A local refinement multi-target doa dynamic tracking method and system

Abstract

The application discloses a kind of local refinement multi-target DOA dynamic tracking method and system, the method is first received array data, and obtains virtual array covariance matrix construction virtual snapshot data.Secondly, angle coarse grid dictionary is established, based on virtual snapshot data, obtain initial DOA candidate, utilize KF state to predict, obtain predicted DOA, predicted angular velocity and predicted covariance matrix, and determine the PSO search radius of each target.Then in PSO search radius, construct covariance fitting target function to carry out continuous domain optimization, obtain the DOA observation value of each target of current frame.Finally, DOA observation value is distributed to corresponding trajectory, obtains current frame DOA state estimation, for the prediction and search of next time frame, until output complete DOA trajectory.The application improves virtual aperture and distinguishable capacity, reduces PSO global search difficulty, improves the stability of multi-target continuous DOA tracking.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and direction of arrival (DOA) estimation technology. Specifically, it relates to a multi-target DOA dynamic tracking method based on nested arrays, sparse Bayesian learning (SBL), particle swarm optimization (PSO), and Kalman filtering (KF). It can be used in scenarios such as radar, wireless sensing, unmanned platform positioning, and electronic reconnaissance. Background Technology

[0002] DOA estimation is an important research topic in the field of array signal processing, and it is widely used in scenarios such as radar detection, sonar localization, wireless communication, electronic reconnaissance, and unmanned platform perception. In multi-target dynamic scenarios, the target azimuth angle changes over time, and the angular interval between different targets may gradually decrease or remain relatively close. Therefore, the method not only needs to obtain the DOA estimation result for a single frame, but also needs to keep the estimation result smooth and stable over continuous time frames, and avoid trajectory jitter and correlation errors caused by noise, spurious peaks, or short-term observation biases.

[0003] Existing subspace-based DOA estimation methods, such as Multiple Signal Classification (MUSIC) and Rotation Invariant Subspace (ESPRIT), possess high resolution capabilities, but their performance depends on a high signal-to-noise ratio (SNR), a sufficient number of snapshots, and accurate signal subspace estimation. Under conditions of low SNR, limited snapshots, or multiple nearest-neighbor targets, problems such as spectral peak broadening, spurious peak enhancement, missed detection of weak targets, and decreased target resolution easily arise. MUSIC-based methods typically require spectral peak searching on an angular grid, and their estimation accuracy is limited by the grid spacing. Increasing the grid density significantly increases the computational cost.

[0004] Nested arrays can achieve longer virtual array apertures through differential co-arraying, improving degrees of freedom and angular resolution without significantly increasing the number of physical array elements. However, existing nested array-based DOA estimation methods mostly focus on single-frame angle estimation. If fixed grid search or traditional spectral peak search is still used, grid mismatch, spurious peak interference, and unstable cross-frame correlation still exist in dynamic multi-target tracking scenarios.

[0005] SBL can improve the accuracy and noise resistance of DOA estimation by utilizing the sparsity of the angular domain, but it usually relies on a preset angular grid, which can introduce grid mismatch error when the actual DOA deviates from the grid points. Using a finer grid to improve accuracy increases computational complexity. Intelligent optimization algorithms such as PSO can perform optimization in a continuous angular domain, reducing gridding error, but if the search is performed directly across the entire angular range, the search space is large, the computational efficiency is low, and it may be affected by local extrema.

[0006] Furthermore, KF can be used for dynamic target tracking, predicting the current target position based on historical states and performing smooth updates. However, conventional KF methods are highly dependent on the quality of single-frame observations and target association results. When the angular spacing between multiple targets is small, their motion trajectories are close to each other, or single-frame DOA observations are affected by noise, false peaks, or grid mismatch, problems such as incorrect association, trajectory jumps, or local tracking instability can easily occur.

[0007] Therefore, existing DOA dynamic tracking methods still suffer from problems such as insufficient estimation accuracy under low signal-to-noise ratio and limited snapshot conditions, mesh mismatch, low efficiency of continuous domain refinement, and insufficient cross-frame correlation stability in near-neighbor target scenes. There is an urgent need for a multi-target DOA tracking method that can integrate nested array virtual aperture, sparse Bayesian estimation, intelligent optimization continuous refinement, and dynamic filtering tracking constraints to improve estimation accuracy, tracking stability, and computational efficiency in dynamic multi-target scenes. Summary of the Invention

[0008] The purpose of this invention is to provide a locally refined multi-target DOA dynamic tracking method and system to solve problems such as insufficient DOA estimation accuracy, mesh mismatch, unstable cross-frame correlation, and trajectory jitter in near-neighbor multi-target scenes under low signal-to-noise ratio and limited snapshot conditions.

