Nonlinear multi-target tracking method based on converted state probability hypothesis density filter

Abstract

The present application belongs to the technical field of multi-target tracking application, and particularly relates to a nonlinear multi-target tracking method based on a conversion state probability hypothesis density filter. The method reconstructs a nonlinear system of multi-targets into a linear system by using a conversion state, and obtains a Gaussian mixture probability hypothesis density algorithm of the conversion state by combining with a GM-PHD filter. Compared with a traditional nonlinear multi-target tracking method, such as a GM-PHD of an extended Kalman filter and a GM-PHD of an unscented Kalman filter, the present application has higher tracking precision and lower execution time.

Description

Technical Field

[0001] This invention belongs to the field of multi-target tracking application technology, specifically relating to a nonlinear multi-target tracking method based on transition state probability hypothesis density filtering. Background Technology

[0002] With the increasing demand for target tracking, multi-target tracking of nonlinear systems has become a research hotspot. In practical tracking scenarios, the system models for target tracking often exhibit nonlinear characteristics due to diverse sensor data types, complex target motion processes, and state and measurement models built in heterogeneous coordinate systems. Therefore, compared to target tracking methods applicable to linear systems, nonlinear target tracking methods can track not only nonlinear targets more effectively but also linear targets, thus having a wide range of applications. However, in practical applications, many problems still exist, such as model complexity, unknown number of targets, complex target behavior modeling, uncertain noise, high computational cost, and long execution time.

[0003] Multi-target tracking (MMT) is a core technology in nonlinear target tracking. Essentially, it uses sensor measurements to estimate the state and number of multiple targets, finding wide application in autonomous driving, robotics, and intelligent monitoring. Traditional MMT research primarily addresses the uncertainty in the relationship between targets and measurements through data association methods. These methods construct association hypotheses between measurements and targets and combine each association probability to obtain the final MMT result. Traditional data association MMT algorithms include global nearest neighbor, joint probabilistic data association, and multi-hypothesis tracking. However, these algorithms experience a sharp increase in computational complexity as the number of targets increases or severe clutter occurs, due to the exponential growth in the number of hypotheses. To address this issue, MMT-based multi-target tracking algorithms using Random Finite Sets (RFS) have been proposed. These algorithms naturally address the representation of multi-target probability density by representing multi-target states and measurements as random finite sets. They also unify target emergence, death, derivation, missed detection, and clutter into a Bayesian framework, allowing concepts such as state-space models and Bayesian recursion from single-target tracking to be directly applied to multi-target tracking. This effectively avoids the inherent data association problems of traditional MMT, making the computation more efficient and easier to implement.

[0004] The Probability Hypothesis Density (PHD) filter is a classic RFS-based Multi-Target Tracking (MMT) algorithm. It estimates the state and number of targets by propagating the first moment of the posterior probability density of multiple targets within a Bayesian framework for multi-target tracking. This first moment is the PHD, and its integral over any region represents the expected number of targets contained in the RFS within that region. PHD filters improve computational efficiency while avoiding data correlation. Currently, there are two main methods for implementing PHD filters: Gaussian Mixture PHD (GM-PHD) and Sequential Monte Carlo PHD (SMC-PHD). SMC-PHD requires an additional particle clustering process for multi-target state extraction, and the large number of particles significantly reduces its computational efficiency. In contrast, the GM-PHD algorithm has higher computational efficiency, using a weighted Gaussian mixture distribution to approximate the posterior strength. However, GM-PHD is only applicable to linear conditions. Therefore, improving GM-PHD under nonlinear conditions is a focus of much research. Summary of the Invention

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

[0006] The technical solution for implementing the present invention is as follows:

[0007] A nonlinear multi-target tracking method based on transition state probability hypothesis density filtering includes the following steps:

[0008] Step 1: Establish a transformation state model between the target state in the nonlinear Cartesian coordinate system and the target state in the polar coordinate system;

[0009] Step 2: For the new target model using the probability hypothesis density method in Cartesian coordinates, construct the probability hypothesis density PHD of the new target in the transition state using the state transition relationship;

[0010] Step 3: Construct the prediction PHD of the surviving target in the transition state for the posterior component of the surviving target in the polar coordinate system;

[0011] Step 4: The PHD of the newly formed target obtained in Step 2 is superimposed with the predicted PHD of the surviving target to obtain the predicted PHD of the transition state of multiple targets.

