A multi-target tracking method

Abstract

The present invention relates to the field of target tracking technology, and in particular, to a multi-target tracking method, including: establishing a nonlinear state equation and a nonlinear measurement equation of an ocean target detected by a radar sensor; determining a covariance matrix of a Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm based on the equation; using a mean square root cubature Kalman filtering algorithm to process the predicted covariance matrix to obtain a calculation result; determining the square root of the covariance matrix of the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm according to the calculation result; obtaining the predicted state at the next moment according to the square root of the predicted covariance matrix, the target state at the current moment and the predicted state, obtaining the updated target state according to the updated covariance matrix square root, the predicted state at the next moment and the measurement, and realizing tracking and trajectory estimation of ocean targets. The present invention estimates the number and state of ocean targets more stably and accurately in nonlinear scenarios, and improves the accuracy of multi-target tracking.

Description

Technical Field

[0001] The present invention relates to the technical field of target tracking, and in particular to a multi-target tracking method. Background Art

[0002] Multi-target tracking is the process of determining the number and state of multiple dynamic targets based on the measurement information obtained by the radar sensor. In the actual multi-target tracking problem, the observation of the radar sensor has random errors, and when the detection probability is small, false alarms and missed alarms are prone to occur; usually, the number of targets is an unknown quantity, and there is clutter interference in the radar detection area, and targets are born and disappear; there is uncertainty in the trajectory of the target. The above problems make multi-target tracking technology challenging.

[0003] The commonly used methods of current multi-target tracking methods include two categories: the first one uses traditional multi-target tracking methods, including: joint probabilistic data association methods, multi-hypothesis tracking methods. This type of method is based on data association to solve the multi-target tracking problem, and is accompanied by a large number of data association assumptions, which increases the computational complexity; the second one uses a method based on random finite sets. This method has natural advantages in the application of multi-target tracking. It not only solves the potential estimation problem in multi-target tracking, but also avoids the data association problem caused by the correspondence between unknown observations and target states.

[0004] In practical applications, the area detected by the radar is often accompanied by different clutter interferences, and the target motion pattern is often nonlinear. Therefore, it is particularly important to adopt a multi-target tracking method that can handle nonlinear low detection probability scenarios. At present, the methods for such scenarios include: particle filter (BP) algorithm and sequential Monte Carlo (SMC) method. These two methods use particles to solve the problem of multi-target tracking in nonlinear scenarios. However, the number of particles scattered is the main influencing factor of tracking accuracy. When the number of particles is too large or too small, false alarms or missed detections will occur respectively. At the same time, particles are prone to degradation, which leads to a decrease in tracking accuracy. At the same time, Gaussian nonlinear filtering methods for nonlinear scenarios mainly include: extended Kalman filtering method, unscented Kalman filtering method and cubature Kalman filtering method. The extended Kalman filtering method needs to calculate the Jacobian matrix when linearizing the system, and has only first-order accuracy; the unscented Kalman filtering method obtains a series of sampling point sets and transfers them through nonlinear functions. When the scale parameter is too small, the covariance matrix cannot remain positive, thereby affecting the stability of the filter; the cubature Kalman filtering method approximates the target by transferring volume points using nonlinear functions according to the third-order spherical-radial volume criterion. However, the covariance square root failure is prone to occur during the transfer process, which leads to filtering errors.

[0005] The present invention mainly solves the above problems and provides a more stable and accurate target tracking solution, thereby achieving the purpose of improving the multi-target tracking accuracy.

[0006] For example, a Chinese patent with publication number CN113409363A discloses a multi-target tracking method based on BP-Poisson multi-Bernoulli hybrid filtering algorithm, including: (1) initializing the algorithm; (2) predicting the target state; (3) updating the target state; (4) pruning the Poisson component and the MBM component in the target state; (5) box particle resampling the Poisson component and the MBM component; (6) estimating the target state to obtain a global target state estimate. The multi-target tracking method based on BP-Poisson multi-Bernoulli hybrid filtering algorithm provided by the invention has the advantages of high tracking accuracy, fast calculation speed, and distinguishable tracks.

[0007] For example, a Chinese patent with publication number CN106204645A discloses a multi-target tracking method, including: synchronously tracking and extracting multiple measuring points (multiple targets), and optimizing each tracking measuring point, which relates to the field of vibration testing and analysis, and can realize the synchronous extraction of vibration signals of multiple measuring points on the test structure, and provide data support for subsequent analysis, such as structural modal analysis; the present invention is suitable for structural deformation and vibration testing and analysis.

