Multi-target tracking algorithm based on potential probability hypothesis density

Abstract

A challenge is brought to accurate tracking of the target in multi-target tracking, environment change, sensor limitation and uncertain dynamic target number. Based on multi-feature assistance, a Gaussian mixture potential probability hypothesis density filter and unscented Kalman filtering, the invention provides a multi-target tracking model of the Gaussian mixture potential probability hypothesis density filter based on multi-feature assistance. The method comprises the following steps: constructing a state set containing state information on the basis of considering target dynamics; doppler information and amplitude information are introduced through a measurement module, and a combined measurement likelihood function containing the azimuth, the Doppler information and the amplitude information is established; and deriving an MFGM-CPHD filtering process based on a GM-CPHD filter, and updating a Gaussian component mean value and a covariance by adopting a UKF (Unscented Kalman Filter). In a multi-target tracking task, compared with a GM-CPHD filter and a DI-GM-CPHD filter, the filter provided by the invention has higher tracking precision and better performance.

Description

Technical Field

[0001] The invention relates to a multi-target tracking algorithm based on potential probability hypothesis density, and belongs to the field of target tracking. Background Art

[0002] Target tracking algorithm is a kind of computational method that continuously detects and tracks single or multiple moving targets in dynamic scenes. Its basic goal is to estimate the state parameters of the target based on the time series data obtained by the sensor, and maintain the identity and trajectory consistency of the target under noise and uncertainty conditions. Target tracking technology can achieve continuous tracking of dynamic targets. This technology plays a vital role in many fields such as resource detection, environmental monitoring, and security monitoring. It is of great significance to improve monitoring efficiency and optimize resource utilization.

[0003] Target tracking can be divided into single target tracking and multi-target tracking. Single target tracking generally refers to the technology of tracking only one moving target in a dynamic environment. It aims to accurately estimate and continuously update the position, velocity and other state parameters of the target. It can usually provide stable tracking effects under conditions of simple background or obvious target separation. Multi-target tracking refers to the technology of simultaneously tracking multiple targets in complex scenes. It needs to identify and maintain the independent identity of all targets and their dynamic trajectories, so as to provide a detailed description and analysis of the movement path and interaction of each target, and ensure that the dynamic behavior and overlapping status of the targets can be correctly analyzed in target-dense areas. Target tracking technology has developed rapidly, but it still faces huge challenges, especially in complex scenes, where the performance of multi-target tracking is not ideal. The variability of the environment, the diversity of targets and the limitations of sensors all pose challenges to the accurate detection and tracking of targets.

[0004] In the past, significant research progress has been made in the field of object tracking. Algorithms for single object tracking include correlation filters (CF), Kalman filters (KF), particle filters (PF), etc. Although these methods perform well in specific scenarios, most of them are designed for simple backgrounds and single targets.

[0005] With the continuous evolution of technology and the application needs of modern engineering, the attention to the problem of Multi-Target Tracking (MTT) has been increasing. In the early stage of MTT research, the focus was mainly on data association methods, such as Multiple Hypothesis Tracking (MHT), Probabilistic Data Association (PDA) and Joint Probabilistic Data Association (JPDA). These methods estimate and associate the positions and trajectories of multiple targets through a probabilistic framework, laying the foundation for the development of subsequent algorithms. However, the computational complexity of these methods in high clutter environments limits their practical application scope.

[0006] Since then, the emergence of random finite set (RFS) theory has provided a new mathematical model for multi-target tracking algorithms. RFS theory allows the randomness of the number of targets to be modeled, which is more in line with the needs of actual scenarios. The target set is represented in the form of a random finite set, where each element represents a target and its attributes are random variables, which more accurately reflects the uncertainty of the target set. Building a target tracking model for random finite sets and improving the performance of multi-target tracking algorithms have become an important direction of current research.