[0009] To achieve the above objectives, this invention employs the following technical solution: A nested array is used to receive narrowband far-field signals from each time frame, and a continuous virtual uniform linear array covariance matrix is ​​reconstructed based on differential co-array. In the initial two frames, a coarse-grid SBL is used to obtain sparse spectral peaks in the angular domain, and MUSIC candidates are used as initial verification. Then, PSO is used to refine the candidate DOAs locally in the continuous domain and optimize the covariance fitting. In subsequent frames, the target DOA and angular velocity are predicted by KF. The PSO search radius is determined based on the predicted covariance matrix and the adaptive measurement variance. The PSO is used to minimize the covariance fitting objective function to obtain the current frame's DOA observation value. Subsequently, observation allocation is completed according to the principle of closest predicted angle, and KF updates or prediction results are executed based on an information threshold decision.

[0010] In one aspect, this invention provides a method for localized refinement of multi-target DOA dynamic tracking, comprising the following steps:

[0011] S1: Construct a nested array to receive the first... Frame array data and calculate sample covariance matrix.

[0012] S2: Preprocess the sample covariance matrix obtained in step S1 to obtain the virtual array covariance matrix. Construct virtual snapshot data based on the virtual array covariance matrix.

[0013] S3: Establish a coarse-grid dictionary of angles in the initial two frames, and run SBL using the virtual snapshot data obtained in step S2 as the observation input to obtain the prior information source power. Calculate the MUSIC verification candidate using the virtual array covariance matrix obtained in step S2, and input the SBL candidate and MUSIC candidate together into PSO for local continuous domain refinement to obtain the initial DOA estimate.

[0014] S4: Calculate the covariance fitting cost of each group of initial DOA candidates in step S3 using the virtual array covariance matrix obtained in step S2, and select the group with the smallest cost as the initial two-frame DOA estimate. Initialize the angle, angular velocity, and error covariance of KF using the initial two-frame DOA estimate, retain the source power prior obtained in step S3, and initialize the measurement variance and process noise to form the initial state and source power prior parameters required for subsequent frame tracking.

[0015] S5: For subsequent frames, perform a one-step prediction using the KF state initialized in step S4 or updated in step S7 of the previous frame to obtain the predicted DOA, predicted angular velocity, and predicted covariance matrix. Combine this with the measurement variance updated in step S8 to determine the PSO search radius for each target.

[0016] S6: Within the PSO search radius determined in step S5, construct the covariance fitting objective function using the current frame virtual array covariance matrix obtained in step S2 and the source power prior updated in step S8, and use PSO to perform continuous domain optimization to obtain the DOA observation values ​​of each target in the current frame.

[0017] S7: Assign the DOA observations obtained in step S6 to the corresponding trajectories according to the principle of minimizing the distance from the predicted DOA in step S5, calculate the innovation and its variance, and perform threshold decision. If the observation is valid, perform KF update; if the observation is invalid, retain the prediction result of step S5 to obtain the DOA state estimate for the current frame.

[0018] S8: Record the DOA state estimate of the current frame obtained in step S7, and update the source power prior, measurement variance and process noise using the current frame observations and new information; return the updated KF state, error covariance and prior parameters to step S5 for prediction and search in the next time frame until the complete DOA trajectory is output.

[0019] In another aspect, the present invention also provides a multi-target DOA dynamic tracking system with local refinement, comprising the following modules:

[0020] The virtual snapshot data module is used to construct a nested array and receive the first... The frame array data is processed and the sample covariance matrix is ​​calculated. The preprocessing is then performed to obtain the virtual array covariance matrix. Virtual snapshot data is then constructed based on the virtual array covariance matrix.

[0021] The local continuous domain refinement module is used to establish an angle coarse grid dictionary. It runs SBL with virtual snapshot data as the observation input, and uses the virtual array covariance matrix to refine through local continuous domain to calculate MUSIC verification candidates and obtain initial DOA candidates.

[0022] The PSO search radius module is used to predict the DOA, angular velocity, and covariance matrix based on the initial DOA candidates and the KF state, and to determine the PSO search radius for each target.