[0012] Step 5: Update the multi-target transition state prediction PHD obtained in Step 4 using the measurement set obtained by the sensor, and obtain the updated PHD of the multi-target transition state.

[0013] Step 6: Prune, merge, and limit the number of components in the updated PHD of the transition states obtained in Step 5 to obtain a simplified set of updated Gaussian components of the transition states.

[0014] Step 7: Using the updated Gaussian component set obtained in Step 6, extract the target transformation state estimation results and target quantity estimation results in the coordinate system where the measurement model is located;

[0015] Step 8: Based on the multi-target update transformation state obtained in Step 7, the state transformation relationship between the target state in the Cartesian coordinate system and the target state in the polar coordinate system is calculated and the estimated state of the multi-target in the original coordinate system is obtained, which is regarded as the final target state estimation result.

[0016] Optionally, the probability hypothesis density (PHD) of the newly formed target in the second step of the present invention is:

[0017]

[0018] in, The new target model represented by polar coordinates, i.e., the Gaussian mixture component, Indicates weight, The mean and covariance of the i-th Gaussian component after transformation, J b x represents the number of new target Gaussian components. c Let N represent the transformed random variable, and let N() represent the Gaussian distribution.

[0019] Optionally, the predicted PHD of the surviving target in the third step of the present invention is:

[0020]

[0021]

[0022]

[0023] in, These are the target states of the surviving targets. The transition matrix of the transition state under the given conditions, the process noise input matrix of the transition state, and the process noise of the transition state; p represents the predicted mean and predicted covariance of the i-th surviving Gaussian component.S J represents the survival probability of the target. k-1 This represents the number of Gaussian components in the multi-objective PHD at time k-1.

[0024] Optionally, the prediction PHD of the multi-objective transition state described in this invention is:

[0025]

[0026] Among them, J k|k-1 =J k-1 +J b Indicates prediction of PHDD k|k-1 (x c The number of Gaussian components; These represent the predicted PHDD. k|k-1 (x c The weights, mean, and covariance of the i-th Gaussian component.

[0027] Optionally, the specific process of step five in this invention is as follows:

[0028] First, an updated PHD is established for multiple targets not detected by sensors, i.e., (1-p d )D k|k-1 (x c ), where p d Indicates the probability that the target is detected.

[0029] Secondly, an updated PHD is established for the detected multi-targets, i.e. Given the measurement set Z at time k k Each measurement z∈Z of the sensor k It is necessary to traverse the Gaussian mixture component set for predicting PHD. Update each component to obtain D d,k (x c ;z).

[0030] Optionally, the PHD update of the multi-target transition state described in this invention is as follows:

[0031]

[0032] Among them, |Z k | indicates the number of measurements taken at time k.

[0033] Optionally, the pruning in step six of this invention involves setting a pruning threshold W and discarding... Gaussian components.

[0034] Optionally, the merging in step six of this invention is as follows: setting a merging threshold U, and based on the pruned components, first selecting the Gaussian component with the largest weight. Calculate with other Gaussian components distance Will satisfy The Gaussian component sets are merged, and this process is repeated recursively until the distance between the merged Gaussian component sets is greater than U, resulting in the pruned and merged Gaussian component sets.

[0035] Optionally, the number of restricted components in step six of this invention is:

[0036] Set the threshold number of components J max Based on pruning and merging, if Arranged in descending order of weight Sort the results and take the first J. max Construct a Gaussian component set from the Gaussian components. if Then keep all

[0037] Optionally, the process of estimating the target quantity in step seven of this invention is as follows: taking weights. The Gaussian component set is used to obtain the number estimate of the multi-objectives by rounding each weight. The rounding of the weights is the extraction process.