[0007] Based on the RFS theory, Mahler proposed the Probability Hypothesis Density (PHD) filter, which incorporates clutter suppression into a unified framework through finite set statistics and Bayesian analysis to avoid the data association problem between measurements. There are two ways to implement the PHD filter: one is to use the sequential Monte Carlo method, and the other is based on the Gaussian mixture model. Each method has its advantages and limitations. Among them, the Gaussian mixture-based method is more commonly used due to its simplicity and efficiency.

[0008] The PHD filter simplifies the data association problem by estimating the probability density of the existence of the target. It is suitable for processing scenes with many targets and the emergence or disappearance of targets. However, the estimation provided by PHD for the number of dynamically changing targets is not accurate. In order to improve the accuracy of the target number estimation, Mahler proposed the Cardinalized Probabilistic Hypothesis Density (CPHD) filter based on PHD. It not only maintains the data association simplification characteristics of PHD, but also provides more accurate target number information by modeling the distribution function of the target number. Although PHD and CPHD filters have achieved good results in multi-target tracking, it is difficult to achieve high-precision tracking in dense clutter environments.

[0009] In recent years, researchers have paid attention to more feature information, such as amplitude information (AI) and Doppler information (DI). By using more feature information, the performance of the filter can be further enhanced. By introducing AI into the Bayesian filter, the multi-target tracking accuracy is improved to a certain extent under the condition of unknown signal-to-noise ratio. However, there are still deficiencies in the adaptability and robustness of dynamic signal-to-noise ratio, especially in high-clutter scenes. How to effectively adapt to the changes in different signal-to-noise ratio levels has become a challenge to be solved. Using DI for data association can improve tracking performance, but it is only applicable to linear systems. When relying on a single measurement information, especially when the target motion is highly nonlinear, the tracking accuracy may be limited. These studies have provided an important foundation for the development of multi-target tracking technology, but its application in specific scenarios still faces challenges. Its contribution lies not only in its respective technical innovations, but also emphasizes the importance of integrating DI and AI in the MTT problem. Summary of the invention

[0010] To address the problem that traditional PHD filters are difficult to accurately track targets in real time when clutter is dense and detection probability is low, the present invention studies a Multi-Feature Aided Gaussian Mixture Cardinalized Probability Hypothesis Density (MFGM-CPHD) filter and proposes a multi-target tracking algorithm based on potential probability hypothesis density.

[0011] The present invention is a multi-target tracking algorithm based on potential probability hypothesis density, the method comprising:

[0012] S1, using MFGM-CPHD filter to expand Doppler information and amplitude information into target measurement information;

[0013] S2. Based on the target measurement information, a new measurement likelihood function is established;

[0014] S3. Based on the CPHD filter, a new update process is introduced to enhance the discrimination between target and clutter.

[0015] Preferably, in S1, in the two-dimensional scene, at the time k-1, there are N k-1 targets. Each target has its own state, which includes the position and velocity in the horizontal and vertical directions. At the next moment k, the state of the target may change. Some targets may disappear, some targets may still be there, and new targets may appear. The state of all targets at time k is represented by the RFS method. This representation method includes two parts: one is the change in the state of the target that survives from time k-1 to time k; the other is the state of the new target that appears at time k. After introducing amplitude information and Doppler information, the measurement of the target at time k includes azimuth measurement, Doppler velocity measurement and amplitude measurement. There may be multiple targets at this moment, and the set of measurement values ​​of all targets can be represented by RFS. This set includes erroneous measurement values ​​such as the actual detected target measurement values ​​and the false alarm clutter measurement set.