[0023] The target DOA observation module is used to construct a covariance fitting objective function using the covariance matrix of the virtual array in the current frame within the PSO search radius, and to perform continuous domain optimization using PSO to obtain the target DOA observations for each target in the current frame.

[0024] The KF update module is used to assign DOA observations to the corresponding trajectories, perform KF updates, and obtain the DOA state estimate for the current frame.

[0025] The DOA trajectory tracking module is used to record the DOA state estimate of the current frame, which is used for prediction and search in the next time frame until the complete DOA trajectory is output.

[0026] Compared with existing technologies, the beneficial effects of this invention are as follows: First, nested array differential co-array improves virtual aperture and resolvability; second, SBL coarse estimation provides sparse angular domain priors, reducing the difficulty of global PSO search; third, PSO directly optimizes covariance fitting of the target in continuous angular domains, reducing angular deviation caused by grid mismatch; fourth, KF prediction enables the PSO search domain to adaptively shrink with target motion, thereby improving tracking stability and computational efficiency; fifth, the observation allocation mechanism based on the principle of closest predicted angle and innovation threshold decision can reduce mismatch and trajectory jump caused by noisy observations, improving the stability of multi-target continuous DOA tracking. Attached Figure Description

[0027] Figure 1 This is a flowchart of the dynamic DOA tracking method based on nested array SBL-PSO-KF of the present invention;

[0028] Figure 2 This is a comparison diagram of the actual trajectory and the estimated trajectory in a single simulation using the method of the present invention;

[0029] Figure 3 This is a graph showing the RMSE changes of the method of this invention and other methods at different time frames;

[0030] Figure 4 This is a comparison chart of the RMSE of the method of the present invention and other methods under different signal-to-noise ratio conditions;

[0031] Figure 5 This is a comparison chart of the RMSE of the method of the present invention and other methods under different snapshot numbers. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and embodiments. The following embodiments are used to illustrate the technical solutions of this invention and are not intended to limit the scope of protection of this invention.

[0033] In one aspect, this invention provides a locally refined multi-target DOA dynamic tracking method, such as... Figure 1 As shown, it includes the following steps:

[0034] S1 Nested Array Receiver Model

[0035] This embodiment uses a nested array consisting of two subarrays. The first subarray contains... There are array elements, and the spacing between the array elements is... The second subarray contains There are array elements, and the spacing between the array elements is... ,in , Let wavelength be denoted as λ. Taking the first element as the reference point, the set of physical element positions can be represented as:

[0036]

[0037] in To represent taking the union, These are the element indices for the first and second subarrays, respectively.

[0038] In an embodiment, The corresponding normalized array element position is Let the first... Frame Existence A narrowband far-field signal, its DOA vector is , Indicates the first The first goal in DOA of the frame If we represent the transpose operation, then the array received data can be represented as:

[0039]

[0040] in It is a direction matrix. It is a direction vector. It is the imaginary unit. For virtual array element positions, For array element index, For the noise term that follows a Gaussian distribution, For signal vectors, For the first The target information source at time... The complex baseband signal waveform.

[0041] The sample covariance matrix is:

[0042]

[0043] in The number of snapshots per frame. This indicates the conjugate transpose.

[0044] S2 Nested Array Virtualization Preprocessing

[0045] Calculate the position difference of all element pairs based on their physical positions to form a differential co-array lag set. Average the covariance elements corresponding to the same lag to remove redundancy from the differential co-array. Then, search for continuous lag intervals from zero lag outwards, extracting a continuous virtual uniform array portion, denoted as the sequence. .

[0046] The correlation sequence corresponding to continuous non-negative lags Constructing a Toeplitz-type virtual array covariance matrix And using the reverse identity matrix Perform forward and backward smoothing to obtain :

[0047]

[0048] in This indicates taking the complex conjugate of the elements. To avoid non-positive definite problems caused by numerical errors, [the following is used:] ... Eigenvalue decomposition is performed, and the lower bound of the eigenvalues ​​is constrained to positive values ​​to obtain the positive-definite virtual array covariance matrix. Further, a deterministic partial Fourier frame is constructed, and the positive-definite covariance matrix is ​​converted into virtual snapshot data. This is for use in SBL iterations.

