Signal source tracking method based on off-grid sparse bayesian learning and glmb smoother

Abstract

The application discloses a signal source tracking method based on off-grid sparse Bayesian learning and GLMB smoother, and belongs to the technical field of array signal processing and multi-target tracking. The application firstly constructs a received signal model containing array element gain and phase errors, jointly estimates off-grid offset and error parameters through off-grid sparse Bayesian learning to obtain a two-dimensional direction of arrival rough estimate; then extracts accurate direction of arrival and angular spread description based on adaptive grid refinement, forms a pseudo-measurement set, and constructs a dynamic measurement noise covariance matrix using likelihood function curvature and local spectral quality; finally, the pseudo-measurement set and the dynamic covariance matrix are input into a generalized labeled multi-Bernoulli smoother, and a continuous tracking trajectory is output in combination with reverse RTS smoothing. The application has high precision and strong robustness under the conditions of array error, grid mismatch and multi-source dynamic scene.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and multi-target tracking, and particularly relates to a signal source tracking method based on off-network sparse Bayesian learning and GLMB smoother. Background Technology

[0002] Currently, in large-scale multiple-input multiple-output (MIMO) systems and high-resolution sensor arrays, two-dimensional direction-of-arrival (DOA) estimation and dynamic tracking of incoherent distributed signal sources are key tasks in array signal processing. Traditional methods, such as multiple signal classification and rotation-invariant subspace techniques, are typically based on ideal point source models and precisely known array steering matrices, performing well in scenarios where the number of sources is known and the array is error-free. In recent years, sparse representation and sparse Bayesian learning methods have been introduced to handle cases with unknown number of sources and low signal-to-noise ratios, achieving sparse reconstruction through discrete grid modeling. Meanwhile, generalized labeled multi-Bernoulli filters and smoothers based on random finite sets have become effective multi-target tracking frameworks for handling varying target numbers and data correlation.

[0003] However, existing technical solutions still have several limitations: First, most methods do not fully consider the element gain and phase error that are common in real arrays, resulting in a significant decrease in estimation performance when the steering vector is mismatched; second, sparse Bayesian learning methods based on fixed discrete grids face the problem of grid mismatch, where deviation of the true direction of arrival from the preset grid will cause estimation bias, while excessively refining the grid will drastically increase the computational burden; finally, existing calibration sensing / off-grid SBL methods mainly stop at front-end DOA estimation, while existing GLMB-type tracking methods do not explicitly utilize front-end off-grid inference results, angular extension descriptors, and their uncertainty information. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a signal source tracking method based on off-grid sparse Bayesian learning and GLMB smoother, comprising: Acquire array measurement data from the incoherent distributed signal source received by the sensor array under conditions of unknown array element gain error and phase error; Based on the array measurement data, and using a preset two-dimensional discrete angle grid, a joint iterative estimation is performed on the array received signal model, which includes off-grid offset, array element gain error, and phase error, to obtain a coarse two-dimensional direction of arrival estimation result. Based on the coarse estimation result of the two-dimensional direction of arrival, a local angle region is determined. Adaptive mesh refinement is performed within the local angle region, and the accurate two-dimensional direction of arrival and the angular extension descriptor corresponding to the accurate two-dimensional direction of arrival are extracted from the refined mesh to form a pseudo measurement set. Based on the likelihood function curvature information corresponding to the precise two-dimensional direction of arrival and the local spectral quality index corresponding to the angular extension descriptor, a set of dynamic measurement noise covariance matrices corresponding one-to-one with each pseudo-measurement in the pseudo-measurement set is constructed. The pseudo-measurement set and its corresponding dynamic measurement noise covariance matrix set are input into a generalized label multi-Bernoulli smoother to perform joint prediction update and reverse smoothing processing, and output the final multi-target tracking trajectory.

[0005] Optionally, based on the array measurement data and a preset two-dimensional discrete angle grid, a joint iterative estimation is performed on the array received signal model, which includes off-grid offset, array element gain error, and phase error, to obtain a coarse two-dimensional direction-of-arrival estimation result, including: A model of the array received signal, including array element gain error and phase error, is established to transform the two-dimensional direction-of-arrival estimation problem into a sparse reconstruction problem. A discrete angle grid is preset in the two-dimensional angle domain, and the real two-dimensional wave arrival direction is represented as a combination of grid points and off-grid offset. A first-order Taylor expansion is performed on the array guidance model to construct an off-grid array receiving signal model that includes the off-grid offset, array element gain error and phase error. By introducing intermediate variables, the off-grid array received signal model is decomposed into an observation layer model and a sparse representation layer model, forming a two-level sparse modeling structure. Under the off-network sparse Bayesian learning framework, the intermediate variables, spatial distribution matrix, source-level time coefficient matrix, off-network offset, and array element gain error and phase error are jointly iteratively estimated to obtain a two-dimensional spatial spectrum, and a coarse estimation result of the two-dimensional direction of arrival is extracted based on the two-dimensional spatial spectrum.