[0008] The above patents all have the problems raised by this background technology: first, the above patents implement multi-target tracking technology in nonlinear scenarios through the BP method, which can effectively solve the problem of multi-target tracking in nonlinear scenarios. However, when the particles are degraded or the number of particles is too large, it is easy to cause complex calculations, reduced tracking accuracy, and over-detection. When the number of particles is small, it leads to missed detection during target tracking. Secondly, a multi-target tracking method involves a high degree of clutter interference in actual scenarios, that is, the problem of multi-target tracking in low detection probability scenarios, which is easy to lead to reduced tracking accuracy and cannot accurately estimate the number of targets and motion status. Summary of the invention

[0009] To solve the above technical problems, the present invention proposes a multi-target tracking method, which first establishes a multi-target tracking state equation and a measurement equation in a nonlinear low detection probability scenario; secondly, a root mean square cubature Kalman filter algorithm is used to process the target tracking state equation and the measurement equation to obtain a square root covariance matrix in the prediction and update process; based on the prediction and update square root covariance matrix, the prediction and update steps of the Poisson multi-Bernoulli mixture algorithm implemented by the Gaussian mixture are determined; finally, the algorithm is used to complete the estimation of the target state in the nonlinear low detection probability scenario, obtain the target state value, and realize target tracking in the scenario, thereby achieving the purpose of more stably and accurately estimating the number and state of targets in the nonlinear low detection probability scenario and improving the accuracy of multi-target tracking.

[0010] To achieve the above object, the present invention provides the following technical solutions:

[0011] A multi-target tracking method includes the following specific steps:

[0012] Step S1: establishing a nonlinear state equation and a nonlinear measurement equation of the ocean target detected by the radar sensor;

[0013] Step S2: determining the covariance matrix of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the nonlinear state equation and the nonlinear measurement equation; the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm includes a prediction process and an update process; the covariance matrix includes a prediction covariance matrix and an update covariance matrix;

[0014] Step S3: Processing the prediction covariance matrix using a root mean square cubature Kalman filter algorithm to obtain calculation results; the calculation results include state prediction mean, prediction error covariance matrix square root, measurement prediction mean, innovation covariance square root, cross-covariance matrix, Kalman gain, update mean and update error covariance matrix square root;

[0015] Step S4: determining the covariance matrix square root of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the calculation result, wherein the covariance matrix square root includes the prediction covariance matrix square root and the update covariance matrix square root;

[0016] Step S5: According to the square root of the predicted covariance matrix, the target state at the current moment and the predicted state, the predicted state at the next moment is obtained; according to the square root of the updated covariance matrix, the predicted state at the next moment and the measurement, the updated target state is obtained to complete the tracking and trajectory estimation of the ocean target.

[0017] Specifically, the nonlinear state equation and nonlinear measurement equation of the ocean target in step S1 are expressed as:

[0018] xk =Fx k-1 +u k-1

[0019] z k =h(x k )+υ k

[0020] Among them, x k represents the target state value at time k, z k represents the nonlinear measurement equation at the kth moment in the tracking process, F represents the nonlinear state transfer matrix, h(·) represents the nonlinear measurement transfer function, u k-1 Indicates that the mean is 0 and the covariance matrix is ​​Q k-1 The process noise, υ k Indicates that the mean is 0, and the covariance matrix is ​​R k The measurement noise.

[0021] Specifically, the calculation steps of the prediction process in step S2 are as follows:

[0022] Step S201: Calculate the Gaussian form of the newly generated Poisson intensity at the kth moment in the ocean target tracking process, denoted as:

[0023]

[0024] Among them, λ b represents the Gaussian form of the Poisson intensity of the new target, γ represents the new target sign, J γ，k represents the number of Gaussian components at the kth moment in the tracking process, w q，γ，k represents the new target weight of the qth Gaussian component at the kth moment in the tracking process, N(·) represents the Gaussian distribution, represents the new target mean of the qth Gaussian component at the kth moment in the tracking process, P q，γ，k represents the new target covariance matrix of the qth Gaussian component at the kth moment in the tracking process;

[0025] Step S202: Calculate the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, which is expressed as:

[0026]

[0027] Among them, μ k-1 represents the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, J k-1 represents the number of Gaussian components at the k-1th moment in the tracking process, w q，k-1 represents the new target weight of the qth Gaussian component at the k-1th moment in the tracking process, represents the new target mean of the qth Gaussian component at the k-1th moment in the tracking process, Pq，k-1 represents the new target covariance matrix of the qth Gaussian component at the k-1th moment in the tracking process;

[0028] Step S203: Calculate the Poisson intensity density function of the predicted part at time k during the tracking process, which is expressed as:

[0029]

[0030] Among them, μ k|k-1 represents the predicted Poisson intensity density function at time k predicted by time k-1, λ b represents the Poisson intensity of the new target, J k-1 represents the target state value x at time k k The number of Gaussian components, W q，k|k-1 =w q，k-1 p s f represents the target prediction weight of the qth Gaussian component at time k predicted by k-1 time, p s =0.99 represents the target survival probability, f represents the state transition probability, represents the target prediction mean of the qth Gaussian component at time k predicted by k-1 time, F represents the nonlinear state transfer matrix, P q，k|k-1 =Q k +F Pq，k-1 F T represents the target prediction covariance matrix of the qth Gaussian component at time k predicted by time k-1, Q k represents the process noise covariance matrix, F T represents the transpose of F;

[0031] Step S204: Calculate the predicted Bernoulli-Gaussian mixture parameters during the tracking process:

[0032]

[0033] in, represents the prediction weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian weight of the i-th Bernoulli component in the a-th global hypothesis at the k-1-th moment in the tracking process, represents the predicted mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian mean of the i-th Bernoulli component in the a-th global hypothesis, represents the predicted covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Gaussian covariance matrix of the i-th Bernoulli component in the a-th global hypothesis.