[0049] S3 SBL rough estimate

[0050] In the initial two frames, the continuous angular space is first discretized into a grid within a set range to generate... There are several candidate angles. For each candidate angle... Construct an array guide vector Therefore, the dictionary matrix Let the sparse power vector be... , Indicates the first Prior information about the source power corresponding to each grid point, and using Construct a diagonal matrix The SBL iteration includes:

[0051]

[0052]

[0053]

[0054] in The model predicts the covariance matrix of the received data. For noise power, This is the posterior mean matrix. It is a virtual snapshot matrix. Indicates the first The first angle The posterior mean of each snapshot. Let the posterior covariance matrix be the first... Diagonal elements. After SBL iteration converges, from Selected from The peak values ​​are used as coarse candidates for SBL. To enhance the robustness of the initial stage, this embodiment also calculates the MUSIC spectral peak as a verification candidate. Both the SBL and MUSIC candidates enter the PSO local continuous refinement stage, and finally the optimal initial DOA is selected by the covariance fitting cost.

[0055] S4 tracking requires initial state and prior parameters

[0056] The optimization variables for PSO refinement search are Dimensional DOA vector. For candidate centers. and search radius Limit the search boundary of each dimension to And crop to the set range The PSO particle position represents a set of DOA estimates, and the velocity and position are updated as follows:

[0057]

[0058]

[0059] in For the first Particle positions, For particle velocity, For the individual's optimal position, The optimal position globally. This indicates the generation of random decimals between 0 and 1. Inertia weight. The learning factor decreased linearly from 0.9 to 0.6. Speed ​​limit The number of PSO particles in this embodiment Maximum number of iterations .

[0060] The objective function for minimizing the covariance fitting cost in PSO is:

[0061]

[0062]

[0063] in, Represents the trace of a matrix. This represents taking the determinant of a matrix. This indicates taking the natural logarithm. Simulated covariance matrix under candidate angles For diagonal add-ins, Covariance fitting cost function The virtual array covariance matrix of the current frame. Compared to directly searching for MUSIC spectral peaks, this objective function directly measures the fit between the model covariance and the virtual array covariance, and can more effectively utilize the source power prior obtained by SBL to select the initial DOA estimate.

[0064] S5 Determine the PSO search radius for each target.

[0065] After completing the initial two-frame estimation, a constant velocity state model is established for each target:

[0066]

[0067] in For the first The first goal in DOA of the frame For the first The first goal in Angular velocity of the frame, This is the state transition matrix, used to predict the angle of the current time frame based on the angle and angular velocity of the previous time frame. This is the observation matrix, used to extract DOA measurements from the state vector. The frame interval is used to perform one prediction step based on the state of the previous frame.

[0068]

[0069]

[0070] in, Including the predicted first The target's DOA and angular velocity, To predict the covariance matrix, process noise Based on the equivalent angular acceleration perturbation constructed under the constant velocity model, its intensity is determined jointly by the basic process noise and the current measurement variance, and the update formula is:

[0071]

[0072]

[0073] in For process noise intensity, It is a function with maximum value. The target is the current measurement noise variance. To preset the basic process noise, This represents the lower limit of process noise. Current measurement variance. Represented as:

[0074]

[0075] in, Forgetting factor, This is the current DOA observation value. The lower bound of the variance is used to prevent the filter from over-relying on single-frame observations.

[0076] For the One objective is to calculate the innovation variance based on the prediction covariance matrix and the measurement variance. The PSO search radius is obtained from the chi-square threshold:

[0077]

[0078] in, This represents the truncation function. This represents the chi-square distribution threshold. In this embodiment, the threshold probability is 0.99. , .

[0079] S6 obtains the DOA observation values ​​of each target in the current frame.

[0080] Therefore, the PSO search center is used to predict the DOA of the KF, and the search radius adaptively changes with the target uncertainty. When the target motion is stable, the search range is reduced, and when the observation is uncertain, the search range is appropriately expanded. Using the virtual array covariance matrix of the current frame obtained in step S2 and the source power prior updated in step S8, the covariance is used to fit the target cost. PSO is then used for continuous domain optimization to obtain the DOA observation values ​​of each target in the current frame.

[0081] S7 Observation Allocation and Kalman Update

[0082] After PSO outputs the current frame's DOA observations, it assigns the observations to the corresponding target trajectories based on the principle of proximity to the center of the KF predicted angle. Then, it calculates innovation and its measurement variance for each trajectory and uses a threshold decision to determine the reliability of the observation. If the innovation is within the allowable range, the angle and angular velocity states are corrected according to the KF update formula. If the innovation is outside the allowable range, the predicted state is retained as the current frame result, and the next frame continues to be corrected using new observation data. For the dual-target case, the output sequence can be rearranged according to angle order after the update to maintain stable result numbering.