[0006] Optionally, a local angular region is determined based on the coarse estimation result of the two-dimensional direction of arrival (DOA). Adaptive mesh refinement is performed within the local angular region, and the precise two-dimensional DOA and the angular extension descriptor corresponding to the precise two-dimensional DOA are extracted from the refined mesh to form a pseudo-measurement set, including: Based on the coarse estimation result of the two-dimensional direction of arrival, a local angle region is determined, and adaptive mesh refinement is performed on high-power candidate mesh points within the local angle region; On the refined local mesh, the accurate two-dimensional direction of arrival is extracted by maximizing the local modified log-likelihood function; Within the local support region of the precise two-dimensional direction of arrival, the local refined power spectrum is normalized and weighted, and the azimuth spread and elevation spread are calculated by weighted second moments to form the pseudo-measurement set.

[0007] Optionally, the adaptive mesh refinement includes: When a candidate grid point is located in the middle region of the grid, a new grid point is inserted along the diagonal direction, and the spatial power corresponding to the original grid point is allocated to the newly inserted grid point and the original grid point according to a preset weight. When candidate grid points are located in the grid edge region, the adjusted weight allocation ratio is used for refinement. The refined local power spectrum is then re-normalized. Refinement stops when the spacing between the refined grids is less than a preset threshold or the number of refinement layers reaches a preset upper limit.

[0008] Optionally, the joint iterative estimation is implemented using a variational Bayesian inference method, which alternately updates intermediate variables, spatial distribution matrix, source-level time coefficient matrix, off-network offset, array element gain error, phase error, and the posterior distribution of corresponding hyperparameters until the normalized error is lower than a preset threshold or the maximum number of iterations is reached.

[0009] Optionally, the pseudo-measurement set and its corresponding dynamic measurement noise covariance matrix set are input into a generalized label multi-Bernoulli smoother to perform joint prediction update and reverse smoothing processing, outputting the final multi-target tracking trajectory, including: Under the framework of label random finite set, the labeled multi-target state of the previous time step is used as the prior. Combined with the pseudo-measurement set of the current time step and its corresponding dynamic measurement noise covariance matrix set, the joint prediction and update of generalized label multi Bernoulli filtering is performed to obtain the posterior density of the multi-target state of the current time step. Based on the posterior density of the multi-objective state, trajectory pruning and truncation are performed, and multi-objective trajectories are extracted; Based on the linear state transition model and process noise covariance, the extracted multi-target trajectories are subjected to inverse RTS smoothing to output the final multi-target tracking trajectory.

[0010] Optionally, constructing the set of dynamic measurement noise covariance matrices corresponding to each pseudo-measurement includes: Based on the precise two-dimensional direction of arrival, the central angle measurement variance is constructed using the curvature information of the corresponding local modified log-likelihood function at the estimated point. Based on the local support region corresponding to the precise two-dimensional direction of arrival, local spectral quality indicators are extracted, and combined with the local refined grid interval and the central angle measurement variance, angular expansion measurement variance is constructed. The variance of the center angle measurement is combined with the variance of the angle extension measurement to generate the dynamic measurement noise covariance matrix.

[0011] Optionally, the variance of the center angle measurement is obtained based on the negative second derivative of the local modified log-likelihood function at the estimation point, the inverse approximation of the Hessian matrix, or the Laplace approximation; the variance of the angle extension measurement includes a baseline uncertainty term, a position uncertainty propagation term, and a quantization error term.

[0012] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0013] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: 1. By introducing joint modeling of array element gain, phase error, and off-grid offset, and performing joint estimation under the variational Bayesian framework, the estimation bias of two-dimensional direction of arrival caused by array steering vector mismatch is reduced, and the estimation robustness under the condition of array error is improved. 2. By extracting accurate two-dimensional direction of arrival and angular spread descriptors from the local refined spectrum, a pseudo-measurement set for incoherent distributed signal sources is constructed, enabling the spatial spread information of distributed sources to participate in subsequent tracking, rather than relying solely on the center angle. 3. By constructing a dynamic measurement noise covariance matrix based on local likelihood function curvature information and local spectral quality index, the adaptive transfer of the front-end off-grid sparse Bayesian learning estimation results and their uncertainties to the back-end generalized label multi-Bernoulli smoother is realized, which improves the accuracy of multi-target association and tracking under different confidence measurement conditions. 4. By employing joint prediction and update of generalized label multi-Bernoulli filtering and inverse RTS smoothing, continuous and smooth trajectory results can be output in scenarios of target birth, survival, death and cross motion, thereby improving the overall tracking robustness and trajectory continuity. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a real trajectory diagram of an embodiment of the present invention; Figure 2 This is a diagram of the azimuth-elevation tracking trajectory according to an embodiment of the present invention. Figure 3 This is a tracking trajectory diagram according to an embodiment of the present invention; Figure 4 This is an enlarged view of the trajectory according to an embodiment of the present invention; Figure 5 This is a potential estimation diagram according to an embodiment of the present invention; Figure 6 This is an error diagram of the Generalized Optimal Subpattern Assignment (GOSPA) according to an embodiment of the present invention; Figure 7 This is a flowchart of a method according to an embodiment of the present invention; Figure 8 This is a schematic diagram of local angle extension descriptor extraction in an embodiment of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] Example 1 This embodiment provides a signal source tracking method based on off-network sparse Bayesian learning and GLMB smoother, including: Step S1: Modeling of incoherent distributed signal source reception measurements including array gain phase error; In a large-scale MIMO system, a uniform rectangular array structure is adopted, with several array elements in both the horizontal and vertical directions. For multiple incoherent distributed signal sources, a power distribution model of their azimuth-elevation plane is established. The gain error and phase error of the array elements are jointly modeled as a diagonal complex gain-phase error matrix, which is then multiplied by the ideal array steering matrix to obtain the equivalent steering matrix containing the error.

