Nonlinear multi-target tracking method based on transition state probability hypothesis density filtering

Abstract

The invention belongs to the technical field of multi-target tracking application, and particularly relates to a non-linear multi-target tracking method based on transition state probability hypothesis density filtering. According to the method, a multi-target nonlinear system is reconstructed into a linear system by utilizing a conversion state, a Gaussian mixture probability hypothesis density algorithm of the conversion state is obtained by combining GM-PHD filtering, and compared with a traditional nonlinear multi-target tracking method, namely, an extended Kalman GM-PHD method and an unscented Kalman GM-PHD method, the algorithm has the advantages that the algorithm is simple in structure and easy to implement. The method has the advantages of high tracking precision and low execution time.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-target tracking applications, and particularly relates to a non-linear multi-target tracking method based on converted state probability hypothesis density filtering. Background Art

[0002] With the continuous increase in the demand for target tracking, the multi-target tracking problem for non-linear systems has become one of the research hotspots in target tracking. In actual tracking scenarios, the system model of target tracking often exhibits non-linear characteristics due to various reasons such as diverse sensor data types, complex and maneuverable target motion processes, and state and measurement models built on heterogeneous coordinate systems. Based on this, compared with the target tracking methods applicable to linear systems, the target tracking methods for non-linear systems can not only more effectively track non-linear targets, but also track linear targets, and have a wide range of applications. However, in actual applications, many problems still exist, such as complex models, unknown target numbers, complex target behavior modeling, uncertain noise, high computational complexity, and long execution time.

[0003] The multi-target tracking (MMT) algorithm is one of the core technologies of non-linear target tracking. Essentially, it uses sensor measurements to estimate the states and numbers of multiple targets and has extensive applications in the fields of autonomous driving, robotics, and intelligent monitoring. Traditional multi-target tracking research mainly solves the uncertainty of the relationship between targets and measurements through data association methods. These methods obtain the final multi-target tracking results by constructing association hypotheses between measurements and targets and combining each association probability. Traditional data association multi-target tracking algorithms include global nearest neighbor, joint probabilistic data association, and multi-hypothesis tracking, etc. However, when the number of targets increases or there is severe clutter, due to the exponential growth of the number of hypotheses, the computational complexity increases sharply. To solve this problem, multi-target tracking algorithms based on random finite set (RFS) have been proposed. Such algorithms represent multi-target states and measurements as random finite sets, thus naturally handling the representation problem of multi-target probability density, and unifying target birth, death, derivation, missed detection, and clutter into the Bayesian framework, and enabling concepts such as state space models and Bayesian recursion in single-target tracking to be directly applied to the multi-target tracking field, effectively avoiding the inherent data association problems of traditional MMT, so the calculation is more efficient and easier to implement.

[0004] The Probability Hypothesis Density (PHD) filter is a classic Random Finite Set (RFS)-based Multiple Measurement Fusion (MMT) algorithm. It estimates the states and number of targets by propagating the first moment of the multi-target posterior probability density in the Bayesian framework of multi-target tracking. This first moment is the PHD, and the integral of this first moment over any region represents the expected number of targets contained in the RFS in that region. The PHD filter improves computational efficiency while avoiding data association. Currently, there are mainly two methods to implement the PHD filter: the Gaussian Mixture PHD (GM-PHD) algorithm and the Sequential Monte Carlo PHD (SMC-PHD) algorithm. SMC-PHD requires an additional particle clustering process for multi-target state extraction, and a large number of particles seriously reduce the computational efficiency of SMC-PHD. In contrast, the GM-PHD algorithm has higher computational efficiency, and it uses a weighted Gaussian mixture distribution to approximate the posterior intensity. However, GM-PHD is only applicable to linear conditions. Therefore, improving GM-PHD under non-linear conditions is also the focus of many research works. Summary of the Invention

[0005] Based on this, the present invention provides a non-linear multi-target tracking method based on Converted State Gaussian Mixture Probability Hypothesis Density (CS-GMPHD), which can be used for multi-target tracking in a non-linear system where the targets move at a constant speed and the sensor has azimuth and range observation information.

[0006] The technical solution of the present invention is implemented as follows:

[0007] A non-linear multi-target tracking method based on converted state probability hypothesis density filtering, comprising the following steps:

[0008] Step 1: Establish a converted state model between the target state in the non-linear target Cartesian coordinate system and the target state in the polar coordinate system.