[0016] Preferably, in S2, the measurement likelihood function is mainly divided into an azimuth measurement likelihood function and a Doppler likelihood function. In view of the high clutter environment problem existing in multi-target tracking, a measurement module is proposed. At a certain moment k, target measurement information including target position measurement, Doppler velocity measurement and amplitude measurement is introduced to jointly constitute the state vector of the target at moment k. These measurement information are integrated and represented by RFS. Afterwards, a target state equation is established and measurement noise is processed. By constructing a noise matrix and a noise covariance matrix, these noises can be modeled and processed. In order to describe the probability of obtaining a specific measurement value under a given target state, a target measurement likelihood function is derived. By maximizing the likelihood function, the optimal estimate of the target state can be obtained. When multiple targets are considered, the measurement model can be expanded to a joint measurement likelihood function. By optimizing the joint measurement likelihood function, multi-target tracking and estimation can be achieved.

[0017] Preferably, the S3 includes:

[0018] S31, deriving the MFGM-CPHD filtering process based on the GM-CPHD filter;

[0019] S32. Update the mean and covariance of the Gaussian classification by using UKF.

[0020] Preferably, in said S3, on the basis of adding Doppler information and amplitude information to the measurement equation, a new filtering process, namely MFGM-CPHD filtering, is derived based on the GM-CPHD filter. At time k, the intensity function of the target state set has a corresponding mean and covariance, and it is necessary to calculate multiple Sigma sampling points and weight values ​​for the Gaussian component. After calculating the sampling points and their corresponding weights, the state equation is used to perform a single-step prediction on the sampling points. In the MFGM-CPHD prediction step, the predicted measurement value is first estimated based on the measurement equation. Since the added amplitude and Doppler information do not affect the target state transfer, the potential distribution function and intensity function of the previous moment (k-1 moment) remain unchanged, and the calculation of the relevant mean and covariance has a specific result. After the target measurement is expanded by introducing the amplitude and Doppler measurement information, the measurement likelihood function and clutter density in the original GM-CPHD filter update process are replaced by the new joint measurement likelihood function and joint clutter density, and the multi-target updated potential distribution function and intensity function of the MFGM-CPHD filter at time k can be obtained.

[0021] Preferably, in the S3, in the UKF algorithm, first, according to the current state estimate and covariance matrix, a group of Sigma points are generated by the Sigma point generation algorithm. Next, these Sigma points are used to perform a one-step prediction to calculate the predicted state variables and covariance matrix. For each Sigma point, the state equation of the system is applied to obtain the corresponding predicted value, and the mean of the state prediction is calculated. Similarly, by transforming the predicted Sigma point with the observation equation, the predicted mean of the observed quantity and the covariance matrix of the observed prediction can be obtained. Finally, the Kalman gain calculation and state update are used to calculate the Kalman gain matrix, which represents the influence of the observation information on the state update. The Kalman gain matrix is ​​used to combine the prediction and actual observation information to obtain a new state estimate. The updated state estimate and the observed error covariance will be adjusted according to the Kalman gain to reflect the introduction of new information. Through the above process, UKF can provide accurate state estimation in nonlinear systems, gradually calculate the mean and covariance in the update step, and adaptively process the dynamic characteristics and observation noise of the system.