[0038] Optionally, the process of estimating the transition state of the target in step seven of the present invention is as follows: based on Gaussian component sets Get each component Number of corresponding target states The corresponding target state is Then the transition state of multiple targets at time k

[0039] Beneficial effects:

[0040] This invention addresses nonlinear multi-target tracking systems where the target moves at a constant velocity and the sensor provides azimuth and range observation information. It proposes a nonlinear multi-target tracking method based on probability hypothesis density filtering of transition states. This invention utilizes transition states to reconstruct the nonlinear system of multiple targets into a linear system and combines GM-PHD filtering to obtain a Gaussian mixture probability hypothesis density algorithm for the transition states. Compared with traditional nonlinear multi-target tracking methods—Extended Kalman GM-PHD and Unscented Kalman GM-PHD methods—this invention achieves higher tracking accuracy and lower execution time.

[0041] This invention can be used for road planning and obstacle avoidance in unmanned vehicles, target detection and recognition in intelligent monitoring systems, and nonlinear multi-target tracking in systems such as drones. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart of a nonlinear multi-target tracking method based on probability hypothesis density filtering of transition states according to the present invention.

[0044] Figure 2 This is a diagram showing the actual motion trajectories of all targets during the experiment of this invention.

[0045] Figure 3 This is a comparison diagram of the average OSPA distance of the present invention with that of the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity 1.

[0046] Figure 4 This is a comparison of the average target estimation results of the present invention with the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity 1.

[0047] Figure 5 This is a comparison of the average execution time of the present invention with that of the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity 1.

[0048] Figure 6 This is a comparison of the average OSPA distance of the present invention with that of the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity of 5.

[0049] Figure 7 This is a comparison of the average target estimation results of the present invention with the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity of 5.

[0050] Figure 8 This is a comparison of the average execution time of the present invention with that of the Extended Kalman GM-PHD method and the Unscented Kalman GM-PHD method under clutter intensity of 5. Detailed Implementation

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

[0052] It should be noted that, in the absence of conflict, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0053] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is illustrated below with examples:

[0055] The nonlinear multi-target tracking problem based on random finite sets is described as follows: given the estimated states of multiple targets at time k-1 (the motion state of each target and the number of targets at time k), the states of multiple targets at time k are estimated using a nonlinear system consisting of a target motion model and a measurement model, and the measurement data from the sensor at time k.

[0056] This invention addresses the nonlinear multi-target tracking problem by proposing a nonlinear multi-target tracking algorithm based on transition state probability hypothesis density filtering. The flowchart of this method is shown below. Figure 1 As shown, the specific implementation steps are as follows:

[0057] Step 1: Establish the state transition relationship between the target state in the nonlinear Cartesian coordinate system and the target state in the polar coordinate system;

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

[0059] First, establish a nonlinear system model, namely, establish a uniform motion model of a single target in the Cartesian coordinate system (Equation (1)) and a nonlinear measurement model in the polar coordinate system using azimuth and range as observation information (Equation (2)):

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

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

[0062] in, s x,k and s y,k This represents the position of the target on the x-axis and y-axis in the two-dimensional plane at time k. v represents the target's velocity along the x-axis and y-axis in the two-dimensional plane at time k; k-1 To represent process noise that follows a Gaussian distribution N(0,Q), we can assume... z represents the acceleration of the target along the x-axis and y-axis in the two-dimensional plane at time k; k =[θ r] T θ and r represent the azimuth and range obtained by the sensor at time k, respectively; wk represents the measurement noise that follows a Gaussian distribution N(0,R); F, B, and h(x k The following are the details:

[0063]

[0064] Where T represents the sampling period of the sensor.

