Off-grid sparse reconstruction direct positioning method based on grid refinement
By employing a grid refinement and sparse reconstruction method, combined with sparse Bayesian inference and Taylor expansion, the problem of off-grid in the direct localization algorithm is solved, achieving high-precision localization of radiation sources with relatively low computational complexity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-01-19
- Publication Date
- 2026-05-12
AI Technical Summary
Existing direct positioning algorithms suffer from off-grid issues in radiation source localization, resulting in large positioning errors and high computational complexity, making it difficult to improve positioning accuracy and robustness with lower computational complexity.
A sparse reconstruction method based on mesh refinement is adopted. The mesh is refined by sparse Bayesian inference and Taylor expansion, and the location of the radiation source is determined by combining the maximum likelihood criterion.
It significantly improves the accuracy and robustness of radiation source localization with relatively low computational complexity, reduces localization errors, and increases computational efficiency.
Smart Images
Figure CN122019937A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of passive positioning technology, specifically to a direct positioning method based on grid refinement and sparse reconstruction, which can be used for satellite positioning of radiation sources. Background Technology
[0002] Direct localization, as an optimal localization framework, typically obtains the global optimum through an exhaustive search of the gridded location parameter space. However, the actual radiation source is not precisely located on the location parameter grid, and the resulting grid mismatch (off-grid) inevitably leads to localization errors, i.e., the off-grid problem.
[0003] Some scholars have combined traditional two-step localization methods with direct localization methods, integrating the advantages of low complexity in traditional methods and high accuracy in direct localization. While this reduces the global search range, it also introduces some of the disadvantages of the two-step method into the direct localization method. Adaptive mesh refinement direct localization algorithms can first perform a coarse estimate of the radiation source, and then perform a fine estimate around its position and angle, effectively reducing the computational load of the direct localization algorithm. However, increasing the number of meshes only increases the probability of the radiation source being covered by the mesh; it does not fundamentally solve the problem of off-grid localization.
[0004] In direct localization, Hao et al. introduced the idea of off-grid sparse Bayesian derivation into indoor direct localization, establishing a dynamic grid sparse Bayesian off-grid direct localization model, effectively reducing grid quantization error. Ye Hongzhen addressed the off-grid problem by considering the off-grid quantity and channel attenuation deviation, using a first-order Taylor expansion to approximate the true overcomplete dictionary, thus estimating off-grid quantity and channel attenuation. However, under large initial grid conditions, the accuracy of the first-order Taylor expansion is low, leading to large off-grid localization errors. Therefore, how to further improve the accuracy and robustness of off-grid localization with relatively low computational complexity is a pressing technical problem in this field.
[0005] In existing direct localization algorithms, it is necessary to divide the region of interest into discrete grids and search for the global optimum at each grid location to achieve localization. However, the discretization of the region inevitably leads to the grid deviation problem, that is, the actual location of the radiation source is not located on the preset grid, resulting in parameter grid quantization error. Summary of the Invention
[0006] The purpose of this invention is to provide a direct localization method for off-grid sparse reconstruction based on mesh refinement, which can further improve the accuracy and robustness of off-grid localization with less computational complexity.
[0007] To achieve the above objectives, the present invention employs the following technical solution: A direct localization method for out-of-mesh sparse reconstruction based on mesh refinement includes: The region of interest is initially divided into grids, and a sparse representation model of the observed signal is constructed. Based on the sparse representation model of the observed signal, sparse Bayesian inference is performed to obtain the preliminary localization result of the radiation source; based on the Taylor expansion of the overcomplete dictionary and using the offset matrix in different coordinate directions, the sparse representation model is characterized in different forms; then, based on the offset matrix in each coordinate direction, the preliminary grid is refined and split into new grids through iteration. Based on the results of the mesh refinement and the spatial power of each new mesh after iteration, the mesh corresponding to the preliminary location results is further searched using the maximum likelihood criterion to determine the location of the radiation source in the new mesh, so as to achieve a fine search.