[0022] Beneficial results of the present invention. The present invention aims at the problem that the traditional PHD filter is difficult to accurately track the target in real time when the clutter is dense and the detection probability is low. Based on multi-feature (MF) assistance, Gaussian mixture potential probability hypothesis density (GM-CPHD) filter, and unscented Kalman filter (UKF), the present invention proposes a multi-target tracking model based on multi-feature aided Gaussian mixture potential probability hypothesis density (MFGM-CPHD) filter. The model includes three modules: target state module, measurement module and filter module. Specifically: (1) The present invention constructs a state set containing state information such as target position and speed, and considers the dynamics of target generation, disappearance and movement to obtain the state information of the target at different positions and times. (2) In view of the high clutter environment problem in multi-target tracking, the present invention proposes a measurement module. The measurement module introduces Doppler information and amplitude information, expands the target measurement state, and establishes a joint measurement likelihood function containing azimuth, Doppler information and amplitude information, which enhances the discrimination between the target and clutter. This helps to estimate the target state more accurately, thereby achieving higher tracking accuracy and stronger anti-interference ability in multi-target tracking tasks, and improving the performance of the algorithm. (3) In view of the problem of uncertain number of dynamic targets in multi-target tracking, in the filtering module, the present invention derives the MFGM-CPHD filtering process based on the GM-CPHD filter, and uses UKF to update the mean and covariance of the Gaussian component, thereby improving the accurate estimation of the dynamic evolution of the number and state of the target. The MFGM-CPHD filter proposed in the present invention has carried out a large number of simulation experiments in a simulated high-clutter and known signal-to-noise ratio environment, and uses the target number estimation mean and the optimal sub-pattern assignment (OSPA) mean curve to evaluate the multi-target tracking effect, and is compared with other methods. Comparative studies show that the MFGM-CPHD filter proposed in this invention is improved over the GM-CPHD filter and the DI-GM-CPHD filter that only uses Doppler information in multi-target tracking tasks, and has higher tracking accuracy and better performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1The overall structure diagram of the multi-target tracking model based on multi-feature assisted MFGM-CPHD filter;

[0024] Figure 2 Measurement model structure diagram;

[0025] Figure 3 MFGM-CPHD filtering process and iterative solution structure diagram;

[0026] Figure 4 MFGM-CPHD target number estimation results;

[0027] Figure 5 MFGM-CPHD OSPA distance;

[0028] Figure 6 MFGM-CPHD target number tracking results;

[0029] Figure 7 MFGM-CPHD OSPA distance. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0031] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0032] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but is not intended to be a limitation of the present invention. The multi-target tracking algorithm based on potential probability hypothesis density of this embodiment is to first initialize and introduce Doppler information and amplitude information to expand the target measurement state. Then, based on the state information of the current target, predict the possible position and state of the target at the next moment, and predict the measurement data that the sensor may receive at the next moment. After that, the measurement screening step is performed, and by setting the threshold (d Z ≤σ Z ) to determine whether the measured data is valid, where (d Z ) represents the difference between the measured data and the predicted measurement, (σ Z) represents the preset screening threshold. If the measurement data passes the screening, that is, the difference is within an acceptable range, the state is updated, the valid measurement data is used to correct the state estimation of the target, and pruning and merging operations are performed to optimize the accuracy and efficiency of target tracking. Subsequently, the system evaluates the current tracking performance and determines whether the tracking effect meets the preset performance standard (OSPA<40) by calculating the optimal sub-pattern assignment (Optimal Sub Pattern Assignment, OSPA) distance. If it does, the number of targets is estimated and the state is extracted to obtain the accurate number and state information of the targets in the current scene. Finally, the system outputs the tracking results and ends the current tracking process. On the contrary, if the measurement data does not pass the screening, or the OSPA distance does not meet the preset standard, it is considered that there is clutter interference in the current tracking process. The system will not update the state, but directly output the current tracking result and end the process. The overall implementation structure block diagram is shown as follows. Figure 1 This embodiment implements a multi-target tracking algorithm based on potential probability hypothesis density, including:

[0033] S1. Use the MFGM-CPHD filter to expand the Doppler information and amplitude information into the target measurement information.

[0034] Considering multiple targets existing at a certain moment, the state of each target consists of the position and velocity in the horizontal direction and the position and velocity in the vertical direction. The state model in the MFGM-CPHD filter is constructed in a two-dimensional scene.

[0035] In multi-target tracking, the core applications of RFS theory include modeling the uncertainty of the number of targets, describing the tracking objects in the form of a set, and predicting and updating the target set. The target set is represented in the form of a random finite set, where each element represents a target and its attributes are random variables. This processing method more accurately reflects the uncertainty of the target set.

[0036] In the present invention, the target state set is represented as a random finite set, which includes not only the states of the surviving targets, but also the state sets of the newly generated targets and the target states that survive from the previous moment to the current moment. This representation method can capture the dynamic changes of the target, including the generation, disappearance and movement of the target, and provides a comprehensive and flexible mathematical framework for multi-target tracking.