[0034] Specifically, the update process includes: an undetected target update step, a first detected target update step, and a detected target update step; the update process calculation steps of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm are as follows:

[0035] Step S301: Undetected target update step, setting the Gaussian form of the Poisson intensity density function at the kth moment in the tracking process to:

[0036]

[0037] Where μ represents the Poisson part sign, represents the number of Gaussian components at time k, represents the new target weight of the qth Gaussian component at time k, represents the new target mean of the qth Gaussian component at time k, represents the new target covariance matrix of the qth Gaussian component at time k;

[0038] Compute the Poisson intensity update posterior density function:

[0039] μ k|k =q D μ k|k-1

[0040] Among them, q D represents the probability of missed detection of the target;

[0041] Step S302: the first detected target update step, calculates the multi-Bernoulli component probability density function, which is recorded as:

[0042]

[0043] in, represents the updated probability density function of the i-th Bernoulli component in the a-th global hypothesis at time k, J k|k-1 represents the number of Gaussian components of the multi-Bernoulli component at time k, z k represents the observed value corresponding to the target state at time k, w q，k|k represents the update weight of the qth multi-Bernoulli Gaussian component at time k, represents the Gaussian mean of the qth multi-Bernoulli component at time k, P q，k represents the covariance matrix of the qth multi-Bernoulli Gaussian component at time k;

[0044] Parameter w q，k|k , and P q，k The calculation is as follows:

[0045]

[0046] Among them, Rk represents the measurement noise covariance matrix, H represents the nonlinear measurement matrix, and p D =0.96 indicates the probability of detection;

[0047] Step S303: Detected target update step, calculate the corresponding weight, target existence probability and probability density function, recorded as:

[0048]

[0049]

[0050] in, represents the Gaussian update weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the Gaussian prediction weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the probability of existence of Gaussian prediction of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the number of Gaussian components of the i-th Bernoulli component in the a-th global hypothesis at time k-1, H k represents the nonlinear measurement matrix at time k, represents the probability of existence of Gaussian update of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the updated covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Indicates that the target was missed.

[0051] Specifically, the covariance matrix in step S2 includes a prediction covariance matrix and an update covariance matrix, and the prediction covariance matrix and the update covariance matrix are calculated as follows:

[0052]

[0053]

[0054] Among them, H T represents the transpose of the matrix H.

[0055] Specifically, the specific calculation steps for calculating the result in step S3 are as follows:

[0056] Step S401: Predict the covariance matrix by Cholesky decomposition Recorded as in, Represents the covariance matrix The predicted value; chol() represents the Cholesky decomposition function;

[0057] Step S402: Generate predicted volume point x using the third-order spherical radial volume criterion q，k|k-1 and weight w q =1 / 2n, n represents the system state dimension, the transfer volume point f k (·) represents the nonlinear state function;

[0058] Step S403: Calculate the state prediction mean

[0059] Step S404: Calculate the square root of the prediction error covariance matrix: in, Γ Q，k-1 Indicates Q k-1 The root mean square of the matrix, Tria represents the matrix Perform QR decomposition operation;

[0060] Step S405: Generate updated volume point x q，+ , using the nonlinear measurement function h k (.) transfer, get the transfer volume point

[0061] Step S406: Calculate the measurement prediction mean

[0062] Step S407: Calculate the square root of the innovation covariance: in, Γ R，k Represents R k-1 The root mean square of the matrix, Tria represents the matrix ([λ z，+ , Γ R，k ]) Perform QR decomposition operation; calculate the cross-covariance matrix as in,

[0063] Step S408: Calculate the Kalman gain as The updated mean is calculated as

[0064] Step S409: Calculate the square root of the updated error covariance matrix:

[0065] Specifically, the square root of the prediction covariance matrix in step S4 is calculated as follows:

[0066] Specifically, the updated covariance matrix square root in step S4 is calculated as follows:

[0067] Specifically, the predicted state at the next moment is obtained in step S5, and the square root of the predicted covariance matrix is ​​used to represent the uncertainty of the predicted state. The target state, the predicted state and the uncertainty are input as initial values ​​into the prediction process in the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; the target state and the predicted state are iterated through the prediction process, and the predicted state at the next moment is output, and the predicted states output by the prediction process are connected in chronological order to form the target initial trajectory.

[0068] Specifically, the updated target state is obtained in step S5, and the uncertainty of the updated target state is represented by the square root of the updated covariance matrix; the predicted state, measurement and updated target state uncertainty at the next moment are input as initial values ​​into the update process in the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; the predicted state and measurement are iterated through the update process, the updated state is output, the initial trajectory of the target is updated, and the final trajectory of the target is formed.

[0069] A computer-readable storage medium stores computer instructions, which execute the steps of a multi-target tracking method when the computer instructions are executed.