[0008] Furthermore, the scenario of the method includes a moving observation station and multiple fixed radiation sources, with the observation station performing multiple array snapshots in each observation time slot; The sparse representation model of the observed signal is as follows: ;in , for A set of observation signals and a set of sparse signals in a snapshot. This represents an overcomplete dictionary set of sparse representations under different observation time slots. It is a noise set.
[0009] Furthermore, based on the sparse representation model of the observed signal, sparse Bayesian inference is performed to obtain preliminary localization results of the radiation source, including: Based on the sparse representation model, it is assumed that the noise received in each observation time slot follows a zero-mean Gaussian distribution. Given the sparse signal set and variance, the likelihood function of the observation signal set is constructed. An independent zero-mean complex Gaussian distribution is used to model the sparse signal set. Given a variance vector, a prior distribution of the sparse signal set is constructed. The variance vector contains the spatial power of each row of the sparse signal set. Bayesian inference is implemented using the expectation-maximization algorithm; where: The E-step treats the sparse signal set as a latent variable. Given the sparse signal set, variance vector, and noise precision parameters, it constructs the posterior distribution of the sparse signal set, thereby obtaining the posterior mean matrix, posterior covariance matrix, and array output covariance matrix. In step M, the variance vector and noise accuracy parameters are updated based on the posterior mean matrix, posterior covariance matrix, and array output covariance matrix. When the iteration is complete, the grid where the radiation source is located is determined based on the spatial power corresponding to each grid in the variance vector, thus achieving preliminary positioning.
[0010] Furthermore, based on the Taylor expansion of the overcomplete dictionary and utilizing offset matrices in different coordinate directions, the sparse representation model is characterized in different forms, including: For overcomplete dictionary sets in sparse representation models A first-order Taylor expansion yields a new representation of the sparse representation model: ; in, and They represent For the grid coordinates and The partial derivative matrix obtained by taking the coordinate derivative. for The offset matrix of directions, for The offset matrix of directions, where Indicates the first Each grid Directional offset value and The offset value of the direction; , For the set of observed signals and the set of sparse signals, For a noise set, superscript Indicates transpose; because and They are independent of each other, for In other words, the above formula can be rewritten as: ; in , This can be obtained by maximizing the expected likelihood function, i.e.: ; parameter and The expression is: ; ; Among them, matrix subscript This indicates taking the first element of the matrix. Columns, for example Represents the posterior mean matrix The conjugate of the first List, , Indicates taking the observed signal posterior mean matrix The List.
[0011] Furthermore, based on the offset matrix in each coordinate direction, the initial mesh is iteratively refined and subdivided into new meshes, including: When obtained Direction offset matrix and Direction offset matrix Then, set the number grid The coordinates are Each iteration of the mesh refinement process follows these rules: ; ; ; The above formula can be used to obtain the first... grid Split into two new grids, one of which is a new grid. Its coordinates are Another new grid is the first grid Split new grid The remaining grid after ;in, and It's a new grid. and remaining grid The corresponding space power; The process of splitting a new grid is completed by iterating multiple times until the preset condition of minimum grid spacing is reached.
[0012] Furthermore, based on the mesh refinement results and the spatial power of each new mesh after iteration, the mesh corresponding to the preliminary location results is further searched using the maximum likelihood criterion to determine the location of the radiation source in the new mesh, including: The first of the preliminary location results of the radiation source Each grid cell is used to output the covariance matrix. The matrix after removing the signal components in its two adjacent directions , can be defined as: ; Among them, such as , Represents an overcomplete dictionary set Covariance matrix Corresponding to the The portion of the grid with the largest peak: ; ; in, Indicates the first The largest peak grid The included first The location of the new grid, Represents an overcomplete dictionary set middle The corresponding part, Represents the variance vector middle The corresponding space power; Corrected array output covariance matrix Represented as: ; in For a complete dictionary set middle The corresponding part, For the first Spatial power of the grid with the largest peak value; construct the maximum likelihood function. Let log be the logarithm of the joint distribution, i.e.: ; By maximizing This gives the location of the radiation source in the new grid.