[0009] Step 2: For the newborn target model of the probability hypothesis density method in the Cartesian coordinate system, utilize the state conversion relationship to construct the probability hypothesis density PHD of the newborn target with the converted state.

[0010] Step 3: For the posterior component of the surviving targets in the polar coordinate system, construct the predicted PHD of the surviving targets with the converted state.

[0011] Step 4: The predicted PHD of the surviving targets of the newborn targets obtained in Step 2 is superimposed on the surviving targets to obtain the predicted PHD of the conversion state of multiple targets;

[0012] Step 5: Update the predicted PHD of the conversion state of multiple targets obtained in Step 4 using the measurement set obtained by the sensor to obtain the updated PHD of the conversion state of multiple targets;

[0013] Step 6: Prune, merge, and limit the number of components for the updated PHD of the conversion state obtained in Step 5 to obtain a refined set of updated Gaussian components of the conversion state;

[0014] Step 7: Using the set of updated Gaussian components obtained in Step 6, extract the estimated results of the conversion state of the targets and the estimated results of the target quantity in the coordinate system where the measurement model is located;

[0015] Step 8: Based on the updated conversion state of multiple targets obtained in Step 7 and the state conversion relationship between the target state in the Cartesian coordinate system and the target state in the polar coordinate system, calculate and obtain the estimated state of multiple targets in the original coordinate system, which is regarded as the final target state estimation result.

[0016] Optionally, the probability hypothesis density PHD of the newborn targets in the conversion state described in the present invention in Step 2 is:

[0017]

[0018] where, represents the newborn target model in polar coordinates, i.e., the mixture Gaussian component, represents the weight, the mean and covariance of the i-th Gaussian component after conversion, J b represents the number of Gaussian components of the newborn targets, x c represents the random variable after conversion, and N() represents the Gaussian distribution.

[0019] Optionally, the predicted PHD of the surviving targets in the conversion state described in the present invention in Step 3 is:

[0020]

[0021]

[0022]

[0023] where, are respectively the target states of the surviving targets the transition matrix of the conversion state, the process noise input matrix of the conversion state, and the process noise of the conversion state under the condition; represents the predicted mean and predicted covariance of the i-th surviving Gaussian component, pS Denotes the survival probability of the target, J k-1 Denotes the number of Gaussian components of the multi-target PHD at time k-1.

[0024] Optionally, the predicted PHD of the multi-target conversion state in the present invention is:

[0025]

[0026] where J k|k-1 = J k-1 + J b Denotes the predicted PHD D k|k-1 (x c ) of the number of Gaussian components; Respectively denote the weights, means, and covariances of the i-th Gaussian component of the predicted PHD D k|k-1 (x c ).

[0027] Optionally, the specific process of step five in the present invention is:

[0028] First, establish the updated PHD of the multi-target not detected by the sensor, i.e., (1 - p d )D k|k-1 (x c ), where p d Denotes the probability that the target is detected

[0029] Secondly, establish the updated PHD of the detected multi-target, i.e., Given the measurement set Z k at time k, each measurement z ∈ Z k of the sensor needs to traverse the set of mixture Gaussian components of the predicted PHD Update each component to obtain D d,k (x c ; z).

[0030] Optionally, the updated PHD of the multi-target conversion state in the present invention is:

[0031]

[0032] where |Z k | Denotes the number of measurements at time k,

[0033] Optionally, the pruning in step six of the present invention is: Set a pruning threshold W and discard of the Gaussian components.

[0034] Optionally, the merging in step six of the present invention is: Set a merging threshold U. On the basis of the pruned result, first select the Gaussian component with the largest weight Calculate the distance from other Gaussian components to Merge the Gaussian component sets that meet and recursively iterate until the distances between the merged Gaussian component sets are all greater than U, obtaining the pruned and merged Gaussian component sets

[0035] Optionally, the number of restricted components described in step six of the present invention is as follows:

[0036] Set the component number threshold J max , and on the basis of pruning and merging, if Arrange in descending order of weights, and take the first J max Gaussian components to construct a Gaussian component set If then retain all

[0037] Optionally, the process of target number estimation in step seven of the present invention is as follows: Take the Gaussian component set with weights , and then round each weight to obtain the multi-target number estimation The above-mentioned weight rounding is the extraction process.