[0083] S8 Update Prior Parameters

[0084] Record the DOA state estimate of the current frame obtained in step S7, and update the source power prior, measurement variance and process noise using the current frame observations and information; return the updated KF state, error covariance and prior parameters to step S5 for prediction and search in the next time frame until the complete DOA trajectory is output.

[0085] In another aspect, the present invention also provides a locally refined multi-target DOA dynamic tracking system for implementing the aforementioned multi-target DOA dynamic tracking method, comprising a virtual snapshot data module, a local continuous domain refinement module, a PSO search radius module, a target DOA observation module, a covariance fitting objective function, a KF update module, and a DOA trajectory tracking module.

[0086] The virtual snapshot data module is used to construct a nested array and receive the first... The frame array data is processed and the sample covariance matrix is ​​calculated. The preprocessing is then performed to obtain the virtual array covariance matrix. Virtual snapshot data is then constructed based on the virtual array covariance matrix.

[0087] The local continuous domain refinement module is used to establish an angle coarse grid dictionary, run SBL with virtual snapshot data as observation input, and use the virtual array covariance matrix to refine through local continuous domain to calculate MUSIC verification candidates and obtain initial DOA candidates.

[0088] The PSO search radius module is used to predict the predicted DOA, predicted angular velocity, and predicted covariance matrix based on the initial DOA candidates and the KF state, and to determine the PSO search radius for each target.

[0089] The target DOA observation module is used to construct a covariance fitting objective function using the covariance matrix of the current frame virtual array within the PSO search radius, and to perform continuous domain optimization using PSO to obtain the target DOA observation values ​​for each frame.

[0090] The KF update module is used to assign DOA observations to the corresponding trajectories, perform KF updates, and obtain the DOA state estimate for the current frame.

[0091] The DOA trajectory tracking module is used to record the DOA state estimate of the current frame, which is used for prediction and search in the next time frame until the complete DOA trajectory is output.

[0092] Experimental performance analysis:

[0093] The performance evaluation metric is the root mean square error (RMSE), which can be defined as:

[0094]

[0095] in It is the number of signals. Indicates the number of Monte Carlo simulation experiments. For the first The Monte Carlo experiment The estimated DOA of each signal. For the first The true angle of the signal.

[0096] Signal-to-noise ratio (SNR) is defined as:

[0097]

[0098] in, Indicated by Logarithm with base 0, Expressed as signal power, It is expressed as noise power.

[0099] Simulation experiment parameters: target number Time frame count The two target trajectories are respectively from Linear change to ,Depend on Linear change to This creates a motion scene; single trajectory simulation is acceptable. , Monte Carlo RMSE simulation is acceptable. , , .

[0100] Experimental results: Figure 2 This is a comparison chart of the actual trajectory and estimated trajectory of the method of this invention in a single simulation. As can be seen from the chart, both targets move smoothly along linear trajectories. Target 1... Change to Target 2 is Change to The two trajectories remain separate and do not intersect throughout the entire time frame. The estimated trajectory obtained by the method in this paper basically coincides with the real trajectory, and can achieve continuous and stable tracking in all time frames without obvious jumps or track loss. This indicates that the method has high tracking accuracy and stability in multi-target scenarios.

[0101] Figure 3 This is a comparison of the RMSE of the proposed method with other methods at various time frames. As can be seen from the figure, the RMSE curve of the proposed method is the lowest overall and exhibits the least fluctuation, maintaining a relatively stable error level throughout the time frame changes. In contrast, the error fluctuations of PF (Particle Filter) tracking, DP (Dynamic Programming) tracking, and PDA (Probabilistic Association) tracking are more pronounced, with large peaks appearing in some time frames. This demonstrates that the proposed method, through the joint design of SBL coarse estimation, PSO local fine search, and KF recursive update, can obtain more stable and accurate multi-target DOA tracking results in dynamic multi-target scenarios.