[0070] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of a multi-target tracking method when executing the computer program.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] 1. The present invention proposes a multi-target tracking method. The overall filtering algorithm adopted solves the problems of complex calculation and "combination explosion" of traditional filtering algorithms. In the face of increasing target number and clutter rate, the calculation amount is reduced and the efficiency of target tracking is improved.

[0073] 2. The present invention proposes a multi-target tracking method, which adopts a root mean square cubature Kalman filter algorithm to process nonlinear systems, transfers an error covariance matrix in the form of a square root, always maintains the positive definiteness of the matrix, enhances the numerical accuracy and stability of the algorithm, and can accurately estimate the number of targets in the multi-target tracking process under a nonlinear system.

[0074] 3. The present invention proposes a multi-target tracking method. The overall algorithm adopts a method combining a Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm with a root mean square volumetric Kalman filtering algorithm to achieve multi-target tracking. When facing multi-target tracking in low detection probability scenarios, it can effectively and accurately estimate the number of targets, and the stability of the tracking process is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 A flowchart of a multi-target tracking method of the present invention;

[0076] Figure 2 It is a simulation diagram of the motion trajectory of ocean targets in a strong nonlinear high clutter and low detection probability scenario of a multi-target tracking method of the present invention;

[0077] Figure 3 A target potential estimation diagram of a multi-target tracking method of the present invention in a strong nonlinear high clutter and low detection probability scenario;

[0078] Figure 4 This is a comparison diagram of 0SPA distances in a strong nonlinear, high clutter, and low detection probability scenario of a multi-target tracking method of the present invention;

[0079] Figure 5 The present invention is a schematic diagram of the composition of an electronic device of a multi-target tracking method. DETAILED DESCRIPTION

[0080] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, in the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate the orientation or position relationship based on the orientation or position relationship shown in the accompanying drawings, which is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "No. 1", "No. 2" and "No. 3" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. The present invention is further explained below in conjunction with specific embodiments.

[0081] Embodiment 1:

[0082] See also Figure 1 , an embodiment of the present invention provides: a multi-target tracking method, comprising the following specific steps:

[0083] Step S1: establishing a nonlinear state equation and a nonlinear measurement equation of the ocean target detected by the radar sensor;

[0084] Step S2: determining the covariance matrix of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the nonlinear state equation and the nonlinear measurement equation; the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm includes a prediction process and an update process; the covariance matrix includes a prediction covariance matrix and an update covariance matrix;

[0085] Step S3: Processing the prediction covariance matrix using a root mean square cubature Kalman filter algorithm to obtain calculation results; the calculation results include state prediction mean, prediction error covariance matrix square root, measurement prediction mean, innovation covariance square root, cross-covariance matrix, Kalman gain, update mean and update error covariance matrix square root;

[0086] Step S4: determining the covariance matrix square root of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the calculation result, wherein the covariance matrix square root includes the prediction covariance matrix square root and the update covariance matrix square root;

[0087] Step S5: According to the square root of the predicted covariance matrix, the target state at the current moment and the predicted state, the predicted state at the next moment is obtained; according to the square root of the updated covariance matrix, the predicted state at the next moment and the measurement, the updated target state is obtained to complete the tracking and trajectory estimation of the ocean target.

[0088] In this embodiment, the nonlinear state equation and nonlinear measurement equation of the ocean target in step S1 can be expressed as:

[0089] x k =Fx k-1 +u k-1

[0090] z k =h(x k )+υ k

[0091] Among them, x k represents the target state value at time k, z k represents the nonlinear measurement equation at the kth moment in the tracking process, F represents the nonlinear state transfer matrix, h(·) represents the nonlinear measurement transfer function, u k-1 Indicates that the mean is 0 and the covariance matrix is ​​Q k-1 The process noise, υ k Indicates that the mean is 0, and the covariance matrix is ​​R k The measurement noise.

[0092] In this embodiment, the calculation steps of the prediction process in step S2 are as follows:

[0093] Step S201: Calculate the Gaussian form of the newly generated Poisson intensity at the kth moment in the ocean target tracking process, denoted as:

[0094]

[0095] Among them, λ b represents the Gaussian form of the Poisson intensity of the new target, γ represents the new target sign, J γ，k represents the number of Gaussian components at the kth moment in the tracking process, w q，γ，k represents the new target weight of the qth Gaussian component at the kth moment in the tracking process, N(·) represents the Gaussian distribution, represents the new target mean of the qth Gaussian component at the kth moment in the tracking process, P q，γ，k represents the new target covariance matrix of the qth Gaussian component at the kth moment in the tracking process;

[0096] Step S202: Calculate the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, which is expressed as:

[0097]

[0098] Among them, μ k-1 represents the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, J k-1 represents the number of Gaussian components at the k-1th moment in the tracking process, w q，k-1 represents the new target weight of the qth Gaussian component at the k-1th moment in the tracking process, represents the new target mean of the qth Gaussian component at the k-1th moment in the tracking process, P q，k-1 represents the new target covariance matrix of the qth Gaussian component at the k-1th moment in the tracking process;

[0099] Step S203: Calculate the Poisson intensity density function of the predicted part at time k during the tracking process, which is expressed as:

[0100]

[0101] Among them, μ k|k-1 represents the predicted Poisson intensity density function at time k predicted by time k-1, λ b represents the Poisson intensity of the new target, J k-1 represents the target state value x at time k k The number of Gaussian components, w q，k|k-1 =w q，k-1 p s f represents the target prediction weight of the qth Gaussian component at time k predicted by k-1 time, p s =0.99 represents the target survival probability, f represents the state transition probability, represents the target prediction mean of the qth Gaussian component at time k predicted by k-1 time, F represents the nonlinear state transfer matrix, P q，k|k-1 =Q k +FP q，k-1 F T represents the target prediction covariance matrix of the qth Gaussian component at time k predicted by time k-1, Q k represents the process noise covariance matrix, F T represents the transpose of F;

[0102] Step S204: Calculate the predicted Bernoulli-Gaussian mixture parameters during the tracking process:

[0103]

[0104] in, represents the prediction weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian weight of the i-th Bernoulli component in the a-th global hypothesis at the k-1-th moment in the tracking process, represents the predicted mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian mean of the i-th Bernoulli component in the a-th global hypothesis, represents the predicted covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Gaussian covariance matrix of the i-th Bernoulli component in the a-th global hypothesis.

[0105] In this embodiment, the update process includes: an undetected target update step, a first detected target update step, and a detected target update step; the update process calculation steps of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm are as follows:

[0106] Step S301: Undetected target update step, setting the Gaussian form of the Poisson intensity density function at the kth moment in the tracking process to:

[0107]

[0108] Where μ represents the Poisson part sign, represents the number of Gaussian components at time k, represents the new target weight of the qth Gaussian component at time k, represents the new target mean of the qth Gaussian component at time k, represents the new target covariance matrix of the qth Gaussian component at time k;

[0109] Compute the Poisson intensity update posterior density function:

[0110] μ k|k =q D μ k|k-1

[0111] Among them, q D represents the probability of missed detection of the target;

[0112] Step S302: the first detected target update step, calculates the multi-Bernoulli component probability density function, which is recorded as:

[0113]

[0114] in, represents the updated probability density function of the i-th Bernoulli component in the a-th global hypothesis at time k, J k|k-1 represents the number of Gaussian components of the multi-Bernoulli component at time k, z k represents the observed value corresponding to the target state at time k, w q，k|k represents the update weight of the qth multi-Bernoulli Gaussian component at time k, represents the Gaussian mean of the qth multi-Bernoulli component at time k, P q，k represents the covariance matrix of the qth multi-Bernoulli Gaussian component at time k;

[0115] Parameter w q，k|k , and P q，k The calculation is as follows:

[0116]

[0117] Among them, R k represents the measurement noise covariance matrix, H represents the nonlinear measurement matrix, and p D =0.96 indicates the probability of detection;

[0118] Step S303: Detected target update step, calculate the corresponding weight, target existence probability and probability density function, recorded as:

[0119]

[0120]

[0121] in, represents the Gaussian update weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the Gaussian prediction weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the probability of existence of Gaussian prediction of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the number of Gaussian components of the i-th Bernoulli component in the a-th global hypothesis at time k-1, Hk represents the nonlinear measurement matrix at time k, represents the probability of existence of Gaussian update of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the updated covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Indicates that the target was missed.

[0122] In this embodiment, the covariance matrix in step S2 includes a prediction covariance matrix and an update covariance matrix, and the prediction covariance matrix and the update covariance matrix are calculated as follows:

[0123]

[0124]

[0125] Among them, H T represents the transpose of the matrix H.

[0126] In this embodiment, the specific calculation steps of the calculation result in step S3 are as follows:

[0127] Step S401: Predict the covariance matrix by Cholesky decomposition Recorded as in, Represents the covariance matrix The predicted value; chol() represents the Cholesky decomposition function;

[0128] Step S402: Generate predicted volume point x using the third-order spherical radial volume criterion q，k|k-1 and weight w q =1 / 2n, n represents the system state dimension, the transfer volume point f k (·) represents the nonlinear state function;

[0129] Step S403: Calculate the state prediction mean

[0130] Step S404: Calculate the square root of the prediction error covariance matrix: in, Γ Q，k-1 Indicates Q k-1 The root mean square of the matrix, Tria represents the matrix Perform QR decomposition operation;

[0131] Step S405: Generate updated volume point x q，+ , using the nonlinear measurement function h k (.) transfer, get the transfer volume point

[0132] Step S406: Calculate the measurement prediction mean

[0133] Step S407: Calculate the square root of the innovation covariance: in, Γ R，k Represents R k-1 The root mean square of the matrix, Tria represents the matrix ([λ z，+ , Γ R，k ]) Perform QR decomposition operation; calculate the cross-covariance matrix as in,

[0134] Step S408: Calculate the Kalman gain as The updated mean is calculated as

[0135] Step S409: Calculate the square root of the updated error covariance matrix:

[0136] In this embodiment, the prediction covariance matrix square root of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm in step S4 is calculated as follows:

[0137] In this embodiment, the updated covariance matrix square root of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm in step S4 is calculated as follows:

[0138] In this embodiment, the predicted state at the next moment is obtained in step S5, and the square root of the predicted covariance matrix is ​​used to represent the uncertainty of the predicted state. The target state, the predicted state and the uncertainty are input as initial values ​​into the prediction process in the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; the target state and the predicted state are iterated through the prediction process, and the predicted state at the next moment is output, and the predicted states output by the prediction process are connected in chronological order to form the target initial trajectory.

