individuals. Therefore, the centroid state, shape parameter and number of individuals contained in the cluster target are recursively estimated together in the state vector in the Bayesian multi-target filtering framework, and finally the posterior intensity function at k moment is obtained. The update of the weight is relatively complex, which not only considers the state, but also comprehensively considers the shape and cardinality.

[0114] S5, the cluster target state and shape scale at k moment, i.e. the cluster target joint state, is extracted according to the weight of the Gaussian Gamma component in the posterior intensity function at k moment, realizing integrated joint estimation of the shape scale and centroid state of the radar cluster target;

[0115] S6, the posterior intensity function at k moment is taken as the input at k+1 moment for the next round of iteration, and steps S2-S5 are repeated until the tracking process ends.

[0116] In the embodiment, the step S1 is specifically as follows:

[0117] According to the scene setting algorithm parameters, then the extended state of the cluster target at k moment is represented as

[0118]

[0119] The algorithm parameter setting is shown in Table 1.

[0120] Table 1

[0121]

[0122] The real parameters of each cluster target in the embodiment are shown in Table 2. Since the three targets are born at k=5s, the initial intensity function D 5|5 (ξ5) is initialized as:

[0123]

[0124] Wherein, the weight is 0.03, and Set to:

[0125]

[0126] in, n (j) The true x and y coordinates of target j and the number of individuals contained therein are given in Table 2.

[0127] Table 2

[0128]

[0129] In this embodiment, step S2 is specifically as follows:

[0130] The radar echo is processed to obtain the amplitude information measurement at time k. The radar observes the cluster target and acquires the radar echo data at time k. After the echo data undergoes a radar signal processing procedure including data correction, pulse compression, MTD processing, constant false alarm rate detection, and DOA estimation, the radar amplitude trace at time k is obtained. In this embodiment, the simulation part designs a scenario containing three cluster targets with different shapes and motion states. The parameters of each cluster target are given in Table 2. Then, based on the radar resolution, measurement noise, and the actual target position, the combined measurement with amplitude information at each time is generated, namely Equations (4) and (5). The radar parameters and algorithm parameters are given in Table 1.

[0131] in, This represents a Ricean distribution with a decentralization parameter of s and a scaling parameter of σ, used to simulate the amplitude distribution of real radar echoes. A schematic diagram of cluster target measurement generation used in this embodiment is shown below. Figure 2 As shown. Figure 2 (a) shows the distribution and shape of three cluster targets in the radar field of view. Figure 2 (b) shows the distribution of individual targets within the three cluster targets. Figure 2 (c) shows the distribution of cluster targets, individual targets, and clutter in the location measurement space. Figure 2 (d) Measurements with amplitude information obtained by radar, including measurements of clutter and target generation.

[0132] In this embodiment, step S3 is specifically as follows:

[0133] The posterior intensity function at time k is obtained by predicting the posterior intensity function at time k-1 based on the target survival probability, the motion process and the shape change process of the cluster target, and the exponential forgetting factor of the Gamma distribution, as shown in equation (7). In addition, since the posterior intensity function at time k-1 is in the form of Gaussian-Gamma mixture, the prior intensity function at time k is also in the form of Gaussian-Gamma mixture, which makes the prediction process closed and has an analytical solution. Without loss of generality, the motion model of the cluster considered in the simulation of the embodiment is the CV model, and F in equation (10) is given in Table 1. m ,Q m The expression is as follows:

[0134]

[0135] wherein, denotes the Kronecker product, and the parameters in equation (11) and the process noise covariance matrix Q required in equation (30) are given in Table 1.

[0136] In the embodiment, the step S4 is specifically as follows:

[0137] The posterior intensity function at time k is obtained by updating the prior intensity function at time k based on the joint likelihood function, the position information of the measurement and the Gaussian process regression, and the amplitude information of the measurement and the Gamma distribution, as shown in equation (15). In addition, since the prior intensity function at time k is in the form of Gaussian-Gamma mixture, the posterior intensity function at time k is also in the form of Gaussian-Gamma mixture, which makes the updating process closed. The radar measurement equation considered in the simulation of the embodiment is equation (3), and the measurement equation of each measurement relative to the centroid of the cluster is expressed as follows:

[0138]

[0139] As shown in equation (15), Figure 3 Figure 3 (a) is a schematic diagram of modeling the shape contour of a cluster target, Figure 3 (b) is a radial distance function of the cluster target. Wherein, denote the local azimuth and the global azimuth respectively, and the direction vector s k,i denotes the proportion factor when the individual is located on the surface of the cluster, and it is assumed that the individuals in the cluster target are uniformly distributed on the surface, so μ s takes 2 / 3, takes 1 / 18, is the measurement noise in rectangular coordinates. The parameters required in the updating process are given in Table 1.

[0140] ​In the embodiment, the step S5 is specifically as follows:

[0141] Since the posterior intensity function at time k is in the form of Gaussian Gamma as shown in equation (26), the cluster target state and the shape at time k can be extracted according to the weight in each Gaussian Gamma component, that is, equation (27). If S k cluster targets are extracted at time k, that is, the centroid state of the jth cluster target is wherein the position, velocity, orientation angle and yaw rate are included; and the shape contour is expressed by L uniform sampling points in the direction as follows:

[0142]

[0143] wherein, represents the ith element in the vector contains the number of individual targets

[0144] Through steps S1-S6, the cluster target shape and centroid state can be integrated estimated, and the centroid state, shape contour and number of individual targets of the cluster target are obtained.

[0145] Figure 4 is a radar view in a two-dimensional plane and a cluster target real track, individual target distribution and shape contour diagram (the shape contour is drawn every 5s), wherein the related characteristic parameters of the cluster target are shown in Table 2. It can be seen that the three cluster targets have different shapes and individual numbers, and the shape size changes with time, and moves at a constant speed in a straight line within the radar view range. Figure 5 is a generated position measurement distribution diagram and a comparison diagram of the centroid position estimation after the cluster target in Figure 4 is processed by the proposed method and the comparative method (the method disclosed in CN 114740467A). The measurement in each time includes the measurement generated by the resolution unit and the clutter, and the number of clutters obeys the Poisson distribution with a mean value λ=50 and is uniformly distributed within the radar view range. It can be seen from the cluster target centroid position tracking results of the two algorithms that the centroid position error obtained by the proposed method is smaller and the accuracy is higher. Figure 6 is a comparison diagram of the shape contour estimation after the cluster target in Figure 4 is processed by the proposed method and the comparative method, and the results show that the proposed method can better estimate the shape contour of the arbitrary and time-varying cluster target, and solves the limitation of the comparative method that can only estimate the elliptical shape. In addition, the shape estimation evaluation usually uses the intersection over union (IoU) index, that is, the intersection area of the estimated shape and the real shape is divided by the union area of the estimated shape and the real shape, so 0≤IoU≤1 and the larger the better.Figure 7 is a plot of the intersection over union (IoU) of the two algorithms in Figure 6 Figure 7 (a) is the method of the present application, Figure 7 (b) is the comparative method. It can be seen that the method of the present application gradually converges to the true shape, while the comparative method diverges. Table 3 shows the average single-frame running time of the two methods,

[0146] Table 3

[0147] Method Average single frame run time Proposed method 0.36s Comparative method 1.94s

[0148] The results in the table are obtained by running Matlab on a computer with a 3.8GHz AMD Ryzen 7 5700G processor. The results show that the calculation amount of the present method is significantly reduced compared to the comparative method. The main difference is that the comparative algorithm needs to perform elliptical fitting on the shape, while the present method performs recursive estimation. Figure 8 is a plot of the intersection over union (IoU) of the two algorithms in Figure 4 Figure 8 (a) is the method of the present application, Figure 8 (b) is the comparative method. The results show that the method of the present application can solve the problem of unstable individual number of the comparative method by means of amplitude information. In summary, the method of the present application is superior to the comparative method in estimating the centroid state, shape contour and contained individual number of the cluster target. It can effectively solve the problem of low estimate of the cardinality caused by indistinguishable cluster targets by means of amplitude information, and can estimate the shape contour of irregular shape by Gaussian process regression, thereby realizing integrated estimation of the shape size and centroid state of the radar cluster target.

[0149] ​​In summary, the method of the present application fully considers the measurement generation process of the limited resolution radar for detecting the cluster target, including merging the position and amplitude of the measurement; secondly, the contour of the cluster target is modeled as a star convex shape, the individual target is equivalent to a measurement source, and the contour parameters and the number of individual targets are included in the state vector for recursive estimation. In the Bayesian iteration process, firstly, the intensity function is predicted based on the joint state Markov transition equation; then, according to the measurement equation, the Gaussian process regression and the conjugate property of the Gamma distribution, the intensity function is updated by using the merged measurement with amplitude; finally, the Gaussian Gamma components with weights greater than a set threshold in the posterior intensity function are extracted, and the centroid state, contour and contained individual number of the cluster target are obtained according to the maximum posterior criterion. The method of the present application can simultaneously estimate the centroid state, arbitrary contour and contained target number of the cluster target in the Bayesian filtering framework by using the amplitude information and Gaussian process regression in the scene where the cluster target is indistinguishable, thereby improving the accuracy of state estimation and having lower algorithm complexity. The method of the present application can be applied to the fields of biological cluster tracking, cluster unmanned aerial vehicle tracking and crowd tracking.

[0150] Those skilled in the art will understand that the embodiments described herein are for the purpose of helping the reader to understand the principles of the present application, and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. An integrated estimation method for the external shape and centroid state of a radar cluster target, comprising the following steps: S1. Set algorithm parameters and initialize initial intensity; S2. Perform signal processing on the radar echo to obtain a measurement with amplitude information at time k; First, the radar observes the cluster target and acquires radar echo data at time k. Then, after the echo data undergoes a radar signal processing procedure including data correction, pulse compression, MTD processing, constant false alarm rate detection, and DOA estimation, the measurement with amplitude information at time k is obtained. Finally, the obtained polar coordinate measurement is converted to a rectangular coordinate system and the measurement is divided. S3. Based on the target survival probability, the movement process and shape change process of the cluster targets and the exponential forgetting factor of the Gamma distribution, the joint state Markov transition equation of the cluster targets is obtained. The weights, Gaussian parts and Gamma parts of the Gaussian Gamma components are predicted respectively. After predicting all Gaussian Gamma components contained in the posterior intensity function at time k-1, the prior intensity function at time k is obtained. in, The weights represent the expected number of targets. The Gaussian part includes the centroid state and shape contour information of the cluster targets, and the Gamma part includes the number of targets contained in the cluster targets. S4. Using the measurement set divided in step S2, based on the joint likelihood function, the location information of the measurement and Gaussian process regression, the amplitude information of the measurement and Gamma distribution, update the weight, Gaussian part and Gamma part of the Gaussian Gamma component respectively. After updating all Gaussian Gamma components contained in the prior intensity function at time k, the posterior intensity function at time k is obtained. The cluster's outline is modeled as a star-convex shape. The radial distance at a preset angle is used as the outline parameter to characterize the outline. Measurements are used as the training set, and the update of the outline parameter is recursively estimated using Gaussian process regression in the field of machine learning. The individuals contained in the cluster are equivalent to measurement sources, and the number of individuals is recursively estimated using the conjugate of Poisson distribution and Gamma distribution. S5. Based on the weight of the Gaussian Gamma component in the posterior intensity function at time k, the state and size of the cluster target at time k, i.e., the joint state of the cluster target, are extracted to achieve integrated joint estimation of the size and centroid state of the radar cluster target. S6. Use the posterior intensity function at time k as the input at time k+1 for the next iteration, and repeat steps S2 to S5 until the tracking process ends.

2. The integrated estimation method for the external shape and centroid state of a radar cluster target according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. Set the algorithm parameters according to the scenario, and then set the expansion state of the cluster target at time k as follows: ; Among them, superscript Indicates matrix transpose; This represents the concatenated vector of the cluster target centroid state and the radial distance vector. Indicates the centroid state of the cluster target. This indicates the position of the centroid, i.e., the x and y coordinates. Indicates the velocity of the center of mass. Indicates the orientation angle. Indicates the yaw rate. Indicates the radial distance at a preset angle. express Radial distance vector at a preset angle, Indicates the first A preset angle This represents the corresponding radial distance, that is, the distance from the outer contour to the center position. Indicates the number of individuals included; S12. The initial intensity function is initialized as follows: ； in, Indicates the target state of the cluster. The parameter is Gaussian distribution, The parameter is The Gamma distribution, Represents a Gaussian Gamma component. Indicates the initial number of Gaussian Gamma components; It can be obtained from the number of cluster targets and the initial state.

3. The integrated estimation method for the external shape and centroid state of a radar cluster target according to claim 2, characterized in that, Step S2 is as follows: S21. Set the individual target position at time k as... The location measurement space is divided into a set of disjoint resolvable units. The position of each body is determined by the position measurement function. After mapping to the position measurement space, the resolution cell at time k is obtained. a collection of individuals The expression is as follows: ； ； in, These represent the x and y coordinates, respectively. Indicates the number of resolving units. Denotes the set of individuals at time k; S22, each resolution unit according to Based on detection probability The expression for generating a measurement with amplitude information is as follows: ； Among them, superscript Representing polar coordinates, These represent the measured distance, azimuth, and amplitude, respectively. The expression for the measured position is as follows: ； Among them, measurement noise , This indicates that the mean is 0 and the covariance is... Gaussian distribution; measurement amplitude Let be a positive random variable with the following distribution: , Represents the resolving unit There is The assumption of an individual; S23. Set the clutter positions to be uniformly distributed in the position measurement space, the clutter number to follow a Poisson distribution, and the clutter amplitude distribution to be... Furthermore, clutter will not fall into the same resolution cell as the real target. Ultimately, the set of measurements with amplitude information acquired by the radar at time k is... ; in, Represents the clutter set at time k; S24, Polar coordinate measurement set Transformation to Cartesian coordinate measurement set ; in, Indicates the number of measurements. superscript Represent Cartesian coordinates; then perform measurement and division. Indicates will Divided into a series of non-empty subsets All possible divisions.