[0037] S2. Based on the target measurement information, a new measurement likelihood function is established.

[0038] In this implementation, in order to more accurately capture the target state and distinguish the target from clutter in multi-target tracking, a measurement model is established. This model expands the traditional measurement state by introducing additional measurement information, namely Doppler velocity and amplitude information. After introducing amplitude information and Doppler information, the measurement of the target at time k can be expressed as:

[0039]

[0040] in: For target position measurement, is the Doppler velocity measurement, is the amplitude measurement, M k To measure the number.

[0041] In traditional target tracking systems, measurements usually only contain the position or orientation information of the target. The MFGM-CPHD filter further represents the target measurement as a random finite set. The measurement set of the target at time k is represented by RFS as:

[0042] Z k =θ(X k )∪K k (2)

[0043] Where: K k is the false alarm clutter measurement set, Θ(X k ) is the detected target measurement set, and the detection probability p D,k <1.

[0044] Specifically, each target measurement in the measurement model is associated with three main measurement information: azimuth measurement, Doppler velocity measurement and amplitude measurement. These measurement information are used to construct a joint measurement likelihood function, which replaces the traditional single information measurement likelihood function.

[0045] The measurement equation of the target is:

[0046] z c，k =H c，k x k +w k (3)

[0047] in:

[0048] Where: Vk and Rc.k are the azimuth measurement noise matrix and noise covariance matrix, then the target azimuth measurement likelihood function is:

[0049] g(z c，k |x k )=N(z c，k ;H c，k x k , Rc，k ) (4)

[0050] The Doppler measurement equation is:

[0051] z d，k =h k (x k )+n k (5)

[0052] in:

[0053]

[0054] n k ~N(n k ; 0, R d，k ) (7)

[0055] Where: n k and R d,k are the Doppler measurement noise and the noise variance respectively, then the target Doppler measurement likelihood function is:

[0056] g(z d，k |x k )=N(z d，k ;h k (x k )R d，k ) (8)

[0057] When acquiring amplitude information, the echo signal amplitude is related to the echo average SNR signal, which can usually be modeled as a Rayleigh distribution to represent the probability density of the target amplitude and the clutter amplitude.

[0058] The detection probability is False alarm probability In actual applications, due to the influence of environmental factors, the target echo SNR will fluctuate. Assuming that the SNR is [dB 1 ,dB 2 ] is evenly distributed, and the corresponding value range of S is [S 1 ,S 2 ]. Then the target amplitude likelihood function can be expressed as:

[0059]

[0060] It can be seen from equations (3) and (5) that the target azimuth information and Doppler information are only related to the target state, and the amplitude information is only related to the echo signal SNR. It can be assumed that the azimuth, Doppler and amplitude information are independent of each other. Combining equations (4), (8) and (9), the joint measurement likelihood function of azimuth, amplitude and Doppler information can be expressed as:

[0061] Finally, considering the false alarm clutter measurement set, which is inevitable in the actual tracking environment, assuming that the coordinates, Doppler information, and amplitude information of the clutter measurements are independent of each other, the joint clutter density can be expressed as:

[0062] c(z k )=c(z c，k , z d，k , z a，k )=c(z c，k )c(z d，k )c(z a，k ) (11)

[0063] Where: z c,k is the clutter density function of the azimuth information; z d,k is the Doppler information clutter density function; z a,k is the amplitude information clutter likelihood function, and its expression is:

[0064]

[0065] By distinguishing clutter measurements from target measurements and establishing independent probability density functions for them, the MFGM-CPHD filter can achieve more accurate target state estimation and tracking in complex tracking scenarios. This method of integrating multiple measurement information makes the MFGM-CPHD filter more robust and accurate when dealing with dynamic targets and high clutter environments. Its structure is as follows Figure 2 shown.