[0139] In this embodiment, the updated target state is obtained in step S5, and the uncertainty of the updated target state is represented by the square root of the updated covariance matrix; the predicted state, measurement and updated target state uncertainty at the next moment are input as initial values ​​into the update process in the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; the predicted state and measurement are iterated through the update process, the updated state is output, the initial trajectory of the target is updated, and the final trajectory of the target is formed.

[0140] In order to approach the real environment of ocean target tracking, a strong nonlinear high clutter and low detection probability simulation scenario is set, and a simulation experiment is set up: the performance of a multi-target tracking method in a strong nonlinear high clutter and low detection probability scenario.

[0141] The radar detection area is set to [-2000, 4000]m×[-1000, 2500]m, and there are three targets doing nonlinear motion. The target state is set to (x, y) is the target position component, is the target velocity component, ω k is the target turning rate, the process noise is Gaussian white noise with a mean of 0, and the state transfer matrix is The simulation time is 100s, the sampling time is 1s, the target motion state is, and the target survival probability p s =0.99, the low detection probability p D =0.60, and the high clutter parameter is set to 20.

[0142] After giving the above initial values ​​and simulation parameters, the specific steps in each simulation cycle are as follows:

[0143] Step 1: New target state prediction and update;

[0144] Step 2: Predict and update the status of the surviving target;

[0145] Step 3: Extract the target state to form a trajectory.

[0146] This embodiment uses Matlab language to test the provided method and compares the algorithm of the present invention, the root mean square volumetric Kalman-Gaussian mixed multi-Bernoulli filter algorithm, the extended Kalman-Poisson multi-Bernoulli mixed filter algorithm and the sequential Monte Carlo-Poisson multi-Bernoulli mixed filter algorithm. Monte Carlo simulations are performed 100 times for each of the above four algorithms.

[0147] See also Figure 2 , Figure 2 This is a simulation diagram of the target motion trajectory in a strong nonlinear, high clutter and low detection probability scenario provided by an embodiment of the present invention. The direction indicated by the arrow is the motion direction of the target, and each “.” belongs to clutter.

[0148] See also Figure 3 and Figure 4 , Figure 3 is a potential estimation error diagram in a strong nonlinear high clutter and low detection probability scenario provided by an embodiment of the present invention; Figure 4 This is a comparison diagram of OSPA distances in a strong nonlinear high clutter low detection probability scenario provided by an embodiment of the present invention. Figure 3 It can be seen from the middle curve that in the case of high clutter and low detection probability, the target potential estimation of the four algorithms is significantly lower than the true value. The EKF-PMBM algorithm is second only to the SCKF-GM-MB algorithm. Since the EKF-PMBM algorithm conflicts with the linear assumption principle under the strong nonlinear high clutter and low detection probability, the algorithm diverges and generates estimation errors. At the same time, the EKF-PMBM algorithm has the problem of difficulty in calculating the Jacobian matrix, which makes the calculation more complicated. The SMC-PMBM filtering algorithm has the worst performance in target potential estimation compared with the other three algorithms in this scenario. In the strong nonlinear high clutter and low detection probability scenario, the SMC-PMBM algorithm involves too many sampling particles in the SMC, which is prone to particle degradation, and interferes with the target number estimation. At the same time, when the number of particles increases, the calculation efficiency of the algorithm is greatly reduced. Figure 3 The curve shows that the proposed algorithm has better target potential estimation effect than the other three algorithms. Figure 4 The OSPA distance comparison chart is analyzed. When the OSPA distance is smaller, the performance of the algorithm is better. It can be seen from the curve in the figure that due to the low detection probability setting and the large clutter rate setting, the tracking effects presented by various filtering algorithms are quite different. The filter proposed in the present invention has the smallest OSPA distance and the best effect, followed by the SCKF-GM-MB algorithm. The performance difference between this algorithm and the algorithm of the present invention lies in the MB algorithm. The present invention is applicable to the Poisson-multi-Bernoulli hybrid filtering algorithm. The Poisson-multi-Bernoulli hybrid filtering algorithm is divided into a Poisson part and a multi-Bernoulli hybrid part, which respectively track new targets and existing targets, improving The efficiency and accuracy of the algorithm are compared. When the detection probability of the EKF-PMBM algorithm is set to be low and the clutter rate is set to be high, the EKF has lower computational efficiency and low robustness compared to the SCKF. The OSPA distance is larger and the performance is poorer than the algorithm of the present invention and the SCKF-GM-MB algorithm. The OSPA distance of the SMC-PMBM algorithm in this scenario is the largest, so its performance is relatively poor. When the number of sampling particles of the SMC is large in this scenario, there is a phenomenon of over-detection of the target, and the calculation is more cumbersome. When the number of sampling particles is small, there is a phenomenon of missed detection of the target, which reduces the precision and accuracy of target tracking. In summary, the algorithm of the present invention is superior to the three algorithms compared in target potential estimation and tracking performance in the scenario of strong nonlinearity, high clutter and low detection probability.

