Strong maneuvering multi-target tracking method based on hybrid drive Gaussian process learning

Abstract

The invention discloses a strong maneuvering multi-target tracking method based on hybrid drive Gaussian process learning. The method comprises the following steps: step 1, Gaussian process modeling; step 2, performing hyper-parameter learning; step 3, predicting; step 4, data association; and step 5, updating. According to the method, the model-driven time-varying CV model is integrated into data-driven Gaussian process learning, the advantages of a model driving method and a data driving method are integrated, the tracking instability of pure data driving is improved, any unknown nonlinear target motion model can be learned on line, and the tracking precision is improved. Theoretical limitation of model driving and data driving in maneuvering target tracking is solved, high-precision robust tracking of strong maneuvering multiple targets in a strong confrontation environment is achieved, good tracking precision is kept under the conditions of low detection probability and high measurement noise, robustness of the method is embodied, and the method is suitable for large-scale popularization and application. And a technical support is provided for future distributed combat in a strong confrontation environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of target tracking, and relates to a maneuverable target tracking method, and in particular to a strongly maneuverable multi-target tracking method based on hybrid-driven Gaussian process learning. Background Art

[0002] The development of combat concepts and equipment capabilities has opened up new horizons for the improvement of combat capabilities, but it also means that both sides will face a more complex and confrontational battlefield environment. In other words, the future battlefield will inevitably be a highly confrontational scene, with complex and changeable background clutter distribution, and the tracked targets usually have high speed characteristics and strong maneuverability. The core problem to be solved for maneuverable target tracking is how to reduce the mismatch between the tracking model and the target's true motion model. Traditional maneuverable target tracking methods can be divided into two categories: model-driven and data-driven maneuverable target tracking methods. Both methods have certain theoretical limitations, which are analyzed as follows:

[0003] Typical model-driven maneuvering target tracking methods include adaptive models, interacting multiple models (IMM), variable structure multiple models (VSMM) and various improved versions, which can achieve good tracking performance in specific types of maneuvering target tracking. However, for strong maneuvering targets, model-driven methods that rely on prior model set information face practical application limitations: (1) Once the environment is complex and changeable, the target's motion uncertainty increases, the target's motion model exceeds the range of the prior model set, and the algorithm model is prone to mismatch, resulting in reduced tracking accuracy or even loss of the target. (2) Since the target's motion model and the switching between models are unknown, the model-driven method must accumulate enough observation data to form an appropriate estimate of the motion model. Therefore, the appropriate model estimated by previous observations always lags behind the current target state. (3) For strong maneuvering targets, the acceleration and angular velocity are large, and the changes are usually random. The target motion trajectory may consist of an infinite number of motion models. For model-driven methods, it is impractical to build a very large model set.

[0004] Typical data-driven maneuvering target tracking methods include two categories: maneuvering target tracking methods based on neural networks and maneuvering target tracking methods based on sparse Gaussian processes (GP). Maneuvering target tracking methods based on neural networks also have some problems: (1) For statisticians, it is difficult for neural networks to explain the predictions of learned hidden features and unknown situations. It belongs to "black box" learning and is difficult to apply to safety-critical scenarios. (2) Neural networks can achieve good performance because they construct a sufficiently large and complete data set. For actual application scenarios, objective factors such as the cost and timing of target movement, electromagnetic environment, and task constraints limit the scale and quality of the collected data set. Maneuvering target tracking methods based on sparse GP are currently less studied. They usually use small sample learning, and the tracking quality depends entirely on the sample quality. For strong maneuvering targets composed of an infinite number of motion models, with larger maneuvering parameters and faster changes in clutter environments, the tracking stability of sparse GP maneuvering target tracking methods is poor, which can easily cause problems such as target loss. Summary of the invention

[0005] Aiming at the problem that it is difficult to achieve high-precision robust tracking of highly maneuverable multi-targets in a strong confrontation environment, the present invention provides a method for tracking highly maneuverable multi-targets based on hybrid-driven Gaussian process learning. This method integrates the model-driven time-varying uniform velocity straight line (CV) model into the data-driven Gaussian process motion tracker (GPMT), and uses the time-varying CV model to correct the Gaussian process prediction to achieve the purpose of reducing the prediction error. On this basis, combined with the generalized probabilistic data association (GPDA) algorithm, it is possible to simultaneously track multiple highly maneuverable targets, which not only improves the tracking instability of pure data-driven, but also can learn any unknown nonlinear target motion model online, solving the theoretical limitations of model-driven and data-driven in maneuverable target tracking, and achieving high-precision robust tracking of highly maneuverable multi-targets in a strong confrontation environment.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A method for tracking multiple targets with strong maneuverability based on hybrid driven Gaussian process learning includes the following steps:

[0008] Step 1: Gaussian process modeling

[0009] Gaussian process is used to model the target motion model and observation model. The target motion model and the corresponding observation model are:

[0010]

[0011]

[0012] Where u is the state variable of the x-coordinate, t is the corresponding input variable (time), x is the measurement with additive noise, f represents the unknown target motion model defined by a Gaussian process with zero mean covariance function k(t,t′), and τ is the zero mean covariance function Gaussian white noise;

[0013] Step 2: Hyperparameter Learning

[0014] Select the first d measurements to form a training set, and use maximum likelihood estimation to learn the optimal hyperparameters of the training set The specific steps are as follows:

[0015] Step 2.1: Use the most recent d measurements as the training set The corresponding training set input time vector is The initial distribution of the training set is Its mean and covariance are and m(T t ) is the mean function, k(T t ,T t ) represents the kernel function between the input time vectors;

[0016] Step 22: Establish the negative log-likelihood function of the hyperparameters, and its formula is expressed as:

[0017]

[0018] in, is the covariance matrix, represents the data fitting of the observed target, the complexity penalty term log|M| / 2 is only determined by the covariance and input, and n log 2π / 2 is a normalization constant;

[0019] Step 23: Calculate the partial derivative of θ in the formula of step 22, and then use the gradient method to obtain the optimal hyperparameters at the current moment;

[0020] Step 3: Prediction

[0021] The predicted state of the time-varying CV model is obtained by using the time-varying CV model and Gaussian process for prediction respectively. and covariance Gaussian Process Prediction Status and covariance Then solve the residual weighted norm of the time-varying CV model and Gaussian process prediction and The optimal prediction state and covariance matrix are determined by judging the size of the residual weighted norm. The specific steps are as follows:

[0022] Step 31. Gaussian process prediction:

[0023] The joint distribution p(f,f t |x t-q:t-1 ) is expressed as a Gaussian distribution:

[0024]

[0025]

[0026] Where p(f t |f) is the state transition distribution, p(f|x t-q:t-1 ) is the prior distribution at time t, and is the mean and covariance matrix of the prior distribution, q′ and Q′ represent the mean and covariance of the joint Gaussian distribution, respectively. According to the properties of the joint Gaussian distribution, the mean of the predicted distribution is and covariance for:

[0027]

[0028]

[0029] O t = k(t,t)-J t k(T t ,t)

[0030] J t = k(t,T t )k(T t ,T t ) -1

[0031] Where m(·) = 0, m(t) is the measured input at time t, O t and J t is the matrix in the operation process; similarly, the speed prediction and covariance of the x-coordinate, the position prediction and covariance of the y-coordinate, and the speed prediction and covariance of the y-coordinate are obtained. These prediction states and prediction covariance together constitute the prediction state and the predicted covariance

[0032] Step 32: Time-varying CV model prediction:

[0033] Before prediction, based on the training set X t The last two data x t-2 and x t-1Real-time estimation of x-coordinate speed Its prediction equation is:

[0034]

[0035]

[0036]

[0037]

[0038] Where T d For x t-2 and x t-1 The time difference is obtained, and the speed estimate of the y coordinate is obtained in the same way. F is the state transfer matrix, is the state vector at time t-1, is the prediction covariance matrix, is the state prediction vector, P t-1 is the covariance matrix at time t-1, Q is the process noise covariance;

[0039] Step 3: Optimal prediction selection:

[0040] Calculate the predicted state of the Gaussian process separately and covariance And the predicted state of the time-varying CV model and covariance The residual weighted norm of and The prediction with the smaller residual weighted norm is selected as the optimal prediction. and The formula is as follows:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in and represents the residual vector, and represents the residual covariance matrix, Z tis the measurement vector at time t, H is the measurement matrix, and R is the measurement noise covariance matrix;

[0048] Step 4: Data Association

[0049] The GPDA algorithm is used to complete the correlation matching between the target and the measurement, so as to obtain the associated measurement of the jth target. The specific steps are as follows:

[0050] Step 41: Prediction vector Create a tracking gate for the center and determine the possible measurements based on the tracking gate, expressed as:

[0051]

[0052]

[0053] Where Z t (i) represents the i-th measurement at time t, R is the measurement noise covariance matrix, B t is the residual, N is the number of measurements, H is the measurement matrix, and γ is χ 2 hypothesis testing threshold;

[0054] Step 42: Calculate the probability matrix G:

[0055]

[0056] where g ij To measure the probability density between i and target j, i = 0, ..., m, j = 0, ..., J; the calculation of G is divided into three parts: (1) The first line: g 0j =(nV) -1 (1-P D P G ), represents the probability density between 0 measurement and target j (j≠0), P D is the detection probability, P G is the gate probability, V is the gate volume, and n is the coefficient; (2) The first column: g i0 =λ, which represents the probability density between 0 targets and measurement i (i≠0), λ is the clutter density, 0 targets refer to no targets of interest, which may be new targets or false targets, and 0 measurements refer to no measurements, i.e., the target is not detected; (3) The probability density between measurement i and target j is:

[0057]

[0058] in Z ij represents the i-th measurement of target j at time t, is the prediction of target j at time t, g 00 =0;

[0059] Step 43: Normalize the clustering probability matrix G based on the target and measurement as follows:

[0060]

[0061] Step 44: According to the normalized ε ij and ij Calculate the mutual association probability β between the measurement and the target ij , and obtain the associated measurement of the jth target in:

[0062]

[0063] Where c is the normalization coefficient, ρ is the weight factor, subscript tr is the target index, and subscript r is the measurement index;

[0064] Step 5: Update

[0065] Use Gaussian process to update the state of the target and the training set to get the prediction of the output state and covariance And the mean and variance of the training set distribution are and The specific steps are as follows:

[0066] Step 51: Target status update

[0067] The target state is updated using the associated measurement Z t The x-coordinate component x t Update the state and covariance of the x coordinate, and update the mean And the covariance is:

[0068]

[0069]

[0070]

[0071] in is the Kalman gain, x t is the measurement of the x-coordinate, For state prediction The x-coordinate component of is the prediction covariance The x-coordinate component, C t is the cross-covariance between the training set and the state estimate, is the covariance of the training set at time t-1, J t = k(t,T t )k(T t,T t ) -1 ;

[0072] Step 52: Training set update

[0073] According to the distribution of the training set at time t-1 and the estimated distribution at time t Update the distribution of the training set and get In order to prevent underfitting of the data and ensure real-time tracking of the target movement, the mean and covariance update equations of the distribution of the training set at time t are:

[0074]

[0075]

[0076] in Will and Substituting into the above formula, we get the mean and variance of the updated distribution:

[0077]

[0078]

[0079]

[0080] in is the gain matrix.

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] The present invention integrates the model-driven time-varying CV model into the data-driven Gaussian process learning, which combines the advantages of model-driven and data-driven methods, not only improves the tracking instability of pure data-driven, but also can learn any unknown nonlinear target motion model online, solves the theoretical limitations of model-driven and data-driven in maneuvering target tracking, and realizes high-precision robust tracking of highly maneuverable multi-targets in a strong confrontation environment. It also maintains good tracking accuracy under low detection probability and high measurement noise conditions, which reflects the robustness of the method of the present invention and provides technical support for future distributed operations in a strong confrontation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is the tracking result 1 obtained by the method of the present invention;

[0084] Figure 2 This is the tracking result 2 obtained by the method of the present invention;

[0085] Figure 3is the RMSE of the method of the present invention, GPMT and IMM;

[0086] Figure 4 Detailed comparison of RMSE between the proposed method and IMM;

[0087] Figure 5 RMSE curves of the method of the present invention and IMM;

[0088] Figure 6 The average RMSE of the method of the present invention and IMM varies with the detection probability;

[0089] Figure 7 : This is the curve of average RMSE of the method of the present invention and IMM changing with measurement noise. DETAILED DESCRIPTION

[0090] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0091] The present invention provides a method for tracking multiple targets with strong maneuverability based on hybrid-driven Gaussian process learning. The method aims to estimate the target state using a limited set of prior measurements, that is, using the prior distribution at time t-1. and the measurement z at time t t To estimate the posterior distribution at time t And assume that the coordinate axes are independent of each other, where and Respectively represent the mean and covariance matrix at time t-1, and Respectively represent the mean and covariance matrix at time t. The above process can be expressed as:

[0092] p(f|x t-d+1:t )=∫c·p(z t |f,f t )·p(f t |f)·p(f|x t-q:t-1 )df t

[0093] Among them, the joint distribution p(f,f t |x t-q:t-1 )=p(f t |f)·p(f|x t-q:t-1 ) is used to predict, p(z t |f,f t ) is the measurement distribution, c·p(z t |f,f t)p(f,f t |x t-q:t-1 ) is used to update, f t represents the function estimate at time t, and c is a normalization constant. The specific process is as follows:

[0094] Step 1: Gaussian process modeling

[0095] Gaussian process is used to model the target motion model and observation model. Taking the state estimation of a single dimension as an example, the unknown target motion model f and the corresponding observation model are:

[0096]

[0097]

[0098] Where u is the state variable of the x-coordinate, t is the corresponding input variable (time), x is the measurement with additive noise, f represents the unknown target motion model defined by a Gaussian process with zero mean covariance function k(t,t′), and τ is the zero mean covariance function Gaussian white noise. The kernel function uses the squared exponential (SE) kernel function, and its formula is:

[0099]

[0100] in, is the variance, Λ=diag(l 2 ), the hyperparameter set of the Gaussian process It consists of the parameters of the kernel function and the measurement noise variance, and l is the length scale parameter.

[0101] In the target tracking process, once the relationship between adjacent data samples is understood, the target state estimation can be performed based on this relationship. The kernel function in GP can capture the relationship between different input points. Therefore, the kernel function is used to understand the connection between the training data and model the motion pattern of the target. This process is performed at each time step, making it possible to obtain any changes in the unknown nonlinear function from the training data in real time. In the context of target tracking, the unknown nonlinear function covers all potential maneuvering modes of the target.

[0102] Step 2: Hyperparameter Learning

[0103] Taking the x-coordinate position prediction at time t as an example, the present invention uses the most recent d measurements as the training set The corresponding training set input time vector is The initial distribution of the training set is Its mean and covariance are and m(T t ) is the mean function, k(T t ,T t ) represents the kernel function between the input time vectors. Different hyperparameters have different effects on the data. Therefore, in order to make accurate predictions, it is necessary to learn the training set before prediction to obtain the most appropriate hyperparameters at the current moment. The present invention uses maximum likelihood estimation to solve the problem. First, a negative log-likelihood function of a hyperparameter is established, and its formula can be expressed as:

[0104]

[0105] in, is the covariance matrix, It represents the data fitting of the observed target. The complexity penalty term log|M| / 2 is only determined by the covariance and input, and n log 2π / 2 is a normalization constant. Then the partial derivative of θ in the above formula is calculated, and the optimal hyperparameters at the current moment are obtained using the gradient method.

[0106] Step 3: Prediction

[0107] In the prediction process, due to the existence of clutter and the sparsity of the Gaussian process, the prediction is unstable. Therefore, the present invention proposes to use the time-varying CV model to correct the prediction of the Gaussian process. First, the time-varying CV model and the Gaussian process are used for prediction respectively, and then the residual weighted norms of the time-varying CV model and the Gaussian process prediction are solved, and the optimal prediction state and covariance matrix are determined by judging the size of the residual weighted norm. Because the residual weighted norm can better reflect the state change of the target at the current moment, that is, the degree of deviation between the measured and predicted states, the smaller the residual weighted norm, the smaller the degree of deviation and the higher the accuracy.

[0108] The specific process is as follows:

[0109] Step 31. Gaussian process prediction:

[0110] The joint distribution p(f,f t |x t-q:t-1 ) can be expressed by Gaussian distribution as:

[0111]

[0112]

[0113] Where p(f t |f) is the state transition distribution, p(f|x t-q:t-1 ) is the prior distribution at time t, and is the mean and covariance matrix of the prior distribution, q′ and Q′ represent the mean and covariance of the joint Gaussian distribution respectively. According to the properties of the joint Gaussian distribution, the mean of the predicted distribution can be obtained and covariance for:

[0114]

[0115]

[0116] O t = k(t,t)-J t k(T t ,t)

[0117] J t = k(t,T t )k(T t ,T t ) -1

[0118] Where m(·) = 0, m(t) is the measured input at time t, O t and J t is the matrix in the operation process. Similarly, the speed prediction and covariance of the x-coordinate, the position prediction and covariance of the y-coordinate, and the speed prediction and covariance of the y-coordinate can be obtained. These prediction states and prediction covariance together constitute the prediction state and the predicted covariance

[0119] Step 32: Time-varying CV model prediction:

[0120] Before prediction, based on the training set X t The last two data x t-2 and x t-1 Real-time estimation of x-coordinate speed Its prediction equation is:

[0121]

[0122]

[0123]

[0124]

[0125] Where T d For x t-2 and x t-1 The time difference, similarly, the velocity estimate of the y coordinate can be obtained F is the state transfer matrix, is the state vector at time t-1, is the prediction covariance matrix, is the state prediction vector, P t-1 is the covariance matrix at time t-1, and Q is the process noise covariance.

[0126] Step 3: Optimal prediction selection:

[0127] Calculate the predicted state of the Gaussian process separately and covariance And the predicted state of the time-varying CV model and covariance The residual weighted norm of and The prediction with the smaller residual weighted norm is selected as the optimal prediction. and The formula is as follows:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] in and represents the residual vector, and represents the residual covariance matrix, Z t is the measurement vector at time t, H is the measurement matrix, and R is the measurement noise covariance matrix.

[0135] Step 4: Data Association

[0136] Based on the prediction vector discussed in step 3 At time t, correlation matching between the measurement and the target is performed, and the associated measurement is determined using the GPDA algorithm.

[0137] First, the prediction vector Creating a tracking gate for the center and determining possible measurements based on the tracking gate can be expressed as:

[0138]

[0139]

[0140] Z t(i) represents the i-th measurement at time t, R is the measurement noise covariance matrix, B t is the residual, N is the number of measurements, H is the measurement matrix, and γ is the χ 2 hypothesis testing threshold.

[0141] Then, calculate the probability matrix G:

[0142]

[0143] where g ij is the probability density between measurement i and target j, i = 0,..., m, j = 0,..., J. The calculation of G is divided into three parts: (1) The first row: g 0j =(nV) -1 (1 - P D P G ), which represents the probability density between measurement 0 and target j (j≠0), P D is the detection probability, P G is the gate probability, V is the volume of the gate, and n is a coefficient. (2) The first column: g i0 =λ, which represents the probability density between target 0 and measurement i (i≠0), and λ is the clutter density. Target 0 refers to no target of interest, which may be a new target or a false target, and measurement 0 refers to no measurement, that is, the target is not detected. (3) The probability density between measurement i and target j is:

[0144]

[0145] where Z ij represents the i-th measurement of target j at time t, is the prediction of target j at time t. In addition, g 00 =0.

[0146] Normalize the aggregation probability matrix G based on the target and measurement as:

[0147]

[0148] Finally, calculate the mutual membership association probability β ij of the measurement and the target according to the normalized ε ij and ξ ij , and obtain the associated measurement of the j-th target

[0149]

[0150] where c is the normalization coefficient, ρ is the weight factor, the subscript tr is the target index, and the subscript r is the measurement index.

[0151] Step Five: Update

[0152] This step consists of two parts: target state update and training set update. The state update uses the associated measurement Z t The x-coordinate component x t Update the state and covariance of the x coordinate, and update the mean and covariance for:

[0153]

[0154]

[0155]

[0156] in is the Kalman gain, x t is the measurement of the x-coordinate, For state prediction The x-coordinate component of is the prediction covariance The x-coordinate component, C t is the cross-covariance between the training set and the state estimate, is the covariance of the training set at time t-1, J t = k(t,T t )k(T t ,T t ) -1 .

[0157] In addition, it is also necessary to consider the distribution of the training set at time t-1 and the estimated distribution at time t Update the distribution of the training set and get To prevent underfitting of the data and ensure real-time tracking of the target movement. The update equations for the mean and covariance of the distribution of the training set at time t are:

[0158]

[0159]

[0160] in Will and Substituting into the above formula, we get the mean and variance of the updated distribution:

[0161]

[0162]

[0163]

[0164] wherein is the gain matrix.