[0066] S3, based on the CPHD filter, a new update process is introduced to enhance the distinction between target and clutter, including:

[0067] S31, deriving the MFGM-CPHD filtering process based on the GM-CPHD filter;

[0068] S32. Update the mean and covariance of the Gaussian classification by using UKF.

[0069] In this implementation, after the Doppler information and amplitude information are extended to the measurement equation, the MFGM-CPHD filtering process is derived based on the GM-CPHD filter, and the mean and covariance of the Gaussian classification are updated by using the UKF. This process involves iterative solution. The specific steps are: calculate the sampling points and their corresponding weights; use the state equation to perform a single-step prediction of the sampling points; estimate the predicted measurement value according to the measurement equation; use the actual observation data provided by the sensor to adjust the system state and state variance. The overall structure is as follows: Figure 3 shown.

[0070] Specifically, at time k, the intensity function of the target state set contains the corresponding mean and covariance, which is divided into Gaussian components to calculate multiple Sigma sampling points and weight values. After determining these sampling points and the corresponding weights, a single-step prediction is performed on the sampling points through the state equation. In the MFGM-CPHD prediction step, the predicted measurement value is first estimated based on the measurement equation. Since the introduced amplitude and Doppler information have no effect on the target state transition, the potential function and intensity function at the previous moment remain unchanged, and the calculation results of the relevant mean and covariance have a specific form. After applying the amplitude and Doppler measurement information to the extension of the target measurement, the multi-target updated potential distribution function and intensity function of the MFGM-CPHD filter at time k can be obtained by replacing the measurement likelihood function and clutter density in the original GM-CPHD filter update step with the new joint measurement likelihood function and joint clutter density.

[0071] In this implementation, a set of Sigma points are generated by the Sigma point generation algorithm based on the current state estimate and covariance matrix. Next, these Sigma points are used for one-step prediction to calculate the predicted state variables and covariance matrix. For each Sigma point, the corresponding predicted value is obtained by applying the state equation of the system, and the mean of the state prediction is calculated. Similarly, by transforming the observation equation of the predicted Sigma point, the predicted mean of the observed quantity and its covariance matrix can be obtained. Finally, the Kalman gain matrix is ​​solved through the Kalman gain calculation and state update process. Combined with the Kalman gain matrix and actual observation information, a new state estimate is generated. The updated state estimate and observation error covariance are adjusted according to the Kalman gain to reflect the introduction of new information. In summary, UKF provides accurate state estimation in nonlinear systems, and adaptively processes the dynamic characteristics and observation noise of the system while gradually calculating the mean and covariance in the update step.

[0072] experiment

[0073] 1. Experimental environment

[0074] The experiment was simulated in Matlab 2021. The experimental equipment used the processor Inter(R)Core(TM)i7-9700 CPU@3.00GHz, installed memory 32G, operating system 64-bit Windows 10, GPU model GEFORCE RTX2080Ti, and the experiment was run in GPU mode.

[0075] 2. Experimental conditions and parameter settings

[0076] In order to verify the effectiveness of the MFGM-CPHD filter in the multi-target tracking system and the tracking performance under clutter-intensive conditions, the present invention conducts 100 Monte Carlo simulation experiments. The following experimental conditions are set: three moving targets appear in sequence in a two-dimensional area of ​​a plane. These targets move according to their respective motion characteristics listed in Table 1, and at 45 seconds, the first and third targets meet at a certain point. The observation point is set at the center of the coordinate system.

[0077] Table 1 Target motion parameters

[0078]

[0079] In order to better analyze the tracking performance, the following parameters are set: in the target state equation and measurement equation, the standard deviation of the process noise is set to 5, the standard deviation of the measurement noise is set to 1°, T is set to 1s, and the number of tracking steps is set to 100. In the target state transfer matrix and measurement matrix, the target survival probability is set to 0.99, the detection probability is set to 0.98, and the pruning threshold is set to =10 -5 , the merging threshold is 4, the maximum number of Gaussian components is 100, and the number of clutter is 3. When using OSPA distance to analyze the tracking error, the intercept error is 100 and the order is 2.