[0149] Example 2

[0150] See also Figure 5 An electronic device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of a multi-target tracking method when executing the computer program.

[0151] A computer-readable storage medium stores computer instructions, which execute the steps of a multi-target tracking method when the computer instructions are executed.

[0152] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0153] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0154] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0155] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0156] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. A multi-target tracking method, characterized in that: The specific steps include: Step S1: establishing a nonlinear state equation and a nonlinear measurement equation of the ocean target detected by the radar sensor; Step S2: determining the covariance matrix of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the nonlinear state equation and the nonlinear measurement equation; The Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm includes a prediction process and an update process; the covariance matrix includes a prediction covariance matrix and an update covariance matrix; Step S3: Processing the prediction covariance matrix using a root mean square cubature Kalman filter algorithm to obtain calculation results; the calculation results include state prediction mean, prediction error covariance matrix square root, measurement prediction mean, innovation covariance square root, cross-covariance matrix, Kalman gain, update mean and update error covariance matrix square root; Step S4: determining the covariance matrix square root of the Gaussian mixture Poisson multi-Bernoulli mixture filtering algorithm based on the calculation result, wherein the covariance matrix square root includes the prediction covariance matrix square root and the update covariance matrix square root; Step S5: According to the square root of the predicted covariance matrix, the target state at the current moment and the predicted state, the predicted state at the next moment is obtained; according to the square root of the updated covariance matrix, the predicted state at the next moment and the measurement, the updated target state is obtained to complete the tracking and trajectory estimation of the ocean target.

2. A multi-target tracking method as claimed in claim 1, characterized in that: The nonlinear state equation and nonlinear measurement equation of the ocean target in step S1 are expressed as: x k =Fx k-1 +u k-1 z k =h(x k )+υ k Among them, x k represents the target state value at time k, z k represents the nonlinear measurement equation at the kth moment in the tracking process, F represents the nonlinear state transfer matrix, h(·) represents the nonlinear measurement transfer function, u k-1 Indicates that the mean is 0 and the covariance matrix is ​​Q k-1 The process noise, υ k Indicates that the mean is 0, and the covariance matrix is ​​R k The measurement noise.

3. A multi-target tracking method as claimed in claim 2, characterized in that: The calculation steps of the prediction process in step S2 are as follows: Step S201: Calculate the Gaussian form of the newly generated Poisson intensity at the kth moment in the ocean target tracking process, denoted as: Among them, λ b represents the Gaussian form of the Poisson intensity of the new target, γ represents the new target sign, J γ，k represents the number of Gaussian components at the kth moment in the tracking process, w q，γ，k represents the new target weight of the qth Gaussian component at the kth moment in the tracking process, N(·) represents the Gaussian distribution, represents the new target mean of the qth Gaussian component at the kth moment in the tracking process, P q，γ，k represents the new target covariance matrix of the qth Gaussian component at the kth moment in the tracking process; Step S202: Calculate the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, which is expressed as: Among them, μ k-1 represents the Gaussian form of the Poisson intensity at the k-1th moment in the tracking process, J k-1 represents the number of Gaussian components at the k-1th moment in the tracking process, w q，k-1 represents the new target weight of the qth Gaussian component at the k-1th moment in the tracking process, represents the new target mean of the qth Gaussian component at the k-1th moment in the tracking process, P q，k-1 represents the new target covariance matrix of the qth Gaussian component at the k-1th moment in the tracking process; Step S203: Calculate the Poisson intensity density function of the predicted part at time k during the tracking process, which is expressed as: Among them, μ k|k-1 represents the predicted Poisson intensity density function at time k predicted by time k-1, λ b represents the Poisson intensity of the new target, J k-1 represents the target state value x at time k k The number of Gaussian components, w q，k|k-1 =w q，k-1 p s f represents the target prediction weight of the qth Gaussian component at time k predicted by k-1 time, p s =0.99 represents the target survival probability, f represents the state transition probability, represents the target prediction mean of the qth Gaussian component at time k predicted by k-1 time, F represents the nonlinear state transfer matrix, P q，k|k-1 =Q k +FP q，k-1 F T represents the target prediction covariance matrix of the qth Gaussian component at time k predicted by time k-1, Q k represents the process noise covariance matrix, F T represents the transpose of F; Step S204: Calculate the predicted Bernoulli-Gaussian mixture parameters during the tracking process: in, represents the prediction weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian weight of the i-th Bernoulli component in the a-th global hypothesis at the k-1-th moment in the tracking process, represents the predicted mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the Gaussian mean of the i-th Bernoulli component in the a-th global hypothesis, represents the predicted covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Gaussian covariance matrix of the i-th Bernoulli component in the a-th global hypothesis.