[0019] Discrete grids are preset on a two-dimensional angle plane. For each grid point, the corresponding steering vector and its first-order partial derivatives of the azimuth and elevation angles are calculated. The real DOA is approximated as a linear combination of grid points and angle deviations in the vicinity of its neighboring grid points using a first-order Taylor expansion, thereby obtaining the off-grid DOA received signal model.

[0020] Step S2: Construction of off-network sparse Bayesian learning model; By introducing intermediate variables, the error-guided matrix and the sparse coefficient matrix are decomposed. The observed data is represented as "error-guided matrix × intermediate variable + noise", while the intermediate variable is represented as "sparse signal matrix × attenuation coefficient matrix + fitting error", thus constructing a two-level sparse modeling structure.

[0021] By introducing hierarchical priors in complex Gaussian-gamma form to the noise vector, sparse signal matrix, attenuation coefficient matrix, off-grid deviation vector, and gain phase error, an off-grid sparse Bayesian joint probability model is formed.

[0022] Step S3: Variational Bayesian inference and joint estimation of hyperparameters; A variational Bayesian inference method is employed to decompose the joint posterior distribution into several factors, and the intermediate variables, sparse matrix, off-network bias, noise accuracy, and sparse hyperparameters are iteratively updated alternately. The analytical form of each factor distribution is obtained by minimizing the Kullback-Leibler divergence between the approximate posterior and the true posterior, until the iteration converges.

[0023] After convergence, the two-dimensional spatial power distribution is calculated based on the sparse matrix and the attenuation coefficient matrix to obtain the power spectrum at each angle grid, and candidate grid points with larger power are extracted as rough DOA estimates.

[0024] Step S4: Adaptive mesh refinement and off-mesh DOA extraction; In the adaptive mesh refinement and fine DOA extraction stages, this invention implements the following differentiated refinement strategy to balance computational efficiency and estimation accuracy: (1) Based on the rough DOA results extracted in step S3, for high-power candidate points located in the middle region of the grid, new grid points are inserted in the diagonal direction, and the spatial power of the original grid points is distributed to the newly inserted grid points and the original grid points according to a preset weight. Specifically, new grid points can be inserted between candidate grid points and their diagonally adjacent grid points, and a weighted average method is used to allocate spatial power to the new grid points to improve the angular resolution and estimation accuracy of the local area.

[0025] (2) After the grid points are inserted, the power spectrum of the refined region is re-normalized to ensure that the total signal energy before and after the refinement operation remains constant. This mechanism establishes an energy conservation constraint under dynamic changes in grid density, effectively suppressing numerical instability or algorithm divergence caused by rapid grid refinement, and ensuring the convergence performance of the system in non-stationary multi-objective environments.

[0026] (3) For candidate points located in the edge region of the grid, the refinement process is controlled by adjusting the weight allocation ratio to reduce the computational overhead of edge search and realize on-demand allocation of computing resources. When the grid spacing in all high-power candidate regions is less than the preset threshold, or the number of grid refinement layers reaches the preset upper limit, the refinement iteration is automatically stopped, and then the maximum likelihood extraction process of off-grid DOA is entered, thereby avoiding unnecessary global grid densification while ensuring estimation accuracy and improving overall computational efficiency.

[0027] (4) Construct the local array output covariance matrix on the refined grid, construct the likelihood function with the candidate DOA and the signal components in the adjacent azimuth, and use the maximum likelihood criterion to solve the accurate value of the off-grid DOA to obtain the azimuth and elevation angle estimates that are closer to the true values.

[0028] Step S5: Joint multi-target tracking based on GLMB smoother and RTS smoother; The precise two-dimensional direction of arrival and corresponding angular extension descriptors output by the OG-SBL module at each time step are used to construct a pseudo-measurement set. The dynamic measurement noise covariance matrix set corresponding to each pseudo-measurement is then input into a generalized label-based multi-Bernoulli (GLMB) smoother for joint prediction and updating within a label-randomized finite set framework. Specifically, a unique label is assigned to each signal source, and the birth, survival, and extinction processes of the signal sources are modeled to construct the likelihood function of the pseudo-measurement set. The posterior density of the multi-target state is obtained through the GLMB joint prediction and updating steps.

[0029] After joint prediction and update, the multi-target trajectories are pruned and truncated, and the GLMB hypothesis with the largest weight is selected to extract the multi-target trajectories. Then, based on the linear state transition model and process noise covariance, the RTS (Rauch–Tung–Striebel) smoothing algorithm is used to perform state correction on each trajectory from back to front, so as to obtain a continuous and smooth two-dimensional direction-of-arrival trajectory of the incoherent distributed signal source.

[0030] Example 2 like Figure 7 As shown, this embodiment provides a signal source tracking method based on off-grid sparse Bayesian learning and GLMB smoother, including: Acquire measurement data of the incoherent distributed signal source by the sensor array under unknown element gain and phase error conditions; An array receiving signal model containing off-grid offset, array element gain, and phase error is established based on a preset two-dimensional discrete angle grid. Off-grid sparse Bayesian learning is used to jointly iteratively estimate the sparse representation variables, off-grid offset, array element gain, phase error, and their hyperparameters to obtain a coarse estimation result of the two-dimensional direction of arrival. Based on the coarse estimation result of the two-dimensional direction of arrival, a local angle region is determined. Adaptive mesh refinement is performed on the local angle region, and the accurate two-dimensional direction of arrival is extracted by maximizing the local modified log-likelihood function on the refined mesh. At the same time, the corresponding angle extended descriptor is extracted based on the local refined power spectrum to form a pseudo-measurement set. Based on the curvature information of the local modified log-likelihood function of the precise two-dimensional direction of arrival and the local spectral quality index corresponding to the angular expansion descriptor, a set of dynamic measurement noise covariance matrices corresponding to each pseudo-measurement is constructed. The pseudo-measurement set and its corresponding dynamic measurement noise covariance matrix set are input into a generalized label multi-Bernoulli smoother to perform joint prediction update and inverse RTS smoothing, and output the final multi-target tracking trajectory.

[0031] like Figure 8 As shown, a local support region is constructed near the precise two-dimensional direction of arrival. Based on the normalized weighted result of the local refined power spectrum, the azimuth and elevation angle spreads are extracted by weighted second moments, thus forming pseudo-measurements for subsequent tracking. In the figure, the star-shaped marker represents the estimation center, the white outline represents the local support region, and the elliptical outline represents the angular spread descriptor extracted from the local refined power spectrum.

[0032] The specific process includes: 1. Establishment of system structure and signal model; This invention employs a URA array receiving model, where the URA array element is... The spacing between array elements is , λ Let wavelength be denoted as . Assume it exists. K An ID signal source is incident; the received signal from the ID signal source, which has multipath transmission characteristics, can be represented as follows: (1) (2) (3) in, For the first The center signal of the ID signal source, and the first The multipath signal associated with an ID signal source can be represented as: , For the first The number of multipath signals from each ID signal source; and They represent the first The ID signal source's first The amplitude attenuation coefficient and time delay of the signal along the path. It is the first The center frequency of the ID signal source. It is the first The array steering matrix of the ID signal sources, It is the incident signal source The steering vector of multipath transmission signals. It is the first A vector of attenuation coefficients of an ID signal source propagating along different paths. It is additive noise during signal transmission. The power distribution model of the ID signal source is equivalently characterized by a set of discrete multipath components. When the number of multipaths is large enough and they are densely distributed, the model can effectively approximate the spatial characteristics of a distributed signal source with continuous angular expansion characteristics.

[0033] Based on the spatial sparsity of the ID signal source, the 2-D DOA joint estimation problem is modeled as a sparse reconstruction problem. Furthermore, considering that in real-world scenarios, not all actual DOAs may lie on a predefined mesh, a first-order Taylor expansion off-mesh model is used for error compensation to compensate for mesh mismatch. The specific form of the compensated steering vector is as follows: (4) (5) Off-grid model measurements are represented as follows; (6) (7) (8) The off-grid deviations for azimuth and elevation angles are defined as follows; (9) (10) The sparse representation of the incident signal source measurement Y received by the URA is as follows; (11) Here is the gain phase error matrix. Indicates the gain error of the array elements. Let G represent the phase error; Z and S are the point sparse matrix and the row sparse matrix, respectively; N is additive noise that follows a complex zero-mean distribution; and the specific calculation of matrix G is given by the following formula. (12) 2. Hierarchical prior distribution assumption; The sparse recovery performance of SBL-based methods mainly depends on the sparsity-inducing ability resulting from the adopted prior. The selection of the prior model and sparsity modeling are crucial for the successful application of SBL methods to sparse signal recovery. In this invention, the following initial assumptions are made for ID signal sources with multipath transmission; a. Assume the array-received signals are independent between different snapshots, and the process noise follows a complex Gaussian distribution; noise variance and hyperparameters... Modeled as a gamma distribution; (13) (14) b. For cases where the gain phase error is unknown, assuming that the gain phase error vector coefficients between array elements are independent, the error distribution is also modeled as a complex Gaussian distribution; (15) (16) c. Row sparse matrix S contains A non-zero row, representing There are three incoherent signal sources. Assume each row of S is independent, and assign a complex Gaussian prior distribution to each row of S. (17) (18) d. Assume off-grid deviation Each element in the array follows a uniform distribution. , It is a discrete grid resolution; e. Assuming that the elements of the point sparse matrix Z are independent, we use the complex Gaussian gamma prior to improve its sparsity properties. (19) (20) f. Assume that all off-grid vectors follow a uniform distribution; Based on the above ID signal source model and related assumptions, its joint probability density distribution is expressed as follows: (twenty one) (twenty two) Its joint probability density function can be expressed as: (twenty three) The latent variables and hyperparameters in the above probability density function are solved using the variational Bayesian inference algorithm. The core of this method is to minimize... and the true posterior distribution The parameters are estimated using the KL (Kullback-Leibler) divergence between them. The approximate variational posterior of can be calculated as follows: (twenty four) 3. Hyperparameter estimation; Based on the above parameter assumptions, the solved DOA can be described as the set of angles of the following ID signal sources. Then, the solution is obtained through parameter inference from the probabilistic model. Now, the SBL algorithm based on sparse reconstruction is implemented by iteratively calculating hyperparameters until the termination condition is met.