[0080] 3. Experimental results

[0081] (1) Performance analysis of multi-target tracking based on MFGM-CPHD method

[0082] In order to verify the performance of the MFGM-CPHD filter in the multi-target tracking system, 100 Monte Carlo simulation experiments were conducted to compare it with the GM-CPHD filter and the DI-GM-CPHD filter that only uses Doppler information. The target azimuth information curve, the target number estimation mean curve, and the OSPA distance mean curve were plotted. The results are shown in Figure 2. Figure 4 and Figure 5 shown.

[0083] like Figure 4 As shown in the figure, within the first 20 seconds of tracking, the estimated values ​​of the number of targets by the three filters are close to the true value. At 20 seconds and 45 seconds, the intersection of the new target and the target causes large fluctuations in the GM-CPHD and DI-GM-CPHD filters, while the MFGM-CPHD filter is relatively stable. Throughout the tracking process, the estimated value of the MFGM-CPHD filter is always close to the true value, and the overall tracking effect is the best, while the tracking effect of the GM-CPHD filter is poor. The tracking effect of the DI-GM-CPHD filter is better than that of the GM-CPHD but lower than that of the MFGM-CPHD.

[0084] Depend on Figure 5It can be seen that the OSPA distances of the three filters are roughly the same and relatively stable in the first 20 seconds. After 25 seconds and 45 seconds, there are large fluctuations due to the intersection of the new target and the target, and then it tends to be flat and GM-CPHD is stable at about 30, DI-GM-CPHD is stable at about 25, and MFGM-CPHD is stable at about 20. It can be seen that the MFGN-CPHD filter has the best performance in the entire tracking process.

[0085] Depend on Figure 4 and Figure 5 It can be seen that in a high-clutter environment, the MFGM-CPHD filter can effectively track multiple targets. Compared with the traditional PHD filter and the DI-GM-CPHD filter that only uses Doppler information, the performance of the MFGM-CPHD filter in multi-target tracking can more effectively estimate the number of targets and has better tracking accuracy.

[0086] (2) Multi-target tracking performance analysis of MFGM-CPHD filter at different SNRs

[0087] In order to verify the impact of SNR on the tracking performance of the MFGM-CPHD algorithm, the SNR was set to 10, 15, 20, and 30 dB respectively, with other conditions unchanged, and the OSPA distance and target number estimation curves were plotted. The results are shown in the figure below. Figure 6 and Figure 7 shown.

[0088] Table 2 summarizes the average values ​​of OSPA from 100 Monte Carlo simulation experiments under different SNRs.

[0089] Table 2 Average OSPA distance

[0090]

[0091] Depend on Figure 6 , Figure 7 From Table 2, it can be seen that SNR is a factor that affects the tracking performance of the MFGM-CPHD algorithm. As SNR increases, the discrimination between the target and clutter gradually increases, thereby enhancing the clutter suppression capability, and the OSPA distance gradually decreases, improving the accuracy.

Claims

1. A multi-target tracking algorithm based on potential probability hypothesis density, characterized in that: include: S1. Use MFGM-CPHD filter to expand Doppler information and amplitude information into target measurement information; S2. Based on the target measurement information, a new measurement likelihood function is established; S3. Based on the CPHD filter, a new update process is introduced to enhance the discrimination between target and clutter.