4. A multi-target tracking method as claimed in claim 3, characterized in that: The updating process includes: an undetected target updating step, a first detected target updating step and a detected target updating step; the updating process calculation steps of the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm are as follows: Step S301: Undetected target update step, setting the Gaussian form of the Poisson intensity density function at the kth moment in the tracking process to: Where μ represents the Poisson part sign, represents the number of Gaussian components at time k, represents the new target weight of the qth Gaussian component at time k, represents the new target mean of the qth Gaussian component at time k, represents the new target covariance matrix of the qth Gaussian component at time k; Compute the Poisson intensity update posterior density function: m k|k =q D m k|k-1 Among them, q D represents the probability of missed detection of the target; Step S302: the first detected target update step, calculates the multi-Bernoulli component probability density function, which is recorded as: in, represents the updated probability density function of the i-th Bernoulli component in the a-th global hypothesis at time k, J k|k-1 represents the number of Gaussian components of the multi-Bernoulli component at time k, z k represents the observed value corresponding to the target state at time k, w q，k|k represents the update weight of the qth multi-Bernoulli Gaussian component at time k, represents the Gaussian mean of the qth multi-Bernoulli component at time k, P q，k represents the covariance matrix of the qth multi-Bernoulli Gaussian component at time k; Parameter w q，k|k , and P q，k The calculation is as follows: Among them, R k represents the measurement noise covariance matrix, H represents the nonlinear measurement matrix, and p D =0.96 indicates the probability of detection; Step S303: Detected target update step, calculate the corresponding weight, target existence probability and probability density function, recorded as: in, represents the Gaussian update weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the Gaussian prediction weight of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the probability of existence of Gaussian prediction of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the number of Gaussian components of the i-th Bernoulli component in the a-th global hypothesis at time k-1, H k represents the nonlinear measurement matrix at time k, represents the probability of existence of Gaussian update of the i-th Bernoulli component in the a-th global hypothesis at time k, represents the weight of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the mean of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, represents the updated covariance matrix of the qth Gaussian component of the ith Bernoulli component in the ath global hypothesis at time k, Indicates that the target was missed.

5. A multi-target tracking method as claimed in claim 4, characterized in that: The covariance matrix in step S2 includes a prediction covariance matrix and an update covariance matrix, and the prediction covariance matrix and the update covariance matrix are calculated as follows: Among them, H T represents the transpose of the matrix H.

6. A multi-target tracking method as claimed in claim 5, characterized in that: The specific calculation steps of the calculation result in step S3 are as follows: Step S401: Predict the covariance matrix by Cholesky decomposition Recorded as in, Represents the covariance matrix The predicted value; chol() represents the Cholesky decomposition function; Step S402: Generate predicted volume point x using the third-order spherical radial volume criterion q，k|k-1 and weight w q =1 / 2n, n represents the system state dimension, the transfer volume point f k (·) represents the nonlinear state function; Step S403: Calculate the state prediction mean Step S404: Calculate the square root of the prediction error covariance matrix: in, Γ Q，k-1 Indicates Q k-1 The root mean square of the matrix, Tria represents the matrix Perform QR decomposition operation; Step S405: Generate updated volume point x q，+ , using the nonlinear measurement function h k (.) transfer, get the transfer volume point Step S406: Calculate the measurement prediction mean Step S407: Calculate the square root of the innovation covariance: in, Γ R，k Represents R k-1 The root mean square of the matrix, Tria represents the matrix ([λ z，+ , Γ R，k ]) Perform QR decomposition operation; calculate the cross-covariance matrix as in, Step S408: Calculate the Kalman gain as Calculate the updated mean as Step S409: Calculate the square root of the updated error covariance matrix:

7. A multi-target tracking method as claimed in claim 6, characterized in that: The square root of the prediction covariance matrix in step S4 is calculated as follows:

8. A multi-target tracking method as claimed in claim 7, characterized in that: The updated covariance matrix square root in step S4 is calculated as follows:

9. A multi-target tracking method as claimed in claim 8, characterized in that: The predicted state at the next moment is obtained in step S5, and the square root of the predicted covariance matrix is ​​used to represent the uncertainty of the predicted state. The target state, the predicted state and the uncertainty are input as initial values ​​into the prediction process in the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; the target state and the predicted state are iterated through the prediction process, and the predicted state at the next moment is output, and the predicted states output by the prediction process are connected in chronological order to form the target initial trajectory.

10. A multi-target tracking method as claimed in claim 9, characterized in that: The updated target state is obtained in step S5, and the updated target state uncertainty is expressed by the square root of the updated covariance matrix; the predicted state at the next moment, the measurement and the updated target state uncertainty are input as initial values ​​into the update process of the Gaussian mixture Poisson multi-Bernoulli mixed filtering algorithm; The update process iterates the predicted state and measurement, outputs the updated state, updates the initial trajectory of the target, and forms the final trajectory of the target.

11. A computer-readable storage medium, characterized in that: Computer instructions are stored thereon, and when the computer instructions are executed, the steps of a multi-target tracking method as described in any one of claims 1-10 are executed.

12. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of a multi-target tracking method according to any one of claims 1 to 10 are implemented.

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