[0034] Update the sparse representation X of the angle domain signal; Based on formula (17), the optimal solution for X is calculated as follows: (25) Its posterior mean and covariance matrix are: (26) (27) Update sparse representation error accuracy , The optimal solution is calculated using the following formula; (28) The posterior expectation is; (29) Update the source-level time coefficient matrix (row sparse matrix) ; (30) in; (31) (32) Substituting equations (25) and (26) into equation (24), we get The final variational posterior is; (33) Therefore, The posterior distribution is a complex Gaussian distribution, with its covariance matrix and mean vector as follows: (34) (35) Update the spatial distribution matrix (point sparse matrix) ; exist In the derivation of the optimal variational posterior, assuming that the elements of matrix Z are independent of each other, the following equation holds; (36) therefore, The optimal solution is calculated by the following formula; (37) The posterior covariance and mean are respectively; (38) (39) Update measurement noise accuracy ; (40) and The posterior follows a gamma distribution, and its expected value is calculated as follows; (41) Update source-level sparse control coefficients ; (42) The posterior expectation is; (43) Prior accuracy of updating the sparse coefficient matrix Z ; (44) Its posterior expectation is; (45) Update gain phase error ; (46) Its posterior covariance matrix and mean vector are respectively; (47) (48) Update gain phase error accuracy ; (49) Its posterior expectation is; (50) Update azimuth off-net offset ; (51) Based on the variational Bayesian inference framework, with other model parameters fixed, by maximizing the log-likelihood function, we can obtain... The optimal update formula is: (52) Among them, P and These are the precision matrix and auxiliary vector in the update process, respectively, and are specifically defined in the following form; (53) (54) In addition, to prevent the updated angle from crossing into adjacent grids and causing blurring, the offset needs to be adjusted. Perform constraint processing. If the mesh resolution is... The constraints are as follows; (55) parameter The derivation process and The results are largely consistent. By iteratively estimating the aforementioned hyperparameters, the proposed algorithm eventually converges and yields a sparse solution. This property is guaranteed by the convergence theory of variational Bayesian inference algorithms. Furthermore, the normalization error is defined as: (56) When the normalization error is less than a predefined threshold, or the number of iterations exceeds the pre-set maximum number of iterations. When the algorithm converges, it stops iteratively updating the parameters. Ultimately, the optimal sparse solution for off-network sparse Bayesian learning of incoherent distributed signal sources can be obtained. And can be accessed The norm is then used to calculate the spatial spectrum.

[0035] 4. Adaptive mesh refinement strategy and off-grid DOA extraction method; 4.1 Adaptive Mesh Refinement Strategy; Although the SBL method can improve algorithm performance, its computational complexity increases significantly with the number of grid points. This is because each grid point requires optimization, leading to a sharp increase in computational cost as grid density increases. To mitigate this issue, a mesh refinement process is added to the off-grid SBL process to reduce the number of grid points that need to be processed, thereby improving overall computational efficiency. Specifically, the mesh refinement strategy is carried out in two steps: (1) For points located at the edge of the grid, the corresponding refinement strategy is to take a weighted average of the current grid point and its adjacent grid points on the diagonal, and the weight is halved. This method can effectively reduce the amount of computation in the edge region while maintaining high estimation accuracy.

[0036] (2) For points located in the middle region of the grid, the refinement strategy is to optimize them by calculating the mean of the grid points on their diagonal. This can further reduce the amount of computation while ensuring the accuracy of the estimation in the middle region. The refinement strategy for grid points in the middle region is given by the following formula; (57) (58) in, It is inserted at the grid point The new grid point next to it, It is with grid points The associated spatial power. In this way, more refined grid points can be introduced into space, thereby improving the estimation accuracy.

[0037] To maintain the total power of the local region unchanged before and after refinement, the local power spectra corresponding to the newly inserted grid points and the original grid points are re-normalized to satisfy: ; This represents the set of grid points within a refined local area. This represents the set of grid points within the corresponding local area before refinement. This represents the normalized power corresponding to the refined grid points. This represents the spatial power corresponding to the grid points before refinement.

[0038] Through the aforementioned renormalization process, the spatial power of newly inserted grid points can be calculated and adjusted based on the power of their neighboring grid points, while ensuring the conservation of local total energy before and after each refinement. Furthermore, to avoid over-refining the grid and maintain computational efficiency, a minimum grid interval is set. The parameter iteration process stops when the grid interval is sufficiently small, and all grid points near the true DOA have reached this minimum interval. This grid refinement method significantly improves computational efficiency without reducing estimation accuracy, avoiding the high computational cost of comprehensive optimization of all grid points.

[0039] 4.2 Offline DOA extraction; An off-network extraction method is used to obtain a more accurate estimate of the true DOA. For the th For each selected grid point, the array output covariance matrix, excluding the signal components in its two adjacent directions, is defined as follows: (59) Among them, the guiding vector submatrix and diagonal power matrix Calculate as follows: (60) (61) The corrected array output covariance matrix is ​​then obtained. (62) It is the first The spatial power of a real DOA.