[0038] Optionally, the process of target transition state estimation in step seven of the present invention is as follows: According to the Gaussian component set obtain the number of target states corresponding to each component The corresponding target state is then the multi-target transition state at time k

[0039] Beneficial effects:

[0040] The present invention proposes a non-linear multi-target tracking method based on probability hypothesis density filtering with transition states for a non-linear multi-target tracking system where the targets move at a constant speed and the sensor has azimuth and range observation information. The present invention uses the transition state to reconstruct the non-linear system of multi-targets into a linear system, and combines GM-PHD filtering to obtain the Gaussian mixture probability hypothesis density algorithm with transition states. Compared with the traditional non-linear multi-target tracking methods: GM-PHD of extended Kalman and GM-PHD of unscented Kalman, the present invention has higher tracking accuracy and lower execution time.

[0041] The present invention can be used for road planning and obstacle avoidance of driverless vehicles, target detection and recognition of intelligent monitoring systems, non-linear multi-target tracking of systems such as unmanned aerial vehicles, etc. Description of the Drawings

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0043] Figure 1 It is a flowchart of a non - linear multi - target tracking method based on probability hypothesis density filtering with conversion state for the present invention.

[0044] Figure 2 It is a graph of the true motion trajectories of all targets during the experiment of the present invention.

[0045] Figure 3 It is a comparison effect diagram of the average OSPA distance between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 1.

[0046] Figure 4 It is a comparison effect diagram of the average number of target estimations between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 1.

[0047] Figure 5 It is a comparison effect diagram of the average execution time between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 1.

[0048] Figure 6 It is a comparison effect diagram of the average OSPA distance between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 5.

[0049] Figure 7 It is a comparison effect diagram of the average number of target estimations between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 5.

[0050] Figure 8 It is a comparison effect diagram of the average execution time between the method of the present invention and the GM - PHD method of extended Kalman and the GM - PHD method of unscented Kalman under the clutter intensity of 5. Detailed implementation manners

[0051] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0052] It should be noted that, without conflict, the following embodiments and the features in the embodiments may be combined with each other; and, based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present disclosure.

[0053] It should be noted that the following describes various aspects of embodiments within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present disclosure, those skilled in the art should understand that one aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement an apparatus and / or practice a method. Additionally, this apparatus and / or this method may be implemented using other structures and / or functionality in addition to one or more of the aspects described herein.

[0054] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be illustrated by the following examples:

[0055] The problem of non - linear multi - target tracking based on random finite sets is described as follows: After knowing the estimated states of multi - targets at time k - 1 (the motion state of each target and the number of targets at time k), the non - linear system composed of the target motion model and the measurement model and the measurement data of the sensor at time k are used to estimate the states of multi - targets at time k.

[0056] In view of the problem of non - linear multi - target tracking, the present invention proposes a non - linear multi - target tracking algorithm based on converted state probability hypothesis density filtering. The flowchart of this method is as Figure 1 shown, and the specific implementation steps are as follows:

[0057] Step 1: Establish the state conversion relationship between the target state in the non - linear target Cartesian coordinate system and the target state in the polar coordinate system;

[0058] The specific process of this step is as follows:

[0059] First, establish a non - linear system model, that is, establish a uniform motion model of a single target in the Cartesian coordinate system (Equation (1)) and a non - linear measurement model with azimuth and range as observation information in the polar coordinate system (Equation (2)):

[0060] x k = Fx k-1 + Bv k-1 (1)

[0061] z k = h(x k ) + wk (2)

[0062] wherein, s x,k and s y,k represent the positions of the target on the x-axis and y-axis in the two-dimensional plane at time k, represents the velocities of the target on the x-axis and y-axis in the two-dimensional plane at time k; v k-1 represents the process noise following the Gaussian distribution N(0, Q), and it can be assumed that represents the accelerations of the target on the x-axis and y-axis in the two-dimensional plane at time k; z k = [θ r] T , where θ and r represent the azimuth and range measured by the sensor at time k respectively; wk represents the measurement noise following the Gaussian distribution N(0, R); F, B and h(x k ) are as follows respectively:

[0063]

[0064] wherein, T represents the sampling period of the sensor.