[0013] Furthermore, the maximization The process includes: Define auxiliary quantities: ; ; Substitute the auxiliary variable into the maximum likelihood function and remove the ones with and Unrelated items yield: ; make , to obtain the given optimal time expression: ; Based on the actual location of the radiation source Must be located , Within the range, a new grid is searched using a preset step size, thereby maximizing... : ; in, Indicates the first The location coordinates of the radiation source Indicates the first The largest peak grid The included first The position coordinates of the new grid; That is, the first The final location estimation results of each radiation source.
[0014] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the direct localization method for off-grid sparse reconstruction based on mesh refinement.
[0015] A computer-readable storage medium storing a computer program; when the computer program is executed by a processor, it implements the direct localization method for off-grid sparse reconstruction based on mesh refinement.
[0016] Compared with the prior art, the present invention has the following technical features: This invention selects the grid corresponding to the maximum spatial power spectrum during the sparse Bayesian iteration process. By maximizing the corrected posterior probability density, the location of the new grid is confirmed, achieving adaptive insertion of new grids near the potential radiation source location. Based on this, a small-range grid containing the potential radiation source location is selected, and a more accurate off-grid location estimate is obtained by correcting the array output covariance matrix and maximizing the likelihood function. Compared with existing technologies, this method reduces the lower bound of positioning error by increasing the number of grid points near the actual radiation source location; and improves off-grid positioning accuracy by performing a small-range grid search based on grid refinement. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of a scene where an observation station detects signals from a radiation source; Figure 2 This is a flowchart of the method of the present invention; Figure 3 This is a schematic diagram of the initial mesh division in an embodiment of the present invention; Figure 4 This is a schematic diagram of the off-grid location results of multiple radiation sources in an embodiment of the present invention, where (a) is the grid refinement and update process, and (b) is the off-grid estimation result; Figure 5 This is a schematic diagram illustrating the relationship between the root mean square error (RMSE) and signal-to-noise ratio for locating multiple radiation sources in an embodiment of the present invention. Detailed Implementation
[0018] This invention provides a direct localization method for out-of-grid sparse reconstruction based on mesh refinement. First, the method selects the grid corresponding to the maximum spatial power spectrum in a sparse Bayesian iteration. The new grid location is confirmed by maximizing the corrected posterior probability density, achieving adaptive insertion of new grids near potential radiation source locations. Second, a small-area grid containing the potential radiation source location is selected. A more accurate out-of-grid location estimate is obtained by correcting the array output covariance matrix and maximizing the likelihood function. This algorithm reduces computational complexity by decreasing the total number of grids, while also achieving higher localization accuracy and robustness.
[0019] In the scenario of this invention, there exists a moving observation station, and the observation station is equipped with... An antenna array with individual elements; the observation station moves along a predetermined orbit, respectively at... Observations were conducted at the location and in each observation time slot. Each array of snapshots is sampled. The number of observation locations; there are a total of [number] locations in the scene. A fixed radiation source radiates a carrier wavelength of [wavelength value] intermittently throughout all observation time slots. The signal; taking a point on the Earth's surface in the scene as the origin, constructing a system with the direction of due east as the origin. x The axis, with due north as the direction. y The axis, perpendicular to the Earth's surface, is in the upward direction. z The local coordinate system of the station center of the axis, where the first... The location of each radiation source is , The number of radiation sources, The coordinates are in the local coordinate system of the station center; the observation station constructs a sparse representation model by detecting the signals emitted by the radiation source, performs adaptive grid refinement and off-grid positioning estimation, and finally obtains higher accuracy off-grid positioning results.
[0020] In this scheme, parameters and superscripts in parentheses Indicates matrix transpose, parameter superscript Represents the conjugate transpose of a matrix, with superscript. This represents finding the inverse of a matrix. Represents the trace of a matrix. Describing the F-norm, This indicates the construction of a diagonal matrix. To calculate the determinant of a square matrix, Indicates taking the logarithm. Indicates proportional to, It represents the Hadamah accumulation. Represents the real part of a complex variable. Represent the conjugate of a vector or matrix; detailed steps are as follows: Step 1: Perform preliminary grid division on the region of interest and construct a sparse representation model of the observed signal.
[0021] The observation stations in this scheme will conduct observations of the region of interest. The observations were conducted in several time slots, and the region of interest was initially divided into discretized segments. Given a grid, obtain a set of positions for all grids. The first location set is constructed from this location set. An overcomplete dictionary corresponding to each observation slot , can be represented as: (1) In the above formula, Indicates the first Within the observation time slot corresponding to the first The array guide vector of each grid, For the first The location of each grid; the region of interest can be, for example, a range defined by the satellite's current position, beamwidth, and direction, or a range of areas where radiation sources may exist, defined based on speculation or prior information.
[0022] Assumption and Since the radiation source is located on only a few grids, the observed signal model can be sparsely represented. Therefore, the sparse representation model is: (2) In the above formula, the observed signal for The set of observation signals of a snapshot can be represented as: (3) in, Indicates the first The observation signals acquired in each snapshot across all observation time slots are represented as follows: (4) In the above formula, Indicates the first The observed signal in each observation time slot, .
[0023] Correspondingly, The set of sparse signals corresponding to each snapshot and noise set middle, , Indicates the first Each snapshot captures the sparse signal and noise across all observation time slots; This represents an overcomplete dictionary set of sparse representations under different observation time slots. Indicates the first A complete dictionary for each observation slot.
[0024] Step 2: Based on the sparse representation model of the observed signal, sparse Bayesian inference is performed to obtain preliminary localization results of the radiation source; based on the Taylor expansion of the overcomplete dictionary and using the offset matrix in different coordinate directions, the sparse representation model is characterized in different forms; then, based on the offset matrix in each coordinate direction, the preliminary grid is iteratively refined and split into new grids. Specifically: Step 2.1, Sparse Bayesian inference.
[0025] Based on the sparse representation model (2), it is assumed that the noise received in each observation slot is variance. Given an independent zero-mean Gaussian distribution, then given a sparse signal set... and variance Below, the set of observed signals The likelihood function can be expressed as: (5) in, Indicates a Gaussian distribution. It is the identity matrix; The noise accuracy parameter, i.e., variance. The derivative of .
[0026] To ensure the sparse signal set The sparsity property is modeled using independent zero-mean complex Gaussian distributions, given the variance vector. Below, a sparse signal set can be obtained. The prior distribution is: (6) in, Given the covariance matrix and the variance vector... , Represents a set of sparse signals No. The variance of the row; under a Gaussian distribution, since the mean of a sparse signal is 0, the spatial power and variance of the sparse signal are the same, so here... Simultaneously indicates the first row (i.e., the first row) Spatial power of (grids).
[0027] Solving the model involves obtaining a set of sparse signals. The posterior probability distribution is used to implement Bayesian inference using the Expectation-Maximization (EM) algorithm; the E-step mainly involves... Treating them as latent variables, calculate their expected values; in the M-step, based on the expected values calculated in the E-step, maximize the expected likelihood function and update the hyperparameters. .
[0028] In step E, given , and , The posterior distribution can be expressed as: (7) according to The posterior distribution is obtained, and the posterior mean matrix is calculated. Posterior covariance matrix and array output covariance matrix , can be represented as: (8) (9) (10) In the M-step, hyperparameters The update formulas can be expressed as follows: (11) (12) in The number of array elements at the observation station. for An identity matrix of dimension 1 This represents the number of snapshots in the array. It is the sample covariance matrix. represent of The top 100 largest peak grids (i.e., the peaks sorted from largest to smallest) The manifold matrix corresponding to each grid.
[0029] In calculation Only used The diagonal elements in the array can be calculated by only counting the diagonal elements. To reduce complexity, that is: (13) Among them, matrix subscript and Represent the first and second parts of the matrix respectively. row and number Columns, for example express The List.
[0030] Based on the sparse representation model, the formulas (8)-(12) are iterated continuously. When the maximum number of iterations is reached or other preset iteration requirements are met, the preliminary localization result of the radiation source is obtained, namely the variance vector. The largest indivual The corresponding grid (peak grid).
[0031] Step 2.2, mesh refinement.