[0102] Figure 4 This is a comparison chart of the RMSE of the method of this invention and other methods under different signal-to-noise ratio conditions. As can be seen from the chart, as the signal-to-noise ratio increases from... Increase to The RMSE of all methods generally shows a downward trend, with the proposed method showing a more significant decrease. Under low signal-to-noise ratio (SNR) conditions, the proposed method still maintains a relatively low error; as the SNR increases, its RMSE further decreases and tends to stabilize, outperforming PF tracking, DP tracking, and PDA probabilistic correlation tracking overall. These results demonstrate that the proposed method can effectively utilize SBL sparse estimation and PSO continuous domain refinement to improve angle estimation accuracy under low SNR conditions, and enhances the noise resistance of the tracking process through KF dynamic constraints.

[0103] Figure 5 This is a comparison chart of the RMSE of the proposed method with other methods under different snapshot count conditions. As can be seen from the chart, the estimation error of each method decreases overall with increasing snapshot count, indicating that increasing the snapshot count helps improve the quality of covariance matrix estimation and enhance DOA estimation accuracy. Compared to other comparative methods, the proposed method maintains a low RMSE even with a small number of snapshots, and the error continues to decrease and remain at the lowest level after the snapshot count increases, demonstrating that the proposed method has better estimation stability and accuracy advantages under limited snapshot conditions.

[0104] In summary, the proposed method demonstrates good tracking accuracy and stability in single trajectory tracking, frame-by-frame RMSE, experiments with different signal-to-noise ratios, and different snapshot numbers. Through the synergistic effects of nested array virtual aperture enhancement, SBL angular domain sparse coarse estimation, PSO continuous domain covariance fitting refinement, and KF cross-frame dynamic constraints, the proposed method can effectively reduce estimation errors in multi-target dynamic scenes, mitigate the adverse effects of noise disturbances and limited snapshots, and improve the continuity and robustness of multi-target DOA dynamic tracking.

[0105] The above embodiments are merely preferred embodiments of the present invention. Any equivalent adjustments made by those skilled in the art to the array parameters, number of snapshots, filter parameters, or experimental conditions without departing from the concept of the present invention shall fall within the protection scope of the present invention.

Claims

1. A locally refined multi-target DOA dynamic tracking method, characterized in that, Includes the following steps: S1: Construct a nested array to receive the first... The frame array data is processed and the sample covariance matrix is ​​calculated. The data is then preprocessed to obtain the virtual array covariance matrix. Virtual snapshot data is then constructed based on the virtual array covariance matrix. S2: Establish an angle coarse grid dictionary, run SBL with virtual snapshot data as observation input, use the virtual array covariance matrix to refine through local continuous domain, calculate MUSIC verification candidates, and obtain initial DOA candidates; S3: Based on the initial DOA candidates, use the KF state to make predictions to obtain the predicted DOA, predicted angular velocity and predicted covariance matrix, and determine the PSO search radius for each target; S4: Within the PSO search radius, construct the covariance fitting objective function using the covariance matrix of the virtual array in the current frame, and use PSO to perform continuous domain optimization to obtain the DOA observation values ​​of each target in the current frame. S5: Assign DOA observations to the corresponding trajectories, perform KF update, and obtain the DOA state estimate for the current frame; S6: Record the DOA state estimate of the current frame for prediction and search in the next time frame, until the complete DOA trajectory is output.

2. The locally refined multi-target DOA dynamic tracking method according to claim 1, characterized in that, Step S1 is implemented as follows: A nested array consisting of two subarrays is used, the first subarray containing There are array elements, and the spacing between the array elements is... The second subarray contains There are array elements, and the spacing between the array elements is... ,in , Wavelength; Calculate the position difference of all element pairs based on their physical positions to form a differential co-array lag set; average the covariance elements corresponding to the same lag, then search for continuous lag intervals from zero lag outwards, extracting the continuous virtual uniform array portion, denoted as the sequence. ; The correlation sequence corresponding to continuous non-negative lags Constructing a Toeplitz-type virtual array covariance matrix And using the reverse identity matrix Perform forward and backward smoothing to obtain ,right Perform eigenvalue decomposition and constrain the lower bound of eigenvalues ​​to positive values ​​to obtain the positive definite virtual array covariance matrix; construct deterministic partial Fourier frames and convert the positive definite covariance matrix into virtual snapshot data. .