[0065] Secondly, establish the transformed state model;

[0066] Since there is a non-linear relationship between the target motion state and the sensor observation information under heterogeneous coordinate systems, it is necessary to use the idea of transformed state and combine the motion decomposition process to transform the target state in the Cartesian coordinate system into the target state in the polar coordinate system At this time, the reconstructed motion model and measurement model in the polar coordinate system are shown in Formulas (5) and (6):

[0067]

[0068]

[0069] At this time, since the newly constructed target state directly contains the measurement information of the sensor, the non-linear measurement model is transformed into a linear measurement model, that is, the non-linear system is reconstructed into a linear system. Among them, in θ k and represent the azimuth angle and azimuth angular velocity of the target at time k, r k and represent the range and range velocity of the target at time k; represents the transformed process noise following the Gaussian distribution N(0, Q c ), and it can be assumed that represents the azimuth angle acceleration and range acceleration of the target at time k; and H c are as follows respectively:

[0070]

[0071] Moreover, the target state x in the Cartesian coordinate system k and the target state in the polar coordinate system The conversion relationship between them, that is, the conversion state model is as follows:

[0072]

[0073]

[0074] Step 2: For the newborn target model of the probability hypothesis density method in the Cartesian coordinate system, use the state conversion relationship to construct the probability hypothesis density PHDD of the newborn target with the converted state b (x c );

[0075] In the field of multi-target tracking, due to the dynamic transformation of the target, that is, there are situations such as the birth and death of the tracked target, the state and quantity of the newly added target can be determined according to the data collected by the sensor. Since the target state of the newly born target collected by the sensor is in the Cartesian coordinate system, it needs to be converted to the polar coordinate system. This step is used to obtain the PHD of the newly born target in the converted state (polar coordinate system).

[0076] The known newborn target model of the probability hypothesis density method in the original Cartesian coordinate system, that is, the mixture Gaussian component is where J b represents the number of Gaussian components of the newborn target; represents the weight, mean and covariance of the i-th Gaussian component of the PHD of the newborn target. Use the system conversion state model in Step 1, that is, formula (9), to establish the converted newborn target model in the polar coordinate system, that is, the mixture Gaussian component is where the weight remains unchanged, the mean and covariance of the i-th Gaussian component after conversion. That is, the PHD of the newborn target with the converted state is the following formula:

[0077]

[0078] where

[0079] Step 3: For the posterior component of the surviving target in the polar coordinate system, construct the predicted PHD of the surviving target with the converted state;

[0080] The known PHD of the multi-target estimated at the k-1 moment, that is where

[0081] J k-1 represents the number of Gaussian components of the multi-target PHD at time k-1; represents the weight, mean, and covariance of the i-th Gaussian component of the estimated multi-target PHD at time k-1. The survival probability of the target is p S , using the state equations transformed by formulas (5) and (6) to predict the PHD of the surviving targets in the transformed state at time k as follows:

[0082]

[0083] where are respectively the transition matrix of the transformed state, the process noise input matrix of the transformed state, and the process noise of the transformed state obtained according to formula (7) under the given target state . Accordingly, represents the predicted mean and predicted covariance of the i-th surviving Gaussian component.

[0084] Step 4: Using the predicted PHD of the surviving targets in the transformed state in Step 3 and the PHD of the newly born targets in the transformed state in Step 2, calculate the predicted PHD D of the multi-target transformed state k|k-1 (x c ).

[0085] Combining the PHD D b (x c ) of the newly born targets in the transformed state in Step 2 and the predicted PHD D S,k|k-1 (x c ) of the surviving targets in Step 3, obtain the predicted PHD D k|k-1 (x c ) of the multi-target transformed state as follows:

[0086]

[0087] where J k|k-1 = J k-1 + J b represents the number of Gaussian components of the predicted PHD D k|k-1 (x c ); respectively represent the weight, mean, and covariance of the i-th Gaussian component of the predicted PHD D k|k-1 (x c ).

[0088] Step 5: Using the measurement set obtained by the sensor to update the predicted PHD of the multi-target in the transformed state obtained in Step 4, obtain the updated PHD of the multi-target in the transformed state;

[0089] Based on the measurement set obtained by the sensor and the predicted Gaussian component set of the multi-target's transformed state obtained in Step 4, using the idea of multi-target Bayesian filtering, calculate the updated mixture Gaussian component set of the multi-target's transformed state. This step is to update the predicted PHD in Step 4 using the measurement set obtained by the sensor.

