CN-122019937-A - Grid refinement-based off-grid sparse reconstruction direct positioning method

CN122019937ACN 122019937 ACN122019937 ACN 122019937ACN-122019937-A

Abstract

The invention discloses a grid refinement-based off-grid sparse reconstruction direct positioning method which comprises the steps of carrying out preliminary grid division on a region of interest, constructing a sparse representation model of an observation signal, carrying out sparse Bayesian inference on the basis of the sparse representation model of the observation signal to obtain a preliminary positioning result of a radiation source, carrying out different forms of characterization on the sparse representation model based on Taylor expansion of an overcomplete dictionary and by utilizing offset value matrixes of different coordinate directions, carrying out new grid refinement and splitting on the preliminary grid through iteration based on the offset value matrixes of all coordinate directions, carrying out further search on grids corresponding to the preliminary positioning result by utilizing a maximum likelihood criterion according to the grid refinement and the space power of each new grid after iteration, and determining the position of the new grid where the radiation source is located so as to realize fine search. The method can further improve the positioning accuracy and robustness of the outlier under the condition of smaller calculation complexity.

Inventors

XIE JIAN
Zou Ruijing
WANG LING
TAO MINGLIANG
SUN YANDONG
FAN YIFEI
LIU XIANGYANG
SU JIA
ZHANG ZHAOLIN

Assignees

西北工业大学

Dates

Publication Date: 20260512
Application Date: 20260119

Claims (9)

1. A grid refinement-based off-grid sparse reconstruction direct positioning method is characterized by comprising the following steps of: Preliminary meshing is carried out on the region of interest, and a sparse representation model of the observation signal is constructed; Performing sparse Bayesian reasoning on the basis of a sparse representation model of an observation signal to obtain a preliminary positioning result of a radiation source, performing formal different characterization on the sparse representation model based on Taylor expansion of an overcomplete dictionary and by utilizing offset value matrixes in different coordinate directions, and performing new grid refinement and splitting on the preliminary grid through iteration based on the offset value matrixes in each coordinate direction; and further searching the grids corresponding to the preliminary positioning result by using a maximum likelihood criterion according to the grid refinement splitting result and the space power of each new grid after iteration, and determining the position of the new grid where the radiation source is positioned so as to realize fine searching.
2. The grid refinement-based off-grid sparse reconstruction direct positioning method according to claim 1, wherein a scene of the method comprises a moving observation station and a plurality of fixed radiation sources, and the observation station performs a plurality of array snapshot samples in each observation time slot; the sparse representation model of the observed signal is as follows: Wherein 、 Is that A set of snapshot observation signals and a set of sparse signals, Represented as a set of overcomplete dictionaries sparsely represented under different observation time slots, Is a noise set.
3. The grid refinement-based isolated sparse reconstruction direct positioning method of claim 1, wherein performing sparse bayesian reasoning on the basis of a sparse representation model of an observed signal to obtain a preliminary positioning result of a radiation source comprises: according to a sparse representation model, setting that noise received by each observation time slot obeys zero-mean Gaussian distribution, and constructing a likelihood function of an observation signal set under the given sparse signal set and variance; Modeling a sparse signal set by adopting independent zero-mean complex Gaussian distribution, and constructing prior distribution of the sparse signal set under a given variance vector, wherein the variance vector comprises space power of each row of the sparse signal set; Bayesian inference is implemented by adopting a expectation maximization algorithm, wherein: e, regarding the sparse signal set as a hidden variable, and constructing posterior distribution of the sparse signal set under given sparse signal set, variance vector and noise precision parameters, so as to obtain a posterior mean matrix, a posterior covariance matrix and an array output covariance matrix; And M steps of updating the vector of the variance and the noise precision parameter according to the posterior mean matrix, the posterior covariance matrix and the array output covariance matrix, and determining the grid where the radiation source is positioned based on the space power corresponding to each grid in the variance vector when iteration is completed, so as to realize preliminary positioning.
4. The grid refinement-based outlier sparse reconstruction direct localization method of claim 1, wherein performing formal different characterizations on the sparse representation model based on taylor expansion of the overcomplete dictionary and using offset value matrices of different coordinate directions comprises: for overcomplete dictionary set in sparse representation model Performing first-order Taylor expansion to obtain a new representation form of the sparse representation model: ; Wherein, the And Respectively represent Pair grