A Likelihood-Modified SVGD Interactive Multi-Model Maneuvering Target Tracking Method for Opportunity Array Radar

Abstract

The present invention provides a likelihood-improved SVGD interactive multi-model maneuvering target tracking method for opportunity array radar, including: step 1, modeling the maneuvering target tracking problem, constructing a motion model set, and initializing parameters; step 2, calculating the mixing probability of each model, obtaining an initial mixing estimate, and generating initial mixing particles; step 3, determining the working mode of the opportunity array radar, predicting and updating the particle state; step 4, fusing the model probability update with the state estimate. The present invention solves the problems of particle degradation and particle depletion, and avoids the divergence of the filtering algorithm in the opportunistic tracking scenario. At the same time, the model likelihood is used to realize the adaptive optimization of the SVGD learning rate, which well balances the convergence speed and stability of the algorithm both in a single iteration and in the entire iteration process, ensuring the rapid reconvergence of the algorithm when the opportunity array radar performs the "opportunistic tracking" function.

Description

Technical Field

[0001] The invention belongs to the technical field of target tracking, and in particular relates to a likelihood-improved SVGD interactive multi-model maneuvering target tracking method for opportunity array radar. Background Art

[0002] Opportunistic Array Radar (OAR) is a new type of integrated intelligent radar system that is multifunctional, multi-mode, and works in the full time-space-frequency domain. It has two major characteristics: "unit opportunity deployment" and "radar opportunity operation". On the one hand, the "random deployment" antenna units of the opportunity array radar can provide more and richer array formation methods, which enables the opportunity array radar to have flexible full-airspace beamforming capabilities, and can adjust the beam direction and shape according to the target's motion trajectory and real-time changes in the environment, so as to achieve high-precision and stable search and tracking of maneuvering targets; on the other hand, the opportunity array radar itself has the ability to perceive, recognize and evaluate the environment. Through intelligent learning, the opportunity array radar can autonomously discover opportunities that are beneficial to the radar's survival, and intelligently select the best working mode according to the radar's own resource conditions.

[0003] When facing targets that pose a high threat to the radar itself or when the radar needs to ensure a high level of stealth performance, the opportunity array radar can achieve flexible switching between "active-passive-active", that is, "opportunistic tracking" based on stealth requirements: when the target is far away or the threat level is low, the opportunity array radar will act as an "active radar" and radiate electromagnetic waves with sufficient energy to search and track the target; when the target is close or poses a greater threat to the opportunity array radar itself, in order to ensure safety, the opportunity array radar can adaptively transform into a "passive radar" to reduce the possibility of being discovered and destroyed by the target; after the target is far away and the detection environment is ensured to be safe, the opportunity array radar will transform into an "active radar" again to continue tracking the target.

[0004] This ability to flexibly switch between active and passive radars can effectively ensure the concealment of the opportunity array radar and improve its survivability. However, for a single radar node, this action will lead to the interruption of radar measurement, and the interruption of measurement of maneuvering targets, especially when the target makes a large-scale maneuver during the measurement interruption, often brings great difficulties to the reconvergence of the tracking algorithm, and even leads to the divergence of the filter, causing the target to be lost.

[0005] In the tracking scenario of modern radar maneuvering targets, considering the flexibility of target maneuvering changes, the high nonlinearity of maneuvering actions and the complexity of background noise, the Interacting Multiple Model Particle Filter (IMMPF) algorithm suitable for nonlinear and non-Gaussian conditions has been widely used. In IMMPF, the main reason for the above-mentioned filter divergence lies in the particle degradation and particle impoverishment problems of the particle filter itself: as the number of algorithm iterations increases, the variance of the particle weights gradually increases, the diversity of particles will gradually decrease, and most particles will be concentrated near the target distribution. At this time, facing targets that can perform frequent or large maneuvers, the occurrence of measurement interruption often leads to insufficient effective particles near the target distribution after the measurement is restored, which seriously affects the accuracy of the algorithm and the convergence of the filter.

[0006] At present, there are two mainstream methods to deal with the problem of particle degradation: optimizing resampling strategies and introducing intelligent optimization algorithms. Both methods essentially redistribute particle weights by increasing particle diversity to reduce the variance of weights. Existing optimization resampling strategies include adaptive resampling, linear optimization resampling, divide-and-conquer sampling, etc., while more cutting-edge intelligent optimization algorithms include manta ray foraging optimization algorithm, hunting improved Harris Hawk optimization algorithm, improved gravitational field optimization algorithm, etc. Both methods can improve particle diversity well, thereby alleviating the problems of particle degradation and particle depletion.

[0007] However, whether it is optimizing the resampling strategy or introducing an intelligent optimization algorithm, it is limited to alleviating, but cannot fundamentally and thoroughly solve the particle degradation problem. In addition, most of the existing methods have not considered measurement interruptions such as those that exist in "opportunistic tracking". In scenarios where there is a temporary interruption in target measurement, the location where the target measurement reappears has great uncertainty, depending on the way the target maneuvers. Faced with restored measurements that may appear at different distances and orientations, existing resampling methods based on specific strategies are difficult to achieve stable and good expected results, and the introduced intelligent optimization algorithms often require tuning of multiple parameters to obtain ideal results only for a certain type of restored measurement. Both are not general. Summary of the invention

[0008] Purpose of the invention: The technical problem to be solved by the present invention is to provide a likelihood-improved SVGD interactive multi-model maneuvering target tracking method for opportunity array radar in view of the deficiencies in the prior art. The method is mainly used for tracking maneuvering targets in the "opportunistic tracking" scenario based on concealment requirements by opportunity array radar.

[0009] This method introduces the Stein Variational Gradient Descent (SVGD) method under the framework of the interactive multi-model particle filter (IMMPF), and implements particle updates based on particle flow to completely solve the problems of particle degradation and particle depletion. While improving the accuracy and robustness of maneuvering target tracking, it avoids the divergence of the filter algorithm during "opportunistic tracking". In addition, the model likelihood under the IMMPF framework is used to achieve adaptive optimization of the SVGD learning rate to better balance the convergence speed and stability of the algorithm, and to ensure rapid reconvergence of the algorithm during "opportunistic tracking".

[0010] The method of the present invention comprises the following steps:

[0011] Step 1: Model the maneuvering target tracking problem and construct a motion model set;

[0012] Step 2: Perform input state interaction: calculate the mixing probability of each motion model, obtain the initial mixing estimate, and generate the initial mixing particles;

[0013] Step 3, determine the working mode of the opportunity array radar, and predict and update the particle state;

[0014] Step 4: Perform model probability update and state estimation fusion.

[0015] Step 1 includes: The state equation of the target motion is modeled as:

[0016] ,

[0017] in, and are the target state vector and The target state vector at time t; is the state transfer matrix; is the control matrix; for The system control matrix (i.e., the system input matrix) at time t; for System process noise at the moment;

[0018] Setting the target to have no additional input during the movement, we get: ;

[0019] The observation equation of target motion is modeled as:

[0020] ,

[0021] in, for The observation vector at time instant; is the state observation matrix; for The system observation noise at time .

[0022] Step 2 includes: The expression of the mixing probability is:

[0023] ,

[0024] in, is the mixing probability; From the state transfer matrix, represents the first The motion model is transferred to the The transition probability of a motion model; Indicated in In the round of filtering, The update probability of a motion model; is a normalization constant used to ensure that the sum of the mixing probabilities is 1, .

[0025] In step 2, the initial mixed estimate includes a mixed state estimate and a corresponding error covariance matrix, and the expression of the mixed state estimate is:

[0026] ,

[0027] in, Indicated in In the round of filtering, Hybrid state estimation of a motion model; Indicated in In the round of filtering, The target state estimate obtained from the motion model;

[0028] The expression of the error covariance matrix is:

[0029] ,

[0030] in, Indicated in In the round of filtering, The error covariance matrix corresponding to the mixed state estimation of the motion model; Indicated in In the round of filtering, The error covariance matrix corresponding to the target state estimation of the motion model;

[0031] The sampled The initial mixed particles are expressed as Different from the conventional IMMPF and its improved algorithm, the initial mixed particles obtained here only have particle states and model labels but no weights.

[0032] Step 3 includes:

[0033] Step 3-1, within each motion model, use the state transfer equation to predict the initial mixed particles and obtain the predicted state of the particles:

[0034] In the In the motion model, The predicted state expression of a particle is:

[0035] ,

[0036] in, Indicated in In the round of filtering, The first The predicted state of each particle; Indicates The state transfer matrix corresponding to the motion model; Indicated in In the round of filtering, The first The particle states of the initial mixed particles; represents the system process noise;

[0037] Step 3-2, the execution of the subsequent algorithm is determined according to the working state of the opportunity array radar: if the opportunity array radar is in passive mode at this time, the state fusion is performed based on the current predicted particles and model probabilities, and the process jumps to step 2; if the opportunity array radar is in active mode at this time, the likelihood of each predicted particle is calculated using the obtained observation value, and the model likelihood is further calculated;

[0038] In the In the motion model, The particle likelihood of the predicted particles The expression is: ,

[0039] in, Indicates System observations in round filtering; is the dimension of the observation vector; Indicated in In the round of filtering, predict the particle's innovation; Indicated in In the round of filtering, The innovation covariance of the motion model; Indicates the calculation of the determinant; exp is the natural exponential function; T indicates the matrix transpose;

[0040] In the SVGD framework, particles have no weights, so unlike the conventional model likelihood calculation method, the model likelihood is modified:

[0041] ;

[0042] in For the Model likelihood of the motion model;

[0043] Step 3-3, use the model likelihood to optimize the learning rate of the SVGD algorithm, and use SVGD to update the state of each particle in each motion model:

[0044] In the In the motion model, the SVGD learning rate expression based on likelihood improvement is: ,

[0045] in, Indicated in In the round of filtering, SVGD learning rate for each motion model; represents the global learning rate; represents the normalized model likelihood; is the attenuation factor, where is the attenuation coefficient, represents the sum of the likelihoods of each model in the first round of filtering, Indicates To The maximum value of the sum of the likelihoods of each motion model in round filtering;

[0046] The final adaptive optimization method is: the global learning rate is adjusted by the total model likelihood to obtain the overall learning rate. As the number of iterations increases, the overall learning rate gradually decreases; within each iteration, the overall learning rate is adjusted based on the normalized model likelihood to obtain the SVGD learning rate of each motion model.

[0047] In the In the motion model, Each particle uses SVGD to update the particle state:

[0048] ,

[0049] in, Indicated in In the round of filtering, The first The updated state of each particle; The updated moving direction of the particle is expressed as:

[0050] ,

[0051] in, is the number of particles, is the RBF kernel function, and the Gaussian kernel function is used here , is the kernel width; represents the target distribution; Indicated in In the round of filtering, The first The predicted state of each particle; It has no specific meaning and is only used to indicate the independent variable in the formula; Indicates that in the function In the solution About The gradient of each component; Indicates that in the function In the solution About The gradient of each component.

[0052] Step 4 includes:

[0053] Step 4-1, calculate the predicted probability of each motion model according to the model probability transfer matrix and the current model probability, and normalize the predicted model probability with the model likelihood to update the model probability;

[0054] The calculation formula for the model prediction probability is:

[0055] ,

[0056] in, Indicated in In the round of filtering, The predicted probability of a motion model;

[0057] The expression for model probability update is:

[0058] ,

[0059] in, Indicated in In the round of filtering, The update probability of a motion model; Predict probabilities for the model; is a normalization constant to ensure that the sum of the updated model probabilities is 1, ;

[0060] Step 4-2, calculate the target state estimation and error covariance matrix in each motion model, and perform weighted fusion on them with the updated model probability to obtain the final filtering output result;

[0061] No. The target state estimation expression of the motion model is:

[0062] ;

[0063] in, Indicated in In the round of filtering, The target state estimation obtained by the motion model; Indicated in In the round of filtering, The first The updated state of each particle;

[0064] The expression of the error covariance matrix is:

[0065] ,

[0066] in, Indicated in In the round of filtering, The error covariance matrix corresponding to the target state estimation of the motion model;

[0067] In the In the round filter, the final output result of the likelihood-based improved SVGD interactive multi-model maneuvering target tracking algorithm is:

[0068] ,

[0069] in, Indicates The target state estimate is obtained by round filtering.

[0070] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the described method.

[0071] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is run on a computer, the steps of the method described are executed.

[0072] The present invention has the following beneficial effects: (1) SVGD is applied to the IMMPF framework, and particles are updated to high likelihood regions through particle flow, which completely avoids the use of particle weights, fundamentally solves the problems of particle degradation and particle depletion, improves the accuracy and robustness of maneuvering target tracking, and avoids the divergence of filtering in the "opportunistic tracking" scenario based on concealment requirements; (2) The model likelihood is used to realize the adaptive optimization of the SVGD learning rate, which well balances the convergence speed and stability of the algorithm both in a single iteration and in the entire iteration process, and ensures the rapid reconvergence of the algorithm when the opportunity array radar performs the "opportunistic tracking" function. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of the method of the present invention.

[0074] Figure 2 It is a schematic diagram of the motion trajectory of the maneuvering target, the observation trajectory and the filtering results.

[0075] Figure 3 It is a schematic diagram of filtering error.

[0076] Figure 4 It is a schematic diagram of the overall learning rate change. DETAILED DESCRIPTION

[0077] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0078] like Figure 1 As shown, the embodiment of the present invention provides a likelihood-improved SVGD interactive multi-model maneuvering target tracking method for opportunity array radar, comprising the following steps:

[0079] Step 1: System initialization: Model the maneuvering target tracking problem, build a motion model set, and initialize relevant parameters;

[0080] (1) Establish a tracking model for mobile targets, design the target's motion trajectory, and build a simulation scenario

[0081] The state equation of target motion is modeled as: .in, and They are Moment and The target state vector at time t; is the state transfer matrix; is the control matrix; for The system control matrix (i.e., the system input matrix) at time t; for To simplify the model, the target is set to have no additional input during the movement, that is, .

[0082] The target state vector is specifically expressed as .in, The position, velocity, and acceleration of the target in the x-direction and the position, velocity, and acceleration of the target in the y-direction are represented in sequence. Represents the transpose of a matrix.

[0083] The observation equation of target motion is modeled as: .in, for The observation vector at time instant; is the state observation matrix; for The system observation noise at time .

[0084] The target state observation matrix is ​​specifically expressed as: ;

[0085] In order to verify the method proposed in the present invention, a tracking simulation of a maneuvering target is performed on a two-dimensional plane. In this embodiment, the motion process of the maneuvering target is set as follows:

[0086] The target initial state is defined as ;in It represents the position, velocity, acceleration of the target in the x direction and the position, velocity, acceleration of the target in the y direction. The target moves in a uniform straight line from the 1st to the 25th frame and turns at a rate of speed from the 25th to the 50th frame. Constant speed turning motion, acceleration at frame 50~80 Uniformly accelerated linear motion.

[0087] (2) Constructing a motion model set

[0088] In this embodiment, the uniform velocity (CV) model, the uniform acceleration (CA) model and the constant turning rate (CT) model are selected to construct the target motion model set. Based on the defined target state vector, the state transfer matrices of the three models are , , Respectively expressed as:

[0089] ,

[0090] ,

[0091]

[0092] in, represents the sampling interval;

[0093] (3) Initialization of relevant parameters

[0094] The initial probability of the model is specifically expressed as: Among them, each element They represent the initial probability of the CV model, the initial probability of the CA model, and the initial probability of the CT model respectively; the initial probability of the model can take any value as long as the sum of the initial probabilities of each model is 1.

[0095] The model state transfer matrix is ​​specifically expressed as: Among them, Line The elements of the column represent The model was transferred to The probability of a model;

[0096] Step 2: Input state interaction: Calculate the mixing probability of each model, obtain the initial mixing estimate, and generate the initial mixing particles;

[0097] (1) Calculate the mixing probability

[0098] The model probabilities of each model in the previous iteration are interacted based on the model state transfer matrix to obtain the mixed probability: .

[0099] in, Indicated in In the round of iteration, from the The model was transferred to The mixed probability of the model. It is obtained from the model state transfer matrix, which represents the first The model was transferred to The transition probability of each model; Indicated in In the round of filtering, The update probability of each model; is a normalization constant used to ensure that the sum of the mixing probabilities is 1.

[0100] (2) Obtaining the initial mixed estimate

[0101] Based on the mixed probability, the target state estimation and the corresponding error covariance matrix obtained by each model in the previous iteration are weighted and fused to obtain the initial mixed estimation, including the mixed state estimation and the corresponding error covariance matrix :

[0102] ;

[0103] ;

[0104] in, and Respectively represent The mixed state estimates of the models and the corresponding error covariance matrix; Indicated in In the round of filtering, The target state estimate obtained from the motion model; Indicated in In the round of filtering, The error covariance matrix obtained from the motion model.

[0105] (3) Generate initial mixed particles

[0106] by is the mean, is the covariance, particle number , respectively generate the initial mixed particles under each model .

[0107] Step 3: Determine the working status of the opportunity array radar and predict and update the particles;

[0108] The working state of the opportunity array radar is determined according to the observation results at the current moment: if the observation at the current moment is missing, the opportunity array radar is in "passive mode". At this time, it is impossible to calculate the likelihood and update the particle state based on the observation value, and the estimation and iteration of the target state only rely on the prediction step; if the observation at the current moment is normal, the opportunity array radar is in "active mode". At this time, after completing the prediction of the particle state, the particle likelihood and model likelihood are calculated based on the observation value, and the particle state is further updated.

[0109] Based on the corresponding state transfer matrix, the initial mixed particles under each model are predicted respectively, and the obtained particle prediction state is expressed as: ;in, Indicated in In the round of filtering, The first model The predicted state of a particle.

[0110] Make a judgment: If the observation value at the current moment is empty, execute step a; if the observation value at the current moment is not empty, execute step b.

[0111] Step a: Calculate the target state estimate under each model based on the current predicted particle state and the error covariance matrix :

[0112] ;

[0113] ;

[0114] in, and Respectively expressed in In the round of filtering, The target state estimate of each model and the corresponding error covariance matrix.

[0115] The model probability at this time is used as the updated model probability of this round of filtering, that is, , and perform weighted fusion on the state estimates of each model to obtain the final output of this round of filtering:

[0116] .

[0117] At this point, this round of iteration is complete. Jump to step 2.

[0118] Step b: Calculate the likelihood of each predicted particle in each model based on the observed value at the current moment:

[0119]

[0120] in, Indicated in In the round of filtering, The first model The likelihood of a particle; represents the system observation vector in the kth round of filtering; is the dimension of the observation vector. In this embodiment, ; Indicated in In the round of filtering, The first model predict the particle's innovation; Indicated in In the round of filtering, The innovation covariance of the model; is the covariance matrix of the observation noise; represents the exponential function; Represents the calculation of the determinant.

[0121] In each model, the average of the particle likelihoods is solved and used as the model likelihood of the model:

[0122]

[0123] in, Indicated in In the round of filtering, The model likelihood of the model.

[0124] The learning rate of SVGD is optimized based on the model likelihood, which includes two steps:

[0125] First, calculate the sum of the model likelihoods of this round of filtering , and further calculate the attenuation factor:

[0126]

[0127] in, is the attenuation coefficient; Represents the sum of the likelihoods of each model during the first round of filtering; Indicates To The maximum value of the sum of the likelihoods of each model in the round of filtering. In this embodiment, , .

[0128] Attenuation Factor The design significance of is that for the entire filtering process, when the filtering just starts, the particles in each model have not yet approached the target distribution (reflected in the low likelihood of each model). At this time, the particles updated based on SVGD need to have a higher overall learning rate to achieve rapid approach to the target distribution; when the filtering gradually converges and a large number of particles approach the target distribution (reflected in the overall improvement of the likelihood of each model), it is necessary to appropriately reduce the overall learning rate to ensure that the particles can make more precise adjustments toward the target distribution and avoid unnecessary oscillations.

[0129] Second, calculate the normalized model likelihood: .

[0130] Normalized model likelihood The design significance of is that in each round of filtering, the likelihood of each model is high or low. The particle distribution under the high likelihood model is closer to the target distribution, and such particles need more refined adjustments to further reduce the kernel Stein difference between the target distribution and the target distribution; the particle distribution under the low likelihood model is still a certain distance away from the target distribution, and such particles need a relatively large learning rate to quickly approach the target distribution. Therefore, in the same round of iterations, the learning rates of different models should also be differentiated.

[0131] The optimized SVGD learning rate is expressed as: ;

[0132] in, Represents the global learning rate. In this embodiment, ; is the attenuation factor; is the normalized model likelihood.

[0133] Use SVGD to update the particle state. The updated particle state is expressed as: .

[0134] in, Updated moving direction for particles; is the RBF kernel function. In this embodiment, the Gaussian kernel function is used, which is specifically expressed as , is the kernel width; In this embodiment, the observed distribution of the target is taken as the target distribution, specifically referring to a Gaussian distribution constructed with the target observation value as the distribution center. Indicates that in the function In the solution About The gradient of each component; Indicates that in the function In the solution About The gradient of each component.

[0135] Step 4: Model probability update and state estimation fusion: Calculate the prediction probability of each model, complete the model probability update, and perform weighted fusion on the output of each model to obtain the final state estimation of the target;

[0136] 1) Model probability update

[0137] The model probability is predicted based on the model probability transfer matrix. The predicted model probability is expressed as: .in, Indicated in In the round of filtering, The predicted probability of the model.

[0138] The model prediction probability is normalized using the model likelihood to update the model probability. The updated model probability is expressed as: .in, is a normalization constant used to ensure that the sum of the updated model probabilities is 1.

[0139] (2) State Estimation Fusion

[0140] Calculate the target state estimate under each model based on the state of the currently updated particle and the error covariance matrix :

[0141] ;

[0142] ;

[0143] in, and Respectively expressed in In the round of filtering, The target state estimate of each model and the corresponding error covariance matrix.

[0144] The updated model probability is used to perform weighted fusion on the state estimates of each model to obtain the final output of this round of filtering:

[0145]

[0146] in, Indicates The final target state estimate is obtained by round filtering.

[0147] The experimental environment is a computer equipped with a 13th Gen Intel(R) Core(TM) i5-13400 (16CPUs), 16GB memory, and Intel(R) UHD Graphics 730 GPU processor. In this experimental environment, the simulation of the above specific embodiment is performed based on MATLAB R2019a.

[0148] The simulation results are as follows: Figure 2 The following is a schematic diagram of the motion trajectory, observation trajectory and filtering results of a maneuvering target. The observation values ​​are missing from the 40th to the 65th frames to simulate the observation interruption problem in the opportunistic tracking scenario. Figure 2 As shown, after iterations of the first few frames, the method described in the embodiment of the present invention gradually converges to the vicinity of the target's true trajectory and maintains a high tracking accuracy in the first 40 frames; in the 41st to 50th frames, although the observation values ​​are missing, the target has not changed its motion mode at this time, and the proposed algorithm can still guarantee a certain tracking accuracy; in the 51st to 65th frames, the target maneuvers and changes its motion mode, at which time the observation is still in an interrupted state, and the filtered trajectory gradually deviates from the target's true trajectory; in the 66th to 80th frames, the observation is restored, at which time a large deviation has occurred between the target's estimated position and the target's true position, but after several rounds of iterations, the proposed algorithm has not diverged and can still converge to the vicinity of the target's trajectory, effectively solving the reconvergence problem of filtering in opportunistic tracking scenarios.

[0149] Figure 3 is a schematic diagram of tracking error. Figure 3As shown in the figure, after about 10 frames of iteration, the method of the present invention gradually converges and maintains a low tracking error from the 10th to the 40th frames; from the 41st to the 50th frames, due to the interruption of observation, the target state estimation only relies on the prediction step, so the tracking error increases slightly, but still remains at a low level; from the 51st to the 65th frames, the target estimated trajectory deviates from the true trajectory, and the tracking error gradually increases; from the 66th to the 80th frames, the observation is restored, the tracking error decreases rapidly, and finally reaches the same level before the observation is interrupted.

[0150] Figure 4 It is a schematic diagram of the overall learning rate change. Figure 4 As shown in , in the first 10 frames, the overall learning rate has a significant decrease. The decrease in the overall learning rate means an increase in the sum of the model likelihoods, which is consistent with Figure 3 The results of the significant decrease in tracking error in the first 10 frames are consistent; in the 11th to 40th frames, due to the convergence of the filter, the tracking error tends to be stable, so the overall learning rate only decreases slowly at a small amplitude, which can effectively avoid unnecessary oscillations and improve the stability of the filter; in the 41st to 65th frames, the observation is missing and the overall learning rate remains unchanged; in the 66th to 80th frames, the observation is restored. At this time, although the model likelihood has been greatly reduced in the 66th frame, in order to reduce the influence of noise, the regulation of the attenuation factor used in the present invention depends on the last The maximum value of the sum of the model likelihoods. In this embodiment, =2. Therefore, there is a 2-frame lag in the change of the overall learning rate. At the 68th frame, the overall learning rate is greatly improved, which significantly increases the correction effect of the update step on the filtering result and effectively improves the speed of reconvergence. After that, as the tracking error continues to decrease, the overall learning rate decreases rapidly and eventually converges to the same level before the observation interruption.

[0151] The present invention provides a likelihood-modified SVGD interactive multi-model maneuvering target tracking method for opportunity array radar. There are many methods and ways to implement the technical solution. The above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A likelihood-modified SVGD interactive multi-model maneuvering target tracking method for opportunity array radar, characterized in that: The following steps are involved: Step 1: Model the maneuvering target tracking problem and construct a motion model set; Step 2: Perform input state interaction: calculate the mixing probability of each motion model, obtain the initial mixing estimate, and generate the initial mixing particles; Step 3, determine the working mode of the opportunity array radar, and predict and update the particle state; Step 4: perform model probability update and state estimation fusion; Step 1 includes: The state equation of the target motion is modeled as: X k =FX k-1 +This k-1 +w k-1 , Among them, X k and X k-1 are the target state vector at time k and the target state vector at time k-1 respectively; F is the state transfer matrix; B is the control matrix; u k-1 is the system control matrix at time k-1; w k-1 is the system process noise at time k-1; Setting the target to have no additional input during the movement, we get: X k =FX k-1 +w k-1 ; The observation equation of target motion is modeled as: z k =HX k +v k , Among them, z k is the observation vector at time k; H is the state observation matrix; v k is the system observation noise at time k; Step 2 includes: The expression of the mixing probability is: in, is the mixing probability; π ij represents the transition probability from the i-th motion model to the j-th motion model in the maneuvering target model set; represents the update probability of the i-th motion model in the k-1th round of filtering; c j is the normalization constant, In step 2, the initial mixed estimate includes a mixed state estimate and a corresponding error covariance matrix, and the expression of the mixed state estimate is: in, represents the mixed state estimate of the jth motion model in the kth round of filtering; represents the target state estimate obtained in the i-th motion model in the k-1th round of filtering; The expression of the error covariance matrix is: in, represents the error covariance matrix corresponding to the mixed state estimation of the jth motion model in the kth round of filtering; represents the error covariance matrix corresponding to the target state estimation of the i-th motion model in the k-1th round of filtering; The N initial mixed particles obtained by sampling are expressed as Step 3 includes: Step 3-1, within each motion model, use the state transfer equation to predict the initial mixed particles and obtain the predicted state of the particles: In the jth motion model, the predicted state expression of the nth particle is: in, represents the predicted state of the nth particle under the jth motion model in the kth round of filtering; F j Represents the state transfer matrix corresponding to the j-th motion model; represents the particle state of the nth initial mixed particle under the jth motion model in the kth round of filtering; represents the system process noise; Step 3-2, the execution of the subsequent algorithm is determined according to the working state of the opportunity array radar: if the opportunity array radar is in passive mode at this time, the state fusion is performed based on the current predicted particles and model probabilities, and the process jumps to step 2; if the opportunity array radar is in active mode at this time, the likelihood of each predicted particle is calculated using the obtained observation value, and the model likelihood is further calculated; In the jth motion model, the particle likelihood of the nth predicted particle is The expression is: Among them, z k represents the system observation value in the kth round of filtering; d is the dimension of the observation vector; Indicates the new information of the nth predicted particle in the kth round of filtering; represents the innovation covariance of the jth motion model in the kth round of filtering; det(·) represents the calculation of the determinant; exp is the natural exponential function; T represents the matrix transpose; Modify the model likelihood: in is the model likelihood of the jth motion model; Step 3-3, use the model likelihood to optimize the learning rate of the SVGD algorithm, and use SVGD to update the state of each particle in each motion model: In the jth motion model, the SVGD learning rate expression based on likelihood improvement is: in, represents the SVGD learning rate of the jth motion model in the kth round of filtering; ε ini represents the global learning rate; represents the normalized model likelihood; is the attenuation factor, where λ is the attenuation coefficient, represents the sum of the likelihoods of each model in the first round of filtering, It represents the maximum value of the sum of the likelihoods of each motion model in the k-k0 to k-th round of filtering; The final adaptive optimization method is: the global learning rate is adjusted by the total model likelihood to obtain the overall learning rate, which gradually decreases with the increase of the number of iterations; within each iteration, the overall learning rate is adjusted based on the normalized model likelihood to obtain the SVGD learning rate of each motion model; Step 3 also includes: in the jth motion model, updating the particle state of the nth predicted particle using SVGD: in, represents the updated state of the nth particle under the jth motion model in the kth round of filtering; The updated moving direction of the particle is expressed as: Where N is the number of particles, k(·,·) is the RBF kernel function; p(·) represents the target distribution; represents the predicted state of the mth particle under the jth motion model in the kth round of filtering; In the function logp(·), the solution is About The gradient of each component; In the function k(·,x), the solution is About The gradient of each component.

2. The method according to claim 1, characterized in that: Step 4 includes: Step 4-1, calculate the predicted probability of each motion model according to the model probability transfer matrix and the current model probability, and normalize the predicted model probability with the model likelihood to update the model probability; The calculation formula for the model prediction probability is: in, represents the predicted probability of the jth motion model in the kth round of filtering; The expression for model probability update is: in, represents the update probability of the jth motion model in the kth round of filtering; is the model prediction probability; c is the normalization constant, Step 4-2, calculate the target state estimation and error covariance matrix in each motion model, and use the updated model probability for weighted fusion to obtain the final filtering output result; The target state estimation expression of the jth motion model is: in, represents the target state estimate obtained by the jth motion model in the kth round of filtering; represents the updated state of the nth particle under the jth motion model in the kth round of filtering; The expression of the error covariance matrix is: in, represents the error covariance matrix corresponding to the target state estimation of the jth motion model in the kth round of filtering; In the kth round of filtering, the output result of the likelihood-based improved SVGD interactive multi-model maneuvering target tracking algorithm is: Among them, X k Represents the target state estimate obtained by the kth round of filtering.

3. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 2.

4. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 2 are executed.

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