4. The integrated estimation method for the external shape and centroid state of a radar cluster target according to claim 3, characterized in that, Step S3 is as follows: S31. Based on steps S1-S2, the posterior intensity function at time k-1. The expression is as follows: ； in, This indicates the number of Gaussian Gamma components at time k-1. They represent the first The weights, mean, and covariance of each component. Represents the parameters of the Gamma distribution; S32, the prior strength function at time k The expression is as follows: ； in, The new terms are indicated by the initial algorithm. The expression representing a surviving item is as follows: ； Based on the target survival probability, we obtain: ； in, Indicates the probability of survival; Based on the motion and shape change processes of the clustered targets, the following is obtained: ； in, This indicates a block diagonal operation. Determined by the cluster motion model; the expression for the shape evolution parameters is as follows: ； in, Indicates the forgetting factor, Indicates the sampling time interval. express The identity matrix is ​​obtained from the recursive form of the Gaussian process regression expression. as follows: ； in, A vector representing a preset angle. This represents the prior variance of the signal amplitude. Indicates length measurement; The exponential forgetting factor based on the Gamma distribution is obtained as follows: ； in, This represents the exponential forgetting factor.

5. The integrated estimation method for the external shape and centroid state of a radar cluster target according to claim 4, characterized in that, Step S4 is as follows: S41. Rewrite the prior intensity function at time k in step S32 in Gaussian Gamma mixture form, as follows: ； in, This indicates the number of Gaussian Gamma components predicted at time k. They represent the first The weights, mean, and covariance of each component. Represents the parameters of the Gamma distribution; S42, posterior intensity function at time k The expression is as follows: ； in, This represents the Cartesian coordinate system measurement set obtained in step S24; missed detection items. The prior strength is the same except for the weight. The weight expression is as follows: ； Test items The expression is as follows: ； Based on the measured location information and Gaussian process regression, we obtain: ； in: ； in, Represents the identity matrix; express The first in Individual measurement, This represents the mean of the measurement distribution proportions. Represents the direction vector. Indicates the first The mean of the target shape parameters, Indicates its first Given a preset angle; and since both the radar measurement model and the Gaussian process recursion are nonlinear models, a first-order approximation is performed using extended Kalman filtering, expressed as follows: ； in, This represents the proportion covariance of the measurement distribution; Based on the measured amplitude information and Gamma distribution, we obtain: ； in, The number of measurement sources in the cluster, i.e., the number of individuals included, is calculated using the following formula: ； in, The calculation formula is given by the law of total probability. Based on the conditional probability of the measurement amplitude, the possible sources of the merged measurements are traversed. The possibility of an individual; and The calculation formula is obtained from Bayes' theorem; This represents the maximum number of individual targets that each resolution unit may contain, and can be set according to the density of the cluster and the radar resolution. Based on the joint likelihood function, we obtain: ； in: ； in, Indicates the first The detection probability of each target. Represents measurement in Cartesian coordinates. Indicates clutter rate, This represents the clutter distribution density at a given measurement location; When multiple dense clutters in the scene are clustered as False alarms may occur if: ； This can effectively eliminate the possibility of this situation. Time to determine Composed of clutter, This indicates the boundary between clutter and measurement.

6. The integrated estimation method for the external shape and centroid state of a radar cluster target according to claim 5, characterized in that, Step S5 is as follows: S51. The posterior intensity function at time k in step S42 In Gaussian Gamma mixture form, the expression is as follows: ； in, This indicates the number of Gaussian Gamma components predicted at time k. They represent the first The weights, mean, and covariance of each component. Represents the parameters of the Gamma distribution; S52, Extracting the posterior strength at time k The weight of the middle is greater than the set threshold The components are used to complete the integrated joint estimation of the target shape and centroid state parameters of the radar cluster: ； in, In These represent the mean values ​​of the centroid state and the outline parameters of the cluster target, respectively. S53. Extract according to the maximum a posteriori criterion. In As a centroid state estimate As a parameter for estimating the external profile. As an estimate of the number of individuals included.

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