[0065] Secondly, establish a transition state model;

[0066] Since the relationship between the target's motion state and sensor observation information is nonlinear in heterogeneous coordinate systems, it is necessary to utilize the concept of state transformation and combine it with the motion decomposition process to transform the target state in the Cartesian coordinate system. Convert to target state in polar coordinates The reconstructed motion and measurement models in polar coordinates are shown in equations (5) and (6):

[0067]

[0068]

[0069] At this point, due to the newly constructed target state Since it directly contains the sensor's measurement information, the nonlinear measurement model is transformed into a linear measurement model, that is, the nonlinear system is reconstructed into a linear system. Among these, θ k and Let r represent the azimuth and azimuth velocity of the target at time k. k and This represents the target's range and velocity at time k; This indicates that the distribution follows a Gaussian distribution N(0,Q). c The conversion process noise can be assumed to be... This represents the azimuth acceleration and range acceleration of the target at time k; and H c They are as follows:

[0070]

[0071] Furthermore, the target state x in the Cartesian coordinate system k Target state in polar coordinates The transformation relationship between them, i.e., the transformation state model, is as follows:

[0072]

[0073]

[0074] Step 2: For the newly generated target model using the probability hypothesis density method in Cartesian coordinates, construct the probability hypothesis density (PHDD) of the newly generated target in the transition state using the aforementioned state transition relationship. b (x c );

[0075] In the field of multi-target tracking, targets undergo dynamic changes, including new targets emerging and disappearing. Therefore, the state and number of newly added targets can be determined based on the data collected by sensors. Since the target state of newly added targets collected by sensors is in a Cartesian coordinate system, it needs to be converted to a polar coordinate system. This step is used to obtain the PHD of newly added targets in the converted state (polar coordinate system).

[0076] Given the neologism density method in the original Cartesian coordinate system, i.e., the Gaussian mixture components are... Among them, J b Indicates the number of new Gaussian components of the target; Let represent the weight, mean, and covariance of the i-th Gaussian component of the newborn target PHD. Using the system transformation state model from step one, i.e., formula (9), establish the newborn target model in polar coordinates, where the Gaussian mixture components are... Among them, weight remain unchanged. The mean and covariance of the i-th Gaussian component after transformation. That is, the PHD of the newly formed target in the transformed state is given by the following formula:

[0077]

[0078] in,

[0079] Step 3: Construct the prediction PHD of the surviving target in the transition state for the posterior component of the surviving target in the polar coordinate system;

[0080] Given the PHD of the multi-target algorithm estimated at time k-1, i.e. in,

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

[0082]

[0083] in, These are the given target states Under the given conditions, the transition matrix of the transition state, the process noise input matrix of the transition state, and the process noise of the transition state are obtained according to formula (7). Correspondingly, Let represent the predicted mean and predicted covariance of the i-th surviving Gaussian component.

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

[0085] The new target PHDD, combined with the transition state in step two. b (x c Prediction of the survival target in step three (PHDD) S,k|k-1 (x c ), to obtain the predicted PHDD of the multi-objective transition state. k|k-1 (x c The following formula:

[0086]

[0087] Among them, J k|k-1 =J k-1 +J b Indicates prediction of PHDD k|k-1 (x c The number of Gaussian components; These represent the predicted PHDD. k|k-1 (x c The weights, mean, and covariance of the i-th Gaussian component.

[0088] Step 5: Update the multi-target transition state prediction PHD obtained in Step 4 using the measurement set obtained by the sensor, and obtain the updated PHD of the multi-target transition state.

[0089] Based on the measurement set obtained from the sensors and the Gaussian component set of the multi-target transition state prediction obtained in step four, the updated mixture Gaussian component set of the multi-target transition state is calculated using the idea of ​​multi-target Bayesian filtering. This step uses the measurement set obtained from the sensors to update the PHD predicted in step four.

[0090] This step consists of two processes. The first process is to establish an updated PHD for multiple targets that have been missed (i.e., not detected by the sensor), namely (1-p d )D k|k-1 (x c ), where p d 1-p represents the probability of the target being detected. d This represents the probability that the target was not detected; the second process is to establish an updated PHD for the detected multiple targets, i.e. The process is carried out using the known measurement set Z at time k. k Under the premise that each measurement z∈Z k It is necessary to traverse the Gaussian mixture component set for predicting PHD. Update each component to obtain D d,k (x c The specific calculation process is as follows:

[0091]

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

[0093] At this point, the update of the multi-objective transition state PHDD k (x c That is, it can be expressed as:

[0094]

[0095] Among them, |Z k | indicates the number of measurements taken at time k. This indicates the update of PHDD before processing 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 in the updated PHD of the transition states obtained in Step 5 to obtain a simplified set of updated Gaussian components for the transition states.

[0097] The updated Gaussian component set of the transition state obtained in step 5 is pruned, merged, and the number of components is limited to obtain a simplified updated Gaussian component set of the transition state.

[0098] This step consists of three processes. The first process is pruning, which involves setting a pruning threshold W (W is chosen based on the actual situation, and is usually very small; here, W = 1 × 10⁻⁶). -10 ),give up The Gaussian components are obtained by discarding Gaussian components with negligible weights, resulting in the pruned Gaussian component set. The second process is merging. A merging threshold U is set (U is chosen based on the actual situation; here, U = 2 is acceptable). Based on the pruned components, the Gaussian component with the largest weight is selected first. ), calculate with other Gaussian components distance Will satisfy The Gaussian component sets are merged, and this process is repeated recursively until the distance between the merged Gaussian component sets is greater than U, resulting in the pruned and merged Gaussian component sets. The third process is to retain the maximum term and set a threshold J for the maximum term. max (i.e., the threshold for the number of components, generally taken as J) max =100), based on pruning and merging, if Arranged in descending order of weight Sort the results and take the first J. max Construct a Gaussian component set from the Gaussian components. if Then keep all (at this time After pruning, merging, and retaining the maximum terms of the Gaussian components, the updated PHDD of the processed transition state is obtained. k (x c As shown in the following formula:

[0099]

[0100] in, This indicates the number of Gaussian components in the updated PHD after processing.

[0101] Step 7: Using the updated Gaussian component set obtained in Step 6, extract the target transformation state estimation results and target quantity estimation results in the coordinate system where the measurement model is located.

[0102] This step consists of two processes. The first process is to estimate the number of targets and calculate the weights. Gaussian component sets:

[0103]

[0104] Among them, J k,w yes The number of Gaussian component sets, The number of Gaussian component sets. Based on the obtained... Gaussian component sets Rounding each weight yields a multi-objective quantity estimate. The rounding of the weights is the extraction process.

[0105] The second process is to estimate the target's transition state. according to Gaussian component sets Each component can be obtained Number of corresponding target states The corresponding target state is Then the transition state of multiple targets at time k

[0106] Step 8: Based on the multi-target updated transformation state obtained in Step 7, use the functional relationship between the target state in the original coordinate system and the transformation state to 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.

[0107] Ultimately, we need to obtain the target's state estimate X in the original coordinate system. k Therefore, based on the multi-objective transition state estimates obtained in step seven... Using the functional relationship between the target state and the transformed state in the original coordinate system, i.e., formula (10), the estimated state of each Gaussian component in the original coordinate system is calculated sequentially. The final target state estimation result is obtained.

[0108] In summary, based on steps one through eight above, the filtering results of the nonlinear multi-target tracking algorithm based on the probability hypothesis density filtering of the transition state within one sampling period can be obtained. By repeating steps three through eight, the filtering results of the multi-target tracking algorithm within each sampling period during the sensor detection time can be obtained.

[0109] The effectiveness of the method of the present invention will be tested through simulation experiments. The simulation experiments will compare the results of CS-GMPHD and two classic nonlinear 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). The results will verify the effectiveness of the method of the present invention in terms of tracking accuracy and execution time.