[0040] The corrected log-likelihood function of their joint distribution is calculated as follows: (63) Among them, the definition and A matrix of the following form: (64) (65) By maximizing the log-likelihood function: (66) (67) A higher accuracy DOA can be obtained, and its mathematical form is as follows: (68) 4.3 Dynamic construction of the measurement noise covariance matrix; To enable the GLMB smoother to perceive the uncertainty in the front-end SBL estimation, this invention proposes a method for constructing a dynamic measurement noise covariance matrix. In the off-grid DOA extraction process in step 4.2, for each detected signal source, this invention not only obtains its center direction of arrival... Simultaneously, its angular spread parameter is extracted based on the spatial distribution of the local power spectrum. and Specifically, the angular spread can be calculated using the second-order central moments of the local power spectrum: (69) in, For the first The local grid point neighborhood corresponding to each target (usually including the grid point selected in step 4.2 and its adjacent grid points). For grid points Spatial power at a given location (estimated by SBL, e.g., posterior power at the corresponding grid point) ), The weights are normalized to the accurate DOA estimate obtained by maximizing the local likelihood function in step 4.2. This angular spread parameter reflects the spatial distribution width of the signal source and is of great value for tracking distributed signal sources.

[0041] Based on the above extraction results, for the first... A tracking target whose measurement vector includes azimuth angle Pitch angle Azimuth extension and pitch angle extension Four components, corresponding Measurement noise covariance matrix It is constructed as a diagonal matrix.

[0042] (1) Construction of the measurement variance of the central DOA; According to the Laplace approximation, the variance of the maximum likelihood estimator near the true value can be approximated by the inverse of the negative second derivative (Hessian) of the log-likelihood function at the estimation point. This equivalent approximation includes variance approximations obtained based on the negative second derivative of the local log-likelihood function, the inverse Hessian matrix approximation, or the Laplace approximation.

[0043] In step 4.2, the first The off-grid DOA of each target is achieved by maximizing the locally modified log-likelihood function. Therefore, the measurement variance of its central DOA is constructed as follows: (70) Therefore, the greater the curvature of the locally modified log-likelihood function near the estimation point, the more stable the central DOA estimate of the target and the smaller its measurement variance; conversely, if the curvature is small, the corresponding measurement variance is large.

[0044] (2) Construction of the measurement variance of angular extension; Angular extension and The distribution characteristic parameters are extracted through the local power spectrum, and their estimation accuracy is affected by factors such as local signal-to-noise ratio, spectral peak shape, and grid discretization. To enable the GLMB smoother to adaptively evaluate the reliability of angular spread measurements, this invention proposes a hybrid dynamic variance model. First, a local spectral quality index is defined: (71) in For local support domain The maximum spectral value within the range indicates a more prominent peak and a more reliable measurement. Based on this, the measurement variance of angular expansion is constructed as follows: (72) in The baseline variance calibrated offline; The nominal reference spectral quality level; These represent the intervals of the locally refined mesh in the azimuth and elevation angles, respectively. is a non-negative adjustment coefficient. In Equation (72), the first term reflects the dynamic scaling of baseline uncertainty with spectral quality, the second term couples the estimated variance of the center DOA to the angular expansion variance (because angular expansion extraction depends on the accuracy of the center position), and the third term quantizes the quantization error caused by grid discretization (assuming uniform distribution within the grid). This model integrates the uncertainty of front-end spectral information and back-end state estimation, enabling the GLMB smoother to make more reasonable use of angular expansion measurements.

[0045] (3) Synthesis of the measurement noise covariance matrix; Combining the above four components yields the measurement noise covariance matrix passed to the GLMB update step: (73) This matrix is ​​dynamically updated at each time step based on the SBL estimation results, enabling the GLMB smoother to adaptively adjust its confidence level in measurement information, thereby significantly improving tracking accuracy and robustness in multi-target dynamic tracking scenarios. In practical applications, if the angular expansion feature corresponding to a target is not significant or the local spectral support is insufficient, the corresponding variance term can be set to a large constant to reduce the impact of this expanded measurement component on subsequent tracking results.

[0046] 5. GLMB smoother iterative estimation strategy; To avoid propagating prediction components that generate weak update components and to reduce the computational complexity of truncation, a joint prediction update strategy is adopted in the GLMB filter prediction update step to establish a direct recursion of GLMB densities at two consecutive time steps. Given the GLMB prior density and the observation model, the probability density of the next time step is expressed as: (74) The specific parameter calculations are given below; (75) (76) (77) (78) (79) in, For joint prediction and weight update, The expected survival probability, To measure the likelihood, For single-objective state probability density, To predict spatial density.

[0047] 6. Single ID signal source RTS smoothing; The GLMB smoother adds a reverse RTS smoothing step to the GLMB filter. This removes outliers and eliminates trajectory fragmentation, resulting in a smoothed trajectory. After the forward GLMB filtering is completed, the filtering result of the last time step is used as the initial value for reverse data smoothing. The smoothing process is as follows; (80) (81) (82) (83) in, It is the ID signal source status. For the predicted state, F is a linear transformation matrix. Let Q be the predicted state covariance matrix, Q be the process noise, and D be the smoothing gain matrix. The smoothed state covariance matrix, with superscript... This indicates a smoothed result.