[0032] The sparse representation model mentioned above uses Solving using a single grid is a coarse-grained localization approach. In sparse Bayesian iteration, only the grid closest to the radiation source can be located. Since the radiation source is unlikely to be exactly located on the pre-defined grid, the localization results may not meet the requirements of practical applications. Therefore, it is necessary to refine the previously defined grid. Each grid is refined; during each iteration, each grid is split into two new grids, as follows: A true overcomplete dictionary set can be derived from an original complete dictionary set. Using a first-order Taylor expansion, the sparse representation model can be further written as: (14) in, The original partition in step 1 The set of overcomplete dictionaries under each grid (overcomplete grid). and They represent For the grid coordinates and The partial derivative matrix obtained by taking the coordinate derivative. for The offset matrix of directions, for The offset matrix of directions, where Indicates the first Each grid Directional offset value and The offset value of the direction.
[0033] because and They are independent of each other, for In other words, the above formula can be rewritten as: (15) in , This can be obtained by maximizing the expected likelihood function, i.e.: (16) Among them, parameters and The expression is: (17) (18) Among them, matrix subscript This indicates taking the first element of the matrix. Columns, for example Represents the posterior mean matrix The conjugate of the first List, , Indicates taking the observed signal posterior mean matrix The List.
[0034] Similarly, corresponding The sparse representation model can be written as: (19) in , It can be obtained from the following formula: (20) Among them, parameters and The expression is: (twenty one) (twenty two) When obtained and Then, set the number grid The coordinates are The mesh refinement process is carried out according to the following rules: (twenty three) (twenty four) (25) That is, the above formula can be used to obtain the first... grid Split into two new grids, one of which is a new grid. Its coordinates are Another new grid is the first grid Split new grid The remaining grid after ;in, and It's a new grid. and remaining grid The corresponding spatial power is used to ensure that the total power remains constant after each iteration; that is, the two grids after splitting. , The power values are respectively the power values of the mesh before splitting. Half of it.
[0035] Therefore, the adaptive mesh refinement process obtains the single mesh offset by calculating formulas (8)-(12), (16) and (20). and Next, the mesh is refined and updated according to formulas (23)-(25) to complete one iteration; by iterating the adaptive mesh refinement process multiple times (stopping when the preset number of iterations is reached or the preset accuracy requirement is met), the final result of the refined mesh is obtained. For example, a minimum mesh interval needs to be set to ensure that the iteration stops when all meshes near the real radiation source reach the minimum mesh interval.
[0036] Step 3: Based on the results of the mesh refinement and the spatial power of each new mesh after iteration, the mesh corresponding to the preliminary positioning results is further searched using the maximum likelihood criterion to determine the location of the new mesh where the radiation source is located, so as to achieve a fine search and further improve the positioning accuracy.
[0037] To further reduce the off-grid quantization error, for the preliminary positioning results before grid splitting in step 2, the location of the radiation source is... Each grid cell is used to output the covariance matrix. The matrix after removing the signal components in its two adjacent directions , can be defined as: (26) Among them, parameter subscript Indicates the first The parameters corresponding to the maximum peak grid, such as , Represents an overcomplete dictionary set Covariance matrix Corresponding to the The portion of the grid with the largest peak: (27) (28) in, Indicates the first The largest peak grid The included first The location of the new grid (after mesh refinement, one grid is divided into multiple new grids), Represents an overcomplete dictionary set middle The corresponding part, Represents the variance vector middle The corresponding spatial power.
[0038] Corrected array output covariance matrix It can be represented as: (29) in For a complete dictionary set middle The corresponding part, For the first The spatial power of the grid with the largest peak value can be used to construct the maximum likelihood function. Let log be the logarithm of the joint distribution, i.e.: (30) Define auxiliary quantities: (31) (32) Substitute formulas (31) and (32) into formula (30), and remove the ones that are related to... and Unrelated items can be obtained as follows: (33) make , to obtain the given optimal time expression: (34) Substituting formula (34) into formula (33), we get only with The relevant function was found, but it could not be obtained. Closed-form solution; based on the true location of the radiation source Must be located , Within the range, possible radiation source locations can be searched using a small preset step size, thereby maximizing... ,Right now: (35) in, Indicates the first The location coordinates of the radiation source Indicates the first The largest peak grid The included first The position coordinates of the new grid; That is, the first The final location estimation results of each radiation source are used to complete the direct localization method based on grid refinement and sparse reconstruction.