3. The locally refined multi-target DOA dynamic tracking method according to claim 2, characterized in that, Step S2 is specifically implemented as follows: In the initial two frames, the continuous angular space is discretized into a grid to generate... There are 10 candidate angles; for each candidate angle... Construct an array guide vector dictionary matrix ; Let the sparse power vector be , Indicates the first Prior information about the source power corresponding to each grid point, and using Construct a diagonal matrix Then the dictionary matrix and diagonal matrix The posterior mean matrix is ​​obtained through SBL iteration; then, the elements of the posterior mean matrix are used to calculate... ; After SBL iteration converges, from Selected from One peak value is used as a coarse candidate for SBL; The MUSIC spectral peaks are calculated as verification candidates; both the SBL and MUSIC candidates are refined in the PSO local continuous domain, and the initial DOA estimate is finally selected by the optimal cost of covariance fitting.

4. The locally refined multi-target DOA dynamic tracking method according to claim 3, characterized in that, The specific implementation of the PSO local continuum refinement is as follows: For candidate centers and search radius Limit the search boundary of each dimension to And crop to a set range; PSO particle position represents a set of DOA estimates, and velocity and position are updated: Based on the covariance fitting cost minimized by PSO, the degree of fit between the covariance and the virtual array covariance is measured, and the source power prior obtained by SBL is used to select the initial DOA estimate.

5. The locally refined multi-target DOA dynamic tracking method according to claim 4, characterized in that, The specific implementation of step S3 is as follows: After completing the initial two-frame estimation, a constant velocity state model is established for each target: in For the first The first goal in DOA of the frame For the first The first goal in Angular velocity of the frame, This is the state transition matrix, used to predict the angle of the current time frame based on the angle and angular velocity of the previous time frame. This is the observation matrix, used to extract DOA measurements from the state vector. The frame interval is given; based on the state of the previous frame, a prediction step is performed using KF to obtain... and , Including the predicted first The target's DOA and angular velocity, To predict the covariance matrix, process noise The intensity of the equivalent angular acceleration disturbance constructed according to the constant velocity model is determined by the basic process noise and the current measurement variance. Current measurement variance Represented as: in, Forgetting factor, This is the current DOA observation value. This is the lower limit of the measured variance; For the One objective is to calculate the innovation variance based on the prediction covariance and measurement variance. The PSO search radius is obtained from the chi-square threshold. .

6. The locally refined multi-target DOA dynamic tracking method according to claim 5, characterized in that, Step S5 is implemented as follows: After PSO outputs the current frame DOA observation, it assigns the observation to the corresponding target trajectory according to the principle of being closest to the center of the KF predicted angle; then it calculates the innovation and measurement variance for each trajectory, and uses a threshold decision to determine whether the observation is reliable; If the information is within the allowable range, then the angle and angular velocity states are corrected according to the KF update formula; If the new information is outside the allowed range, the predicted state is retained as the result of the current frame, and the next frame continues to be corrected by the new observation data; for the case of two targets, the output sequence is sorted by angle after the update to keep the result numbering stable.

7. The locally refined multi-target DOA dynamic tracking method according to claim 6, characterized in that, Step S6 is implemented as follows: Record the obtained DOA state estimate for the current frame, and update the source power prior, measurement variance, and process noise using the current frame observations and new information; use the updated KF state, error covariance, and prior parameters for prediction and search in the next time frame until the complete DOA trajectory is output.

8. A locally refined multi-target DOA dynamic tracking system, used to implement the multi-target DOA dynamic tracking method according to any one of claims 1 to 7, characterized in that, Includes the following modules: The virtual snapshot data module is used to construct a nested array and receive the first... The frame array data is processed and the sample covariance matrix is ​​calculated. The data is then preprocessed to obtain the virtual array covariance matrix. Virtual snapshot data is then constructed based on the virtual array covariance matrix. The local continuous domain refinement module is used to establish an angle coarse grid dictionary. It runs SBL with virtual snapshot data as observation input, and uses the virtual array covariance matrix to refine the local continuous domain to calculate MUSIC verification candidates and obtain initial DOA candidates. The PSO search radius module is used to predict the predicted DOA, predicted angular velocity, and predicted covariance matrix based on the initial DOA candidates and the KF state, and to determine the PSO search radius for each target. The target DOA observation module is used to construct a covariance fitting objective function using the covariance matrix of the virtual array in the current frame within the PSO search radius, and to perform continuous domain optimization using PSO to obtain the target DOA observation values ​​for each target in the current frame. The KF update module is used to assign DOA observations to the corresponding trajectories, perform KF updates, and obtain the DOA state estimate for the current frame. The DOA trajectory tracking module is used to record the DOA state estimate of the current frame, which is used for prediction and search in the next time frame until the complete DOA trajectory is output.

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