[0048] Figure 1 This is a real trajectory diagram of an embodiment of the present invention. Multiple incoherent distributed signal sources are set as tracking targets. The birth position and death position of each signal source are clearly marked in the diagram, fully presenting the motion trajectory and dynamic changes of multiple signal sources in the azimuth-elevation plane. This trajectory diagram demonstrates the dynamic tracking scenario established by the present invention for incoherent distributed signal sources with multipath propagation characteristics, providing a benchmark reference for subsequent tracking using the method described in this invention.

[0049] Figure 2 This figure shows the azimuth-elevation tracking trajectory of an embodiment of the present invention, comparing the matching effect of the proposed algorithm (OG-SBL-GLMB-Smoother) with the true tracks. As can be seen from the figure, after employing the off-network sparse Bayesian learning estimation, adaptive mesh refinement, pseudo-measurement extraction, and generalized label multi-Bernoulli smoothing described in this invention, the tracking trajectory closely matches the true trajectory, maintaining stable tracking throughout the entire time series without significant offset or breakage, thus verifying the tracking accuracy of the present invention in multi-source dynamic scenes.

[0050] Figure 3This is a comparison diagram of the overall tracking trajectory in an embodiment of the present invention. This diagram more clearly reflects the estimation effect and trajectory changes of the tracking algorithm within a specific region. As can be seen from the diagram, after applying the joint iterative estimation, adaptive mesh refinement, dynamic measurement noise covariance construction, and smoothing tracking method described in this invention, the tracking trajectory of the OG-SBL-GLMB-Smoother algorithm almost coincides with the true trajectory, accurately capturing the spatial motion characteristics of the signal source; while the MUSIC algorithm exhibits overall deviation, especially in cases of signal source emergence or disappearance. These results demonstrate that the method described in this invention can maintain high tracking accuracy and robustness even under gain-phase error conditions.

[0051] Figure 4 This is a magnified local tracking trajectory diagram for each ID signal source in this embodiment of the invention. This diagram more clearly reflects the estimation effect of the tracking algorithm and the changes in the trajectory within a specific region. Observation shows that the tracking algorithm has a large estimation error at the birth and death moments of the signal source, leading to deviations in the estimated trajectory. However, over time, after using the variational Bayesian inference, off-network offset constraint update, and smooth tracking processing described in this invention, the proposed algorithm can gradually adjust and stabilize the tracking of the signal source. During the period when the signal source persists, the estimated trajectory almost perfectly matches the actual trajectory, indicating that the method of this invention can maintain high tracking accuracy and robustness even under gain and phase error conditions.

[0052] Figure 5 and Figure 6 The results show a comparison of different algorithms on different performance metrics. Among them, Figure 5 The potential estimation curve reflects the estimation of the number of sources over time; Figure 6 The GOSPA error evaluation chart is used to measure the overall error of the estimation results. As can be seen from the potential estimation curve, over the entire observation period, the OG-SBL-GLMB-Smoother algorithm, based on the off-grid sparse Bayesian learning, adaptive mesh refinement, dynamic covariance construction, and GLMB smoothing tracking method described in this invention, provides a more accurate estimate of the number of sources compared to the actual source number curve, and the estimation process is more stable. In contrast, the MUSIC method's estimate fluctuates, exhibiting significant deviations, particularly at the moments of target birth and death. In the comprehensive evaluation based on GOSPA distance, the method of this invention consistently shows a lower error level, indicating that it outperforms the MUSIC method in both accuracy and stability of source number estimation, further validating the technical effectiveness of the method described in this invention.

[0053] comprehensive Figures 1-6Experimental results show that, in complex scenarios with multiple dynamically changing signal sources and gain-phase errors in the array, the OG-SBL-GLMB-Smoother algorithm proposed in this invention significantly outperforms the traditional MUSIC algorithm in terms of trajectory matching degree, source number estimation stability, and overall tracking error. This fully verifies the effectiveness of the integrated framework of "off-network sparse Bayesian learning front-end estimation + angle-extended sensing pseudo-measurement and dynamic covariance construction + GLMB joint prediction update + RTS reverse smoothing", which can achieve high-precision and robust tracking of incoherent distributed signal sources when the array has unknown gain-phase errors.