[0090] This step is divided into two processes. The first process is to first establish the updated PHD of the multi-target that is undetected (i.e., not detected by the sensor), which is (1 - p d )D k|k-1 (x c ), where p d represents the probability that the target is detected, and 1 - p d is the probability that the target is not detected; the second process is to establish the updated PHD of the detected multi-target, which is In this process, given the measurement set Z k at time k, for each measurement z ∈ Z k , it is necessary to traverse the mixture Gaussian component set of the predicted PHD and update each component to obtain D d,k (x c ; z). The specific calculation process is as follows:

[0091]

[0092] Among them, J k|k-1 represents the number of Gaussian components of the PHD D d,k (x c ; z), represents the normalized weight of the Gaussian component at time k, represents the likelihood function value when the measurement value is z at time k, respectively represent the updated state and updated covariance of the i-th Gaussian component of the predicted PHD with respect to z at time k, respectively represent the mean and covariance of the i-th Gaussian component of the predicted PHD at time k, represents the gain matrix, and H c and R respectively represent the transformed measurement matrix and measurement noise.

[0093] At this time, the updated PHD D k (x c ) of the multi-target's transformed state is expressed as:

[0094]

[0095] Among them, |Z k | represents the number of measurements at time k, represents the updated PHD D before processing the Gaussian components (pruning, merging, and retaining the maximum term)k (x c ) The number of Gaussian components.

[0096] Step 6: Prune, merge, and limit the number of components for the updated PHD of the conversion state obtained in Step 5 to obtain a refined set of updated Gaussian components of the conversion state;

[0097] Prune, merge, and limit the number of components for the set of updated Gaussian components of the conversion state obtained in Step 5 to obtain a refined set of updated Gaussian components of the conversion state.

[0098] This step is divided into three processes. The first process is pruning. Set a pruning threshold W (W is determined according to the actual situation and is usually very small. Here, W = 1×10 -10 ) and discard the Gaussian components, that is, discard the Gaussian components with extremely small weights that can be ignored to obtain the pruned set of Gaussian components The second process is merging. Set a merging threshold U (U is determined according to the actual situation. Here, U = 2). Based on the pruned set, first select the Gaussian component with the largest weight ( ), calculate the distance from it to other Gaussian components and merge the set of Gaussian components that satisfy in sequence until the distances between the merged sets of Gaussian components are all greater than U to obtain the pruned and merged set of Gaussian components The third process is to retain the maximum term. Set a maximum term threshold J max (i.e., the component number threshold, generally J max = 100). Based on the pruning and merging, if arrange in descending order of weight and take the first J max Gaussian components to construct a set of Gaussian components If then retain all (at this time After pruning, merging, and retaining the maximum term for the Gaussian components, the processed updated PHD of the conversion state is obtained k (x c ) as follows:

[0099]

[0100] where represents the number of Gaussian components of the processed updated PHD.

[0101] Step 7: Using the updated Gaussian component set obtained in Step 6, extract the estimated results of the transformed state and the estimated result of the number of targets of the target in the coordinate system where the measurement model is located.

[0102] This step is divided into two processes. The first process is to estimate the number of targets and take the Gaussian component set with weights :

[0103]

[0104] where J k,w is the number of Gaussian component sets, the number of Gaussian component sets. According to the obtained Gaussian component set round each weight to obtain the estimated number of multi-targets The rounding of the weights is the extraction process.

[0105] The second process is to estimate the transformed state of the target According to the Gaussian component set the number of target states corresponding to each component can be obtained The corresponding target state is Then the transformed state of the multi-target at time k

[0106] Step 8: Based on the updated transformed state of the multi-target obtained in Step 7, use the functional relationship between the target state in the original coordinate system and the transformed state to calculate and obtain the estimated state of the multi-target in the original coordinate system, which is regarded as the final estimated result of the target state.

[0107] Finally, the state estimate value X of the target in the original coordinate system needs to be obtained k , so based on the estimated value of the transformed state of the multi-target obtained in Step 7 Using the functional relationship between the target state in the original coordinate system and the transformed state, that is, formula (10), calculate the estimated state of each Gaussian component in the original coordinate system in turn to obtain the final estimated result of the target state

[0108] In summary, according to the above Steps 1 to 8, the filtering results of the multi-targets in one sampling period of the non-linear multi-target tracking algorithm based on the transformed state probability hypothesis density filtering can be obtained. By looping Steps 3 to 8, the multi-target filtering results of each sampling period within the sensor detection time can be obtained.

[0109] Next, the effectiveness of the method of the present invention will be tested through simulation experiments. The simulation experiments will verify the effectiveness of the method of the present invention from two aspects: tracking accuracy and execution time according to the comparison results of CS-GMPHD and two classical non-linear multi-target tracking methods under two sets of different clutter parameters: Extended Kalman filter-based GM-PHD (EK-GMPHD) and Unscented Kalman filter-based GM-PHD (UK-GMPHD).

[0110] Among them, the tracking accuracy is measured by Optimal Sub-pattern Assignment (OSPA). The OSPA distance comprehensively considers two aspects: the estimated number of targets and the target state estimation error, and is a metric for comprehensively evaluating the multi-target tracking accuracy. For two finite non-empty subsets X = {x 1 , …, x m}, Y = {y 1 , …, y n}, if m ≤ n, the definition formula of the OSPA distance is as follows:

[0111]

[0112] If m > n, then In formula (25), p ≥ 1 is used to control the sensitivity of the OSPA distance to errors; c > 0 is a truncation parameter used to handle the case of mismatched target numbers; Ω n represents the set of all permutations and combinations on {1, 2, ···, n}; d (c) (x i , y σ(i) ) = min(c, d(x i , y σ(i) )) truncation operation avoids the excessive influence of a few points with too large distances on the overall distance metric. It can be seen from the definition formula of the OSPA distance that the parameters p and c affect the size of the OSPA distance. To further analyze and compare the accuracy of the multi-target algorithms in terms of number estimation, the target cardinality estimation (number of targets) results of the three algorithms at each sampling moment during the observation time are also compared in this experiment. The algorithm execution time is measured by the actual running time of each filter once. The average OSPA distance, average cardinality estimation, and average execution time of M Monte Carlo simulation experiments are used as the final comparison metrics in this experiment.

[0113] Experimental scenario settings: The experimental scenario is in a two-dimensional plane area [-20m, 120m] × [0m, 140m], the sensor is located at the origin of coordinates, and the total observation duration is Ttotal = 100T, where T = 1 second is the sampling period. The target state x performs CV motion, the sensor measurement z includes the azimuth and distance of the target, and the non-linear system model uses equations (1) to (4); the process noise and measurement noise are modeled as Gaussian distributions, that is and where u v = 0.01, u w = [0.02π / 360, 50] T ; The number of targets is 4. Table 1 reflects the initial state, birth time, and survival time of each target. In this experimental scenario, within the total observation time of 100 s, there are 3 target births and 3 target disappearances. The true motion trajectories of the 4 targets are as Figure 2 shown.

[0114] Experimental simulation parameters: The clutter density follows a Poisson distribution with parameter λ, and the clutter distribution follows a uniform distribution, that is, on each sampling, an average of l clutters are generated, and the state of each clutter follows a uniform distribution within the region. In the present invention, two experimental environments with different clutter densities of λ = 1 and λ = 5 are respectively set; the target survival probability p S = 0.99, the detection probability p of the sensor d = 0.99; It is set that p = 1 in the OSPA distance, and the truncation parameter c = 100; The number of Monte Carlo simulations M = 100.

[0115] Figure 3 , Figure 4 and Figure 5 are all the comparison effect diagrams of the CS-GMPHD algorithm with the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 1 in the present invention.

[0116] Among them, Figure 3 represents the comparison diagram of the average OSPA distances of the CS-GMPHD algorithm with the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 1. From Figure 3 it can be seen that after about 12 s, the OSPA distance of the CS-GMPHD algorithm is always lower than that of the EK-GMPHD algorithm and the UK-GMPHD algorithm; and starting from 15 s, the OSPA distance of the CS-GMPHD algorithm remains at about 10, while after 20 s, the OSPA distance of the UK-GMPHD algorithm is basically between 10 and 30, and after 20 s, the OSPA distance of the EK-GMPHD algorithm is basically between 10 and 40; This indicates that the tracking accuracy of the CS-GMPHD algorithm is better than that of the EK-GMPHD algorithm and the UK-GMPHD algorithm.

[0117] Figure 4Figure showing the comparison of the average cardinality estimates between the CS-GMPHD algorithm and the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 1. From Figure 4 It can be seen that after about 4 s, the estimated result of the number of targets by CS-GMPHD is consistent with the true number of targets; while for EK-GMPHD and UK-GMPHD, their estimated results of the number of targets are basically consistent with the true number of targets only after about 20 s. This indicates that in terms of the accuracy of target cardinality estimation, the CS-GMPHD algorithm converges faster compared with EK-GMPHD and UK-GMPHD. And within the sampling period of 100 s, regardless of whether the targets are newly born or disappear in the tracking scenario, CS-GMPHD can quickly and accurately estimate the number of targets, and the accuracy of its cardinality estimation is also better than that of EK-GMPHD and UK-GMPHD.

[0118] Figure 5 Figure showing the comparison of the average execution time between the CS-GMPHD algorithm and the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 1. From Figure 5 It can be seen that under the same tracking conditions, the CS-GMPHD algorithm runs faster than EK-GMPHD and UK-GMPHD. This is because EK-GMPHD needs to perform linearization processing on each target at each time step, involving the calculation of the Jacobian matrix, which greatly increases the computational load and reduces the running time; UK-GMPHD uses the unscented transform and needs to generate and process more sampling points, which also increases the computational complexity; while the CS-GMPHD algorithm uses a coordinate transformation method to transform the nonlinear model into a linear model, greatly reducing the computational complexity and thus improving the execution efficiency.

[0119] Considering the influence of clutter density on the multi-target tracking effect, Figure 6 、 Figure 7 and Figure 8 are all the comparison effect diagrams of CS-GMPHD with EK-GMPHD and UK-GMPGD under the condition of clutter density λ = 5 in the present invention.

[0120] Among them, Figure 6 Figure showing the comparison of the average OSPA distance between the CS-GMPHD algorithm and the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 5. From Figure 6It can be seen that after about 8 s, the OSPA distance of the CS-GMPHD algorithm is always lower than that of the EK-GMPHD algorithm and the UK-GMPHD algorithm; and starting from 18 s, the OSPA distance of the CS-GMPHD algorithm is basically around 10 - 20, while after 20 s, the OSPA distance of the UK-GMPHD algorithm is basically between 20 - 40, and after 20 s, the OSPA distance of the EK-GMPHD algorithm is basically between 20 - 40; and Figure 3 compared, it shows that when the clutter density increases, the OSPA distances of the three algorithms all increase, reflecting that their tracking accuracies all decrease, but the tracking accuracy of the CS-GMPHD algorithm is still better than that of the EK-GMPHD algorithm and the UK-GMPHD algorithm.

[0121] Figure 7 It shows the comparison diagram of the average cardinality estimation of the CS-GMPHD algorithm, the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 5. From Figure 7 it can be seen that after about 16 s, the estimation result of the number of targets by CS-GMPHD basically tends to be consistent with the true number of targets; while for EK-GMPHD and UK-GMPHD, it is only after about 60 s that their estimation results of the number of targets basically match the true number of targets; and Figure 4 compared, it reflects that a larger clutter density also affects the accuracy of the three algorithms in estimating the target cardinality. However, in terms of the accuracy of estimating the target cardinality, the CS-GMPHD algorithm converges faster compared to EK-GMPHD and UK-GMPHD. And within the sampling period of 100 s, whether the target is newly born or disappears in the tracking scenario, CS-GMPHD can still quickly and accurately estimate the number of targets, and its accuracy of cardinality estimation is also better than that of EK-GMPHD and UK-GMPHD.

[0122] Figure 8 It shows the comparison diagram of the average execution time of the CS-GMPHD algorithm, the EK-GMPHD algorithm and the UK-GMPGD algorithm under the condition of clutter density λ = 5. From Figure 8 and Figure 5 the comparison, it can be seen that when the clutter density increases, the execution times of CS-GMPHD, EK-GMPHD and UK-GMPHD all increase, but under the same tracking conditions, the running speed of the CS-GMPHD algorithm is still faster than that of EK-GMPHD and UK-GMPHD.

[0123] Comprehensively Figures 3 to 8, it can be observed that as the clutter density increases, the tracking performance (tracking accuracy, potential estimation accuracy, and execution time) of the three algorithms all decreases. However, the CS-GMPHD algorithm proposed in this paper is still superior to EK-GMPHD and UK-GMPHD in terms of tracking accuracy, potential estimation accuracy, and execution time.

[0124] In summary, as can be seen from the detailed specific steps of the present invention, the proposed nonlinear multi-target tracking method of probability hypothesis density filtering for converting states in the present invention reconstructs the system model by using the idea of state conversion in heterogeneous coordinate systems, converts the nonlinear system model into a linear system model, and cleverly combines the Gaussian mixture implementation process of probability hypothesis density under linear conditions, and proposes an improved algorithm of probability hypothesis density filtering for solving the nonlinear multi-target tracking problem caused by heterogeneous coordinate systems. As can be seen from the simulation comparison experiments of the present invention, the algorithm proposed in the present invention has a good tracking effect and still ensures the superiority of the algorithm under different clutter density conditions.