[0110] Among them, tracking accuracy is measured by Optimal Sub-pattern Assignment (OSPA). OSPA distance comprehensively considers both the number of target estimates and the target state estimation error, and is a metric for comprehensively evaluating the tracking accuracy of multi-target tracking. For two finite non-empty subsets X = {x1, ..., x...} m},Y={y1,…,y n If m ≤ n, then the definition of OSPA distance is as follows:

[0111]

[0112] If m > n, then In equation (25), p≥1 is used to control the sensitivity of OSPA distance to error; c>0 is a truncation parameter used to handle the case of mismatch in the number of targets; Ω n d represents the set of all permutations and combinations on {1, 2, ..., n}; (c) (x i ,y σ(i) )=min(c,d(x i ,y σ(i) The truncation operation avoids excessive influence of a few excessively large points on the overall distance metric. As can be seen from the definition of OSPA distance, parameters p and c affect the magnitude of the OSPA distance. To further analyze and compare the accuracy of multi-objective algorithms in number estimation, this experiment also compared the target potential estimation (number of targets) results of the three algorithms at each sampling time within the observation period. Algorithm execution time was measured using the actual running time of each filter in a single run. This experiment used the average OSPA distance, average potential estimation, and average execution time of M Monte Carlo simulations as the final comparative metrics.

[0113] Experimental setup: The experimental scenario is located within a two-dimensional planar region [-20m, 120m] × [0m, 140m]. The sensor is located at the origin, and the total observation time is T. total=100T, where T=1 second is the sampling period. The target state x undergoes CV motion, and the sensor measures z, including the target's azimuth and distance. The nonlinear system model adopts formulas (1) to (4); the process noise and measurement noise are modeled as Gaussian distributions, i.e. as well as Where u v =0.01, u w =[0.02π / 360,50] T There were four targets. Table 1 shows the initial state, creation time, and survival time of each target. In this experimental scenario, during the total observation time of 100 seconds, there were three instances of target creation and three instances of target disappearance. The actual motion trajectories of the four targets are as follows: Figure 2 As shown.

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

[0115] Figure 3 , Figure 4 and Figure 5 These are comparison images of the CS-GMPHD algorithm, EK-GMPHD algorithm, and UK-GMPGD algorithm under the clutter density λ=1 condition.

[0116] in, Figure 3 This graph compares the average OSPA distance of the CS-GMPHD algorithm with that of the EK-GMPHD and UK-GMPGD algorithms under the clutter density λ=1. Figure 3 It can be seen that after approximately 12 seconds, the OSPA distance of the CS-GMPHD algorithm is consistently lower than that of the EK-GMPHD and UK-GMPHD algorithms. Furthermore, starting from 15 seconds, the OSPA distance of the CS-GMPHD algorithm remains around 10, while the OSPA distance of the UK-GMPHD algorithm is generally between 10 and 30 after 20 seconds, and the OSPA distance of the EK-GMPHD algorithm is generally between 10 and 40 after 20 seconds. This indicates that the tracking accuracy of the CS-GMPHD algorithm is superior to that of the EK-GMPHD and UK-GMPHD algorithms.

[0117] Figure 4This graph compares the mean potential estimates of the CS-GMPHD algorithm with those of the EK-GMPHD and UK-GMPGD algorithms under the clutter density λ=1. Figure 4 It can be seen that after approximately 4 seconds, the CS-GMPHD's estimate of the number of targets is consistent with the actual number of targets; while for EK-GMPHD and UK-GMPHD, it is only after approximately 20 seconds that their estimates of the number of targets are basically consistent with the actual number of targets. This indicates that in terms of the accuracy of target potential estimation, the CS-GMPHD algorithm converges faster than EK-GMPHD and UK-GMPHD. Furthermore, within a 100-second sampling period, regardless of whether the targets are newly created or disappearing in the tracking scene, CS-GMPHD can quickly and accurately estimate the number of targets, and its potential estimation accuracy is also superior to EK-GMPHD and UK-GMPHD.

[0118] Figure 5 This graph compares the average execution time of the CS-GMPHD algorithm with that of the EK-GMPHD and UK-GMPGD algorithms under clutter density λ=1. 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 requires linearization of 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 unscented transformation, which requires generating and processing more sampling points, also increasing computational complexity; while the CS-GMPHD algorithm uses coordinate transformation to convert the nonlinear model into a linear model, greatly reducing computational complexity and thus improving execution efficiency.

[0119] Considering the impact of clutter density on multi-target tracking performance, Figure 6 , Figure 7 and Figure 8 These are comparison images of the effects of CS-GMPHD, EK-GMPHD, and UK-GMPGD under the clutter density λ=5 condition.

[0120] in, Figure 6 This graph compares the average OSPA distance of the CS-GMPHD algorithm with that of the EK-GMPHD and UK-GMPGD algorithms under clutter density λ=5. Figure 6It can be seen that after approximately 8 seconds, the OSPA distance of the CS-GMPHD algorithm is consistently lower than that of the EK-GMPHD and UK-GMPHD algorithms; and from 18 seconds onwards, the OSPA distance of the CS-GMPHD algorithm is generally around 10-20, while the OSPA distance of the UK-GMPHD algorithm is generally between 20-40 after 20 seconds, and the OSPA distance of the EK-GMPHD algorithm is also generally between 20-40 after 20 seconds; and... Figure 3 In comparison, it shows that when the clutter density increases, the OSPA distance of all three algorithms increases, reflecting a decrease in their tracking accuracy. However, the tracking accuracy of the CS-GMPHD algorithm is still better than that of the EK-GMPHD and UK-GMPHD algorithms.

[0121] Figure 7 This graph compares the mean potential estimates of the CS-GMPHD algorithm with those of the EK-GMPHD and UK-GMPGD algorithms under the clutter density λ=5. Figure 7 It can be seen that, approximately after 16 seconds, the CS-GMPHD's estimate of the target number becomes largely consistent with the actual target number; while for EK-GMPHD and UK-GMPHD, it is approximately after 60 seconds that their estimates of the target number become largely consistent with the actual target number; and Figure 4 In comparison, while higher clutter density also affects the accuracy of the three algorithms in target potential estimation, the CS-GMPHD algorithm still converges faster than EK-GMPHD and UK-GMPHD in terms of target potential estimation accuracy. Furthermore, within a 100s sampling period, regardless of whether the target is newly emerging or disappearing in the tracking scene, CS-GMPHD can still quickly and accurately estimate the number of targets, and its potential estimation accuracy is also superior to EK-GMPHD and UK-GMPHD.

[0122] Figure 8 The graph shows a comparison of the average execution time of the CS-GMPHD algorithm with the EK-GMPHD and UK-GMPGD algorithms under the clutter density λ=5. Figure 8 and Figure 5 The comparison shows that the execution time of CS-GMPHD, EK-GMPHD and UK-GMPHD all increases when the clutter density increases. However, under the same tracking conditions, the CS-GMPHD algorithm is still faster than EK-GMPHD and UK-GMPHD.

[0123] comprehensive Figures 3-8It can be observed that as clutter density increases, the tracking performance (tracking accuracy, potential estimation accuracy, and execution time) of all three algorithms decreases. However, the CS-GMPHD algorithm proposed in this paper still outperforms 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 steps of this invention, the nonlinear multi-target tracking method based on probability hypothesis density filtering for state transitions proposed in this invention reconstructs the system model using the idea of ​​state transitions in heterogeneous coordinate systems, transforming the nonlinear system model into a linear system model. It also cleverly combines the Gaussian mixture process of probability hypothesis density under linear conditions, proposing an improved probability hypothesis density filtering algorithm for solving nonlinear multi-target tracking problems caused by heterogeneous coordinate systems. Simulation comparison experiments show that the algorithm proposed in this invention has excellent tracking performance and maintains its superiority even under conditions of varying clutter densities.