[0054] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0055] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0056] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A signal source tracking method based on off-network sparse Bayesian learning and GLMB smoother, characterized in that, include: Acquire array measurement data from incoherent distributed signal sources received by the sensor array under conditions of unknown array element gain error and phase error; Based on the array measurement data, and using a preset two-dimensional discrete angle grid, a joint iterative estimation is performed on the array received signal model, which includes off-grid offset, array element gain error, and phase error, to obtain a coarse two-dimensional direction of arrival estimation result. Based on the coarse estimation result of the two-dimensional direction of arrival, a local angle region is determined. Adaptive mesh refinement is performed within the local angle region, and the accurate two-dimensional direction of arrival and the angular extension descriptor corresponding to the accurate two-dimensional direction of arrival are extracted from the refined mesh to form a pseudo measurement set. Based on the likelihood function curvature information corresponding to the precise two-dimensional direction of arrival and the local spectral quality index corresponding to the angular extension descriptor, a set of dynamic measurement noise covariance matrices corresponding one-to-one with each pseudo-measurement in the pseudo-measurement set is constructed. The pseudo-measurement set and its corresponding dynamic measurement noise covariance matrix set are input into the generalized label multi-Bernoulli smoother to perform joint prediction update and reverse smoothing processing, and output the final multi-target tracking trajectory. Based on the array measurement data, and using a preset two-dimensional discrete angle grid, a joint iterative estimation is performed on the array received signal model, which includes off-grid offset, array element gain error, and phase error, to obtain a coarse two-dimensional direction-of-arrival estimation result, including: A model of the array received signal, including array element gain error and phase error, is established to transform the two-dimensional direction-of-arrival estimation problem into a sparse reconstruction problem. A discrete angle grid is preset in the two-dimensional angle domain, and the real two-dimensional wave arrival direction is represented as a combination of grid points and off-grid offset. A first-order Taylor expansion is performed on the array guidance model to construct an off-grid array receiving signal model that includes the off-grid offset, array element gain error and phase error. By introducing intermediate variables, the off-grid array received signal model is decomposed into an observation layer model and a sparse representation layer model, forming a two-level sparse modeling structure. Under the off-network sparse Bayesian learning framework, the intermediate variables, spatial distribution matrix, source-level time coefficient matrix, off-network offset, and array element gain error and phase error are jointly iteratively estimated to obtain a two-dimensional spatial spectrum, and a coarse estimation result of the two-dimensional direction of arrival is extracted based on the two-dimensional spatial spectrum.

2. The method according to claim 1, characterized in that, Based on the coarse estimation result of the two-dimensional direction of arrival (DOA), a local angular region is determined. Adaptive mesh refinement is performed within this local angular region, and the precise two-dimensional DOA and the corresponding angular extension descriptor are extracted from the refined mesh to form a pseudo-measurement set, including: Based on the coarse estimation result of the two-dimensional direction of arrival, a local angle region is determined, and adaptive mesh refinement is performed on high-power candidate mesh points within the local angle region; On the refined local mesh, the accurate two-dimensional direction of arrival is extracted by maximizing the local modified log-likelihood function; Within the local support region of the precise two-dimensional direction of arrival, the local refined power spectrum is normalized and weighted, and the azimuth spread and elevation spread are calculated by weighted second moments to form the pseudo-measurement set.

3. The method according to claim 2, characterized in that, The adaptive mesh refinement includes: When a high-power candidate grid point is located in the middle region of the grid, a new grid point is inserted along the diagonal direction, and the spatial power corresponding to the original grid point is allocated to the newly inserted grid point and the original grid point according to a preset weight. When high-power candidate grid points are located in the grid edge region, the adjusted weight allocation ratio is used for refinement. The refined local power spectrum is then re-normalized. Refinement stops when the spacing between the refined grids is less than a preset threshold or the number of refinement layers reaches a preset upper limit.

4. The method according to claim 1, characterized in that, The joint iterative estimation is implemented using the variational Bayesian inference method, which alternately updates the intermediate variables, spatial distribution matrix, source-level time coefficient matrix, off-network offset, array element gain error, phase error, and the posterior distribution of the corresponding hyperparameters until the normalized error is lower than a preset threshold or the maximum number of iterations is reached.

5. The method according to claim 1, characterized in that, The pseudo-measurement set and its corresponding dynamic measurement noise covariance matrix set are input into a generalized label multi-Bernoulli smoother to perform joint prediction update and reverse smoothing processing, outputting the final multi-target tracking trajectory, including: Under the framework of label random finite set, the labeled multi-target state of the previous time step is used as the prior. Combined with the pseudo-measurement set of the current time step and its corresponding dynamic measurement noise covariance matrix set, the joint prediction and update of generalized label multi Bernoulli filtering is performed to obtain the posterior density of the multi-target state of the current time step. Based on the posterior density of the multi-objective state, trajectory pruning and truncation are performed, and multi-objective trajectories are extracted; Based on the linear state transition model and process noise covariance, the extracted multi-target trajectories are subjected to inverse RTS smoothing to output the final multi-target tracking trajectory.

6. The method according to claim 1, characterized in that, The construction of the dynamic measurement noise covariance matrix set corresponding to each pseudo-measurement includes: Based on the precise two-dimensional direction of arrival, the central angle measurement variance is constructed using the curvature information of the corresponding local modified log-likelihood function at the estimated point. Based on the local support region corresponding to the precise two-dimensional direction of arrival, local spectral quality indicators are extracted, and combined with the local refined grid interval and the central angle measurement variance, angular expansion measurement variance is constructed. The variance of the center angle measurement is combined with the variance of the angle extension measurement to generate the dynamic measurement noise covariance matrix.

7. The method according to claim 6, characterized in that, The variance of the center angle measurement is obtained based on the negative second derivative of the local modified log-likelihood function at the estimation point, the inverse approximation of the Hessian matrix, or the Laplace approximation; the variance of the angle extension measurement includes the baseline uncertainty term, the position uncertainty propagation term, and the quantization error term.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1-7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-7.

Images