2. The multi-target tracking algorithm based on potential probability hypothesis density according to claim 1 is characterized in that: The S1 includes: in a two-dimensional scene, at the time k-1, there are N k-1 targets. Each target has its own state, which includes the position and velocity in the horizontal and vertical directions. At the next moment k, the state of the target may change. Some targets may disappear, some targets may still be there, and new targets may appear. The state of all targets at time k is represented by the RFS method. This representation method includes two parts: one is the change in the state of the target that survives from time k-1 to time k; the other is the state of the new target that appears at time k. After introducing amplitude information and Doppler information, the measurement of the target at time k includes azimuth measurement, Doppler velocity measurement and amplitude measurement. There may be multiple targets at this moment, and the set of measurement values ​​of all targets can be represented by RFS. This set includes erroneous measurement values ​​such as the actual detected target measurement values ​​and the false alarm clutter measurement set.

3. The multi-target tracking algorithm based on potential probability hypothesis density according to claim 1 is characterized in that: In S2: A measurement module is proposed to address the high clutter environment problem in multi-target tracking. At a certain moment k, target measurement information including target position measurement, Doppler velocity measurement and amplitude measurement is introduced to form the state vector of the target at moment k. These measurement information are integrated and represented by RFS. Afterwards, the target state equation is established and the measurement noise is processed. By constructing a noise matrix and a noise covariance matrix, these noises can be modeled and processed. In order to describe the probability of obtaining a specific measurement value under a given target state, a target measurement likelihood function is derived. By maximizing the likelihood function, the optimal estimate of the target state can be obtained. When multiple targets are considered, the measurement model can be expanded to a joint measurement likelihood function. By optimizing the joint measurement likelihood function, multi-target tracking and estimation can be achieved.

4. The multi-target tracking algorithm based on potential probability hypothesis density according to claim 1 is characterized in that: The S3 includes: S31, deriving the MFGM-CPHD filtering process based on the GM-CPHD filter; S32. Update the mean and covariance of the Gaussian classification by using UKF.

5. The multi-target tracking algorithm based on potential probability hypothesis density according to claim 4 is characterized in that: In the S31, a new filtering process, namely MFGM-CPHD filtering, is derived based on the GM-CPHD filter on the basis of adding Doppler information and amplitude information to the measurement equation. At time k, the target state set intensity function has a corresponding mean and covariance, and multiple Sigma sampling points and weight values ​​need to be calculated for the Gaussian component. After calculating the sampling points and their corresponding weights, the state equation is used to perform a single-step prediction on the sampling points. In the MFGM-CPHD prediction step, the predicted measurement value is first estimated based on the measurement equation. Since the added amplitude and Doppler information do not affect the target state transfer, the potential distribution function and intensity function of the previous moment (k-1 moment) remain unchanged, and the calculation of the relevant mean and covariance has a specific result. After the amplitude and Doppler measurement information are introduced to expand the target measurement, the measurement likelihood function and clutter density in the original GM-CPHD filter update process are replaced by the new joint measurement likelihood function and joint clutter density, and the multi-target updated potential distribution function and intensity function of the MFGM-CPHD filter at time k can be obtained.

6. The multi-target tracking algorithm based on potential probability hypothesis density according to claim 4 is characterized in that: In the S32: In the UKF algorithm, first, according to the current state estimate and covariance matrix, a set of Sigma points are generated by the Sigma point generation algorithm. Next, these Sigma points are used for one-step prediction to calculate the predicted state variables and covariance matrix. For each Sigma point, the state equation of the system is applied to obtain the corresponding predicted value, and the mean of the state prediction is calculated. Similarly, by transforming the observation equation of the predicted Sigma point, the predicted mean of the observed quantity and the covariance matrix of the observation prediction can be obtained. Finally, the Kalman gain calculation and state update are used to calculate the Kalman gain matrix, which represents the influence of the observation information on the state update. The Kalman gain matrix is ​​used to combine the prediction and actual observation information to obtain a new state estimate. The error covariance of the updated state estimate and observation will be adjusted according to the Kalman gain to reflect the introduction of new information. Through the above process, UKF can provide accurate state estimation in nonlinear systems, gradually calculate the mean and covariance in the update step, and adaptively process the dynamic characteristics and observation noise of the system.

Images