[0125] Table 1 Initial information of multi-target motion

[0126]

[0127]

[0128] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A nonlinear multi-target tracking method based on transition state probability hypothesis density filtering, characterized in that: The steps include: Step 1: Establish a conversion state model between the target state in the nonlinear target Cartesian coordinate system and the target state in the polar coordinate system; Step 2: for the new target model of the probability hypothesis density method in the Cartesian coordinate system, using the state conversion relationship, construct the probability hypothesis density PHD of the new target of the conversion state; Step 3: Construct the predicted PHD of the surviving target in the conversion state for the posterior component of the surviving target in the polar coordinate system; Step 4: The PHD of the new target obtained in step 2 is superimposed on the predicted PHD of the surviving target to obtain the predicted PHD of the conversion state of the multi-target; Step 5: Use the measurement set obtained by the sensor to update the predicted PHD of the conversion state of the multiple targets obtained in step 4 to obtain the updated PHD of the conversion state of the multiple targets; Step 6: Prune, merge and limit the number of components of the updated PHD of the conversion state obtained in step 5 to obtain a simplified updated Gaussian component set of the conversion state; Step 7: Using the updated Gaussian component set obtained in step 6, extract the target conversion state estimation result and target quantity estimation result in the coordinate system where the measurement model is located; Step 8: Based on the updated conversion state of the multi-target obtained in step 7, the state conversion relationship between the target state in the Cartesian coordinate system and the target state in the polar coordinate system, calculate and obtain the estimated state of the multi-target in the original coordinate system, which is regarded as the final target state estimation result.

2. According to claim 1, the nonlinear multi-target tracking method based on transition state probability hypothesis density filtering is characterized in that: The probability hypothesis density PHD of the new target in the conversion state of step 2 is: in, represents the new target model in polar coordinates, i.e., the mixed Gaussian components, represents the weight, The mean and covariance of the i-th Gaussian component after transformation, J b represents the number of new target Gaussian components, x c represents the transformed random variable and N() represents Gaussian distribution.

3. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 2 or 3, characterized in that: The predicted PHD of the survival target of the transition state in step 3 is: in, They are the target states of the survival targets. The transfer matrix of the conversion state under the conditions, the process noise input matrix of the conversion state and the process noise of the conversion state; and represents the predicted mean and predicted covariance of the ith surviving Gaussian component, p S represents the survival probability of the target, J k-1 Represents the number of Gaussian components of the multi-target PHD at time k-1.

4. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 3 is characterized in that: The predicted PHD of the multi-objective conversion state is: Among them, J k|k-1 =J k-1 +J b Indicates predicted PHDD k|k-1 (x c )’s number of Gaussian components; Respectively represent the predicted PHDD k|k-1 (x c )’s weight, mean, and covariance of the i-th Gaussian component.

5. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 1, characterized in that: The specific process of step five is as follows: First, the updated PHD of multiple targets not detected by the sensor is established, that is, (1-p d )D k|k-1 (x c ), where p d Indicates the probability of the target being detected Secondly, the updated PHD of the detected multi-targets is established, i.e. The measurement set Z at time k is known k , each sensor measurement z∈Z k Both require traversing the set of mixed Gaussian components to predict PHD Update each component to get D d,k (x c ; z).

6. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 5, characterized in that: The updated PHD of the multi-objective conversion state is: Among them, |Z k | represents the number of measurements at time k, 7. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 1, characterized in that: The pruning in step 6 is as follows: setting a pruning threshold W, discarding Gaussian component of .

8. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 7, characterized in that: The merging in step 6 is as follows: setting a merging threshold U, first selecting the Gaussian component with the largest weight after pruning Calculate and other Gaussian components Distance Will satisfy The Gaussian component sets of are merged, and the process is repeated recursively until the distances between the merged Gaussian component sets are all greater than U, and the pruned and merged Gaussian component sets are obtained.

9. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 8, characterized in that: The number of restricted components in step 6 is: Set the component number threshold J max , based on pruning and merging, if In order of weight from large to small Arrange and take the first J max Gaussian components construct Gaussian component set if Keep all 10. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 1, characterized in that: The process of estimating the target quantity in step 7 is as follows: The Gaussian component set of , and then round each weight to get the number of multi-target estimates The weights are rounded off to the nearest integer, which is the process of extraction; The process of estimating the conversion state of the target in step 7 is as follows: The Gaussian component set Get each component The number of corresponding target states The corresponding target state is Then the conversion state of multiple targets at time k is

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