[0125] Table 1 Initial Information of Multi-Target Motion

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[0128] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A nonlinear multi-target tracking method based on transition state probability hypothesis density filtering, characterized in that, Includes the following steps: Step 1: Establish the state transition relationship between the target state in the nonlinear Cartesian coordinate system and the target state in the polar coordinate system, i.e., the transition state model; Step 2: For the new target model using the probability hypothesis density method in Cartesian coordinates, construct the probability hypothesis density PHD of the new target in the transition state using the state transition relationship; Step 3: Construct the prediction PHD of the surviving target in the transition state for the posterior component of the surviving target in the polar coordinate system; Step 4: Superimpose the PHD of the newly formed target obtained in Step 2 with the predicted PHD of the surviving target in the transition state obtained in Step 3 to obtain the predicted PHD of the transition state of multiple targets. Step 5: Update the multi-target transition state prediction PHD obtained in Step 4 using the measurement set obtained by the sensor, and obtain the updated PHD of the multi-target transition state. Step 6: Prune, merge, and limit the number of components in the updated PHD of the transition states obtained in Step 5 to obtain a simplified set of updated Gaussian components for the transition states. Step 7: Using the updated Gaussian component set obtained in Step 6, extract the target transformation state estimation results and target quantity estimation results in the polar coordinate system where the measurement model is located; Step 8: Based on the target state estimation results obtained in Step 7, the estimated state of multiple targets in Cartesian coordinates is calculated and obtained by using the state transformation relationship between the target state in Cartesian coordinates and the target state in polar coordinates. This is considered as the final target state estimation result. The probability hypothesis density (PHD) of the newly formed target in the second step of the state transition is: in, The new target model represented by polar coordinates, i.e., the Gaussian mixture component, Indicates weight, After conversion The mean and covariance of the Gaussian components, This indicates the number of newly generated Gaussian components of the objective. Represents the transformed random variable. Indicates a Gaussian distribution; The predicted PHD of the surviving target in the third step of the transition state is: in, These are the target states of the surviving targets. The transition matrix of the transition state under the given conditions, the process noise input matrix of the transition state, and the process noise of the transition state; and Indicates the first The predicted mean and predicted covariance of each surviving Gaussian component. Indicates the probability of the target's survival. express The number of Gaussian components in a time-varying multi-objective PHD; The prediction PHD of the multi-objective transition state is: wherein, represents the number of Gaussian components of the predicted PHD respectively represent the weight, mean and covariance of the th Gaussian component of the predicted PHD .​ 2. 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 update PHD of multi-targets not detected by the sensor is established, i.e. where, denotes the probability of the target being detected Secondly, the update PHD of the detected multi-target is established, that is , known measurement set at time , each measurement of the sensor needs to traverse the mixed Gaussian component set of the predicted PHD , for each component update, get .

3. The nonlinear multi-target tracking method based on the converted state probability hypothesis density filter according to claim 2, characterized in that, The update PHD of the multi-objective transition state is: wherein represents the number of time measurements, .

4. 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 six is: setting a pruning threshold , discarding gaussian components.

5. The nonlinear multi-target tracking method based on the converted state probability hypothesis density filter according to claim 4, characterized in that, The merging step in step six involves setting a merging threshold. Based on the pruned structure, the Gaussian component with the largest weight is first selected. , , ), calculate with other Gaussian components distance , will satisfy The Gaussian component sets are merged, and this process is repeated recursively until the distance between the merged Gaussian component sets is greater than 1. The pruned and merged Gaussian component sets are obtained. .

6. The nonlinear multi-target tracking method based on transition state probability hypothesis density filtering according to claim 5, characterized in that, The number of restricted components in step six is: Set a threshold for the number of components Based on pruning and merging, if Sort by weight from largest to smallest Arrange the items and take the first few. Construct a Gaussian component set from the Gaussian components. ,if Then retain all .

7. The nonlinear multi-target tracking method based on converted state probability hypothesis density filtering according to claim 1, characterized in that, The step seven aims to estimate the number of targets by taking the set of Gaussian components , and rounding each weight to obtain the number of targets , the rounding being the decimation process. The process of estimating the transition state of the target in step seven is as follows: based on Gaussian component sets To obtain each component ( The number of corresponding target states The corresponding target state is ,but Transition state of multiple objectives at any time .

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