[0039] Example: The scenario for detecting radiation source signals by the motion observation station established in this invention is as follows: Figure 1As shown, a single satellite observation station is set up to observe the radiation source for four time slots. The coordinates are derived from STK, and the specific locations are shown in Table 1. There are two radiation sources in the scene, located at (30.6107°N, 140.2339°E) and (30.3409°N, 140.5707°E) respectively. The transmission carrier frequency... A BPSK signal with a frequency of 1 GHz, a code rate of 1000 bps, and a bandwidth of 1.5 kHz was used. A local coordinate system was constructed with (30.45°N, 140.4°E) as the origin, and an initial grid was divided at 5 km intervals. A positioning search was performed within a range of -30 km to 30 km. Figure 3 As shown. The signal-to-noise ratio is set to 10dB, and the number of snapshots is 64; the specific process is as follows... Figure 2 As shown.
[0040] Table 1. Specific positions of the satellite in different observation time slots.
[0041] The off-grid positioning result diagram of the above embodiment is shown below. Figure 4 As shown; Figure 4 (a) illustrates the process of adaptive insertion of new meshes during the iteration process; Figure 4 (b) shows the final off-grid location results. It can be seen that the method of this application achieves off-grid location of multiple radiation sources.
[0042] With the same observation scenario set up, a fixed number of snapshots of 64, and a signal-to-noise ratio (SNR) ranging from -10dB to 10dB, 200 Monte Carlo analyses were performed in 5dB increments. The root mean square error (RMSE) at each SNR was calculated, and the positioning performance graph is shown below. Figure 5 It can be seen that, compared with the application of sparse Bayesian localization and parameter dictionary-based off-grid localization algorithms in this scenario, this algorithm has higher localization accuracy.
[0043] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A direct localization method for sparse reconstruction of off-grid structures based on mesh refinement, characterized in that, include: The region of interest is initially divided into grids, and a sparse representation model of the observed signal is constructed. Based on the sparse representation model of the observed signal, sparse Bayesian inference is performed to obtain the preliminary localization result of the radiation source; based on the Taylor expansion of the overcomplete dictionary and using the offset matrix in different coordinate directions, the sparse representation model is characterized in different forms; then, based on the offset matrix in each coordinate direction, the preliminary grid is refined and split into new grids through iteration. Based on the results of the mesh refinement and the spatial power of each new mesh after iteration, the mesh corresponding to the preliminary location results is further searched using the maximum likelihood criterion to determine the location of the radiation source in the new mesh, so as to achieve a fine search.
2. The direct localization method for sparse reconstruction based on mesh refinement according to claim 1, characterized in that, The scenario described in the method includes a moving observation station and multiple fixed radiation sources, with the observation station performing multiple array snapshots in each observation time slot; The sparse representation model of the observed signal is as follows: ;in , for A set of observation signals and a set of sparse signals in a snapshot. This represents an overcomplete dictionary set of sparse representations under different observation time slots. It is a noise set.
3. The direct localization method for sparse reconstruction based on mesh refinement according to claim 1, characterized in that, Based on the sparse representation model of the observed signal, sparse Bayesian inference is performed to obtain preliminary localization results of the radiation source, including: Based on the sparse representation model, it is assumed that the noise received in each observation time slot follows a zero-mean Gaussian distribution. Given the sparse signal set and variance, the likelihood function of the observation signal set is constructed. An independent zero-mean complex Gaussian distribution is used to model the sparse signal set. Given a variance vector, a prior distribution of the sparse signal set is constructed. The variance vector contains the spatial power of each row of the sparse signal set. Bayesian inference is implemented using the expectation-maximization algorithm; where: The E-step treats the sparse signal set as a latent variable. Given the sparse signal set, variance vector, and noise precision parameters, it constructs the posterior distribution of the sparse signal set, thereby obtaining the posterior mean matrix, posterior covariance matrix, and array output covariance matrix. In step M, the variance vector and noise accuracy parameters are updated based on the posterior mean matrix, posterior covariance matrix, and array output covariance matrix. When the iteration is complete, the grid where the radiation source is located is determined based on the spatial power corresponding to each grid in the variance vector, thus achieving preliminary positioning.