[0165] Embodiment:

[0166] To more clearly illustrate the method of the present invention, this embodiment describes the process and shows the effects through simulation experiments, but does not limit the scope of this embodiment. There are three experiments in total: Experiment 1 is the performance verification of the method of the present invention under sparse clutter conditions; Experiment 2 is the performance verification of the method of the present invention under dense clutter conditions; Experiment 3 discusses the performance influence of the method of the present invention by clutter, noise, and detection probability.

[0167] Experiment 1: Performance Verification of the Present Invention under Sparse Clutter Conditions

[0168] The simulation scenario and parameter settings are as follows:

[0169] In a two-dimensional space, the size of the target surveillance area is [0, 40 km] × [0, 40 km], and the motion state of the target is represented as X = [x, y, V x , V y T , including position and velocity components. The number of targets is 4, and their initial positions are random. The initial target velocities are randomly assigned within the range of [100, 300] m / s. In addition, the strong maneuvering targets are mainly reflected in two aspects: (1) the velocity is relatively large, with a maximum velocity of 2 Mach (680 m / s), (2) the number of maneuvers is large, set to 10 - 13 times, and the maneuver parameters are randomly set each time, and the parameter variation range is large, with a maximum acceleration of 8 * 9.8 m / s 2 , and the angular velocity range is ω = [-36°, 36°]. The variation range of the target velocity is [100, 680] m / s. The duration of each maneuver is also randomly determined within the range of [8, 10] s. The detection probability P D = 0.98. The number of clutter follows a Poisson distribution λ = 2.5 × 10 -9 m -2 , and the clutter positions are uniformly distributed within the surveillance area. The target motion model can be represented by the following state equation

[0170]

[0171] The first to fourth rows of the state equation represent different motion models. When a = 0 and ω = 0, the target moves in a uniform straight line. When a ≠ 0 and ω = 0, the target moves in a uniform turn. When a = 0 and ω ≠ 0, the target moves in a uniform acceleration. When a ≠ 0 and ω ≠ 0, the target moves in a non-linear motion. The state transition function of the non-linear model is represented by f as:

[0172] f(X t-1 ​)=F 2 X t-1 +Da+F 3 X t-1 -X t-1

[0173] a=[a x ,a y ] T is the acceleration vector; a x ,a y Represents the acceleration components of the x and y coordinate axes respectively; F 1 、F 2 and F 3 The formula is as follows:

[0174]

[0175]

[0176] X t-1 and X t represents the target state; the control matrix D and the process noise matrix U are given by:

[0177]

[0178] Process noise The covariance matrix of is:

[0179]

[0180] The measurement equation of the target is:

[0181] Z t =HX t-1 +η

[0182] Where H:

[0183]

[0184] η is the measurement noise, and its covariance matrix is:

[0185]

[0186] Where ξ x =ξ y =300m.

[0187] The simulation time is 80s. Sampling period T data = 1s. 500 Monte Carlo tests were performed to evaluate the performance of the method of the present invention. The evaluation index root mean square error (RMSE) is:

[0188]

[0189] Where N mc is the Monte Carlo number, set to 500, q i,k and are the true value and the estimated value respectively.

[0190] For the comparison method, the popular model-driven IMM algorithm and data-driven GPMT algorithm are selected as the comparison methods. For the method of the present invention and the GPMT method, the training set, measurement data and noise standard deviation are scaled down at the input, and the state estimation vector is scaled up at the output, with a scaling ratio of 1 / 1000. The training set consists of the first d=8 measurement data samples. Hyperparameter set Initialized by maximum likelihood estimation, where l and are the length scale and variance, respectively, is the measurement noise variance, σ n =300m. After each iteration, the oldest data in the training set is deleted and the new state estimate is added to the training set. ρ = 0.5 in GPDA.

[0191] For IMM, since there is no prior knowledge about the target motion, a standard model combination (CV, CA, CT) is selected, which includes 31 models (1 CV model, 24 CA models, and 6 CT models). For the CV and CA models, the acceleration vector a is:

[0192]

[0193] One element in the formula represents the CV model, and the rest are CA models. For the CT model, the angular velocity ω = [5°, -5°, 10°, -10°, 20°, -20°], the measurement noise covariance matrix is ​​R, and the model probability is Probability transfer matrix The state noise covariance matrix is ​​E = 400 2 I 4 , the process noise matrix is ​​U.