4. The direct localization method for sparse reconstruction based on mesh refinement according to claim 1, characterized in that, Based on the Taylor expansion of the overcomplete dictionary and utilizing offset matrices in different coordinate directions, the sparse representation model is characterized in different forms, including: For overcomplete dictionary sets in sparse representation models A first-order Taylor expansion yields a new representation of the sparse representation model: ； in, and They represent For the grid coordinates and The partial derivative matrix obtained by taking the coordinate derivative. for The offset matrix of directions, for The offset matrix of directions, where Indicates the first Each grid Directional offset value and The offset value of the direction; , For the set of observed signals and the set of sparse signals, For a noise set, superscript Indicates transpose; because and They are independent of each other, for In other words, the above formula can be rewritten as: ； in , This can be obtained by maximizing the expected likelihood function, i.e.: ； parameter and The expression is: ； ； Among them, matrix subscript This indicates taking the first element of the matrix. Columns, for example Represents the posterior mean matrix The conjugate of the first List, , Indicates taking the observed signal posterior mean matrix The List.
5. The direct localization method for sparse reconstruction based on mesh refinement according to claim 1, characterized in that, Based on the offset matrix in each coordinate direction, the initial mesh is iteratively refined into a new mesh, including: When obtained Direction offset matrix and Direction offset matrix Then, set the number grid The coordinates are Each iteration of the mesh refinement process follows these rules: ； ； ； The above formula can be used to obtain the first... grid Split into two new grids, one of which is a new grid. Its coordinates are Another new grid is the first grid Split new grid The remaining grid after ;in, and It's a new grid. and remaining grid The corresponding space power; The process of splitting a new grid is completed by iterating multiple times until the preset condition of minimum grid spacing is reached.
6. The direct localization method for sparse reconstruction based on mesh refinement according to claim 1, characterized in that, Based on the mesh refinement results and the spatial power of each new mesh after iteration, the mesh corresponding to the preliminary location results is further searched using the maximum likelihood criterion to determine the location of the radiation source in the new mesh, including: The first of the preliminary location results of the radiation source Each grid cell is used to output the covariance matrix. The matrix after removing the signal components in its two adjacent directions It can be defined as: ； Among them, such as , Represents an overcomplete dictionary set Covariance matrix Corresponding to the The portion of the grid with the largest peak: ； ； in, Indicates the first The largest peak grid The included first The location of the new grid, Represents an overcomplete dictionary set middle The corresponding part, Represents the variance vector middle The corresponding space power; Corrected array output covariance matrix Represented as: ； in For a complete dictionary set middle The corresponding part, For the first Spatial power of the grid with the largest peak value; construct the maximum likelihood function. Let log be the logarithm of the joint distribution, i.e.: ； By maximizing This gives the location of the radiation source in the new grid.
7. The direct localization method for sparse reconstruction based on mesh refinement according to claim 6, characterized in that, The maximization The process includes: Define auxiliary quantities: ； ； Substitute the auxiliary variable into the maximum likelihood function and remove the ones that are related to and Unrelated items yield: ； make , to obtain the given Optimal time expression: ； Based on the actual location of the radiation source Must be located , Within the range, a new grid is searched using a preset step size, thereby maximizing... : ； in, Indicates the first The location coordinates of the radiation source Indicates the first The largest peak grid The included first The position coordinates of the new grid; That is, the first The final location estimation results of each radiation source.
8. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes a computer program, it implements the direct localization method for off-grid sparse reconstruction based on mesh refinement as described in 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 the processor, it implements the direct localization method for off-grid sparse reconstruction based on mesh refinement as described in any one of claims 1-7.