[0194] The experimental results are analyzed as follows:

[0195] Figure 1 and Figure 2 The tracking results obtained by the method of the present invention are shown, proving that the method of the present invention can achieve satisfactory tracking performance for strong maneuvering targets in a cluttered environment. The RMSE of the method of the present invention, GPMT and IMM are shown in Figure 2. Figure 3 As shown, Figure 4The detailed comparison of RMSE between the proposed method and IMM is shown, and the statistical root mean square error is shown in Table 1. It can be seen that compared with GPMT and IMM, the proposed method shows obvious advantages in state estimation, and the tracking performance of IMM and GPMT is poor. The processing time of each iteration of IMM, GPMT and the proposed method in 500 Monte Carlo experiments is shown in Table 2. It can be seen that the processing time of the proposed method is much larger than that of IMM and slightly larger than that of GPMT.

[0196] Table 1 Average RMSE statistics

[0197]

[0198] Table 2 Processing time statistics

[0199]

[0200]

[0201] Experiment 2: Performance verification of the invented method under dense clutter conditions

[0202] Simulation scenario and parameter settings: In addition to setting the clutter density to λ = 4 × 10 -8 m -2 , other parameters are the same as those in Experiment 1. Figure 5 The RMSE curves of the method of the present invention and IMM are shown in Table 3. The average RMSE statistical results are shown in Table 3. It can be seen that GPMT has completely lost track. Figure 5 In this paper, we only compared the method of the present invention with the IMM method. Figure 5 It can be seen from Table 3 that, compared with IMM and GPMT, the method of the present invention has satisfactory performance advantages.

[0203] Table 3 Average RMSE statistics

[0204]

[0205] Experiment 3: Performance verification of the invented method under different noise and detection probability conditions

[0206] Simulation scenarios and parameter settings: (1) Except that the detection probability is set to 0.98, 0.8, 0.7, 0.6, and 0.5 respectively, other parameters are the same as those in Experiment 1. Figure 6 The curves of the average RMSE of the proposed method and IMM versus detection probability are shown. (2) Except that the standard deviation of the measurement noise is set to 300m, 500m, 800m, 1000m, and 1500m, the other parameters are the same as those in Experiment 1. Figure 7 The curves showing the average RMSE of the method of the present invention and IMM changing with the measurement noise are shown. Figure 6 and Figure 7 It can be seen that the invented method can still have good tracking performance under the conditions of low detection probability and high measurement noise, while the IMM and GPMT methods perform very poorly.

Claims

1. A strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning, characterized in that the method comprises the following steps: Step 1, Gaussian process modeling Use Gaussian process to model the target motion model and the observation model. The target motion model and the corresponding observation model are: Where u is the state variable of the x-coordinate, t is the corresponding input variable, x is the measurement with additive noise, f represents the unknown target motion model defined by a Gaussian process with zero mean covariance function k(t,t′), and τ is the zero mean covariance function Gaussian white noise; Step 2, hyperparameter learning Select the first d measurements to form a training set, and use maximum likelihood estimation to learn the optimal hyperparameters of the training set Step 3, prediction The predicted state of the time-varying CV model is obtained by using the time-varying CV model and Gaussian process for prediction respectively. and covariance Gaussian Process Prediction Status and covariance Then solve the residual weighted norm of the time-varying CV model and Gaussian process prediction and Determine the optimal prediction state and covariance matrix by judging the size of the residual weighted norm; Step 4, data association The GPDA algorithm is used to complete the correlation matching between the target and the measurement, so as to obtain the associated measurement of the jth target. Step 5, update Use Gaussian process to update the state of the target and the training set to get the prediction of the output state and covariance And the mean and variance of the training set distribution are and 2. The strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning according to claim 1, characterized in that the specific steps of step 2 are as follows: Step 2.1: Use the most recent d measurements as the training set The corresponding training set input time vector is The initial distribution of the training set is Its mean and covariance are and m(T t ) is the mean function, k(T t ,T t ) represents the kernel function between the input time vectors; Step 22, establish the negative log-likelihood function of the hyperparameter, and its formula is expressed as: in, is the covariance matrix, Represents the data fitting of the observed target, the complexity penalty term log|M| / 2 is only determined by the covariance and input, and nlog2π / 2 is the normalization constant; Step 23, take the partial derivative of θ in the formula of step 22, and then use the gradient method to obtain the optimal hyperparameter at the current moment.

3. The strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning according to claim 1, characterized in that the specific steps of step 3 are as follows: Step 31, Gaussian process prediction: The joint distribution p(f,f t |x t-q:t-1 ) is expressed as: Where p(f t |f) is the state transition distribution, p(f|x t-q:t-1 ) is the prior distribution at time t, and is the mean and covariance matrix of the prior distribution, q′ and Q′ represent the mean and covariance of the joint Gaussian distribution, respectively. According to the properties of the joint Gaussian distribution, the mean of the predicted distribution is and covariance for: O t =k(t,t)-J t k(T t ,t) J t =k(t,T t )k(T t ,T t ) -1 Where m(·) = 0, m(t) is the measured input at time t, O t and J t is the matrix in the operation process; similarly, the speed prediction and covariance of the x-coordinate, the position prediction and covariance of the y-coordinate, and the speed prediction and covariance of the y-coordinate are obtained. These prediction states and prediction covariance together constitute the prediction state and the predicted covariance Step 32, time-varying CV model prediction: Before prediction, based on the training set X t The last two data x t-2 and x t-1 Real-time estimation of x-coordinate speed Its prediction equation is: Where T d For x t-2 and x t-1 The time difference is obtained, and the speed estimate of the y coordinate is obtained in the same way. F is the state transfer matrix, is the state vector at time t-1, is the prediction covariance matrix, is the state prediction vector, P t-1 is the covariance matrix at time t-1, Q is the process noise covariance; Step 33, optimal prediction selection: Calculate the predicted state of the Gaussian process separately and covariance And the predicted state of the time-varying CV model and covariance The residual weighted norm of and The prediction with the smaller residual weighted norm is selected as the optimal prediction. and The formula is as follows: in and represents the residual vector, and represents the residual covariance matrix, Z t is the measurement vector at time t, H is the measurement matrix, and R is the measurement noise covariance matrix.

4. The strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning according to claim 1, characterized in that the specific steps of step 4 are as follows: Step 41: Prediction vector Create a tracking gate for the center and determine the possible measurements based on the tracking gate, expressed as: Where Z t (i) represents the i-th measurement at time t, R is the measurement noise covariance matrix, B t is the residual, N is the number of measurements, H is the measurement matrix, and γ is χ 2 hypothesis testing threshold; Step 42, calculate the probability matrix G: where g ij is the probability density between measurement i and target j, i = 0, ..., m, j = 0, ..., J; Step 43, normalize the clustering probability matrix G based on the target and the measurement as: Step 44: According to the normalized ε ij and ij Calculate the mutual association probability β between the measurement and the target ij , and obtain the associated measurement of the jth target in: where c is the normalization coefficient, ρ is the weight factor, the subscript tr is the target index, and the subscript r is the measurement index.

5. The strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning according to claim 4, characterized in that The calculation of G is divided into three parts: (1) The first row: g 0j =(nV) -1 (1 - P D P G ), representing the probability density between the zero measurement and the target j (j≠0). P D is the detection probability, P G is the gate probability, V is the volume of the gate, and n is a coefficient; (2) The first column: g i0 =λ, representing the probability density between the zero target and the measurement i (i≠0). λ is the clutter density. The zero target means there is no target of interest, which may be a new target or a false target. The zero measurement means there is no measurement, that is, the target is not detected; (3) The probability density between the measurement i and the target j is: in Z ij represents the i-th measurement of target j at time t, is the prediction of target j at time t, g 00 =0.

6. The strong maneuvering multi-target tracking method based on hybrid-driven Gaussian process learning according to claim 1, characterized in that the specific steps of step 5 are as follows: Step 51, target state update The target state is updated using the associated measurement Z t The x-coordinate component x t Update the state and covariance of the x coordinate, and update the mean And the covariance is: in is the Kalman gain, x t is the measurement of the x-coordinate, For state prediction The x-coordinate component of is the prediction covariance The x-coordinate component, C t is the cross-covariance between the training set and the state estimate, is the covariance of the training set at time t-1, J t = k(t,T t )k(T t ,T t ) -1 ; Step 52, training set update According to the distribution of the training set at time t-1 and the estimated distribution at time t Update the distribution of the training set and get In order to prevent underfitting of the data and ensure real-time tracking of the target movement, the mean and covariance update equations of the distribution of the training set at time t are: in Will and Substituting into the above formula, we get the mean and variance of the updated distribution: in is the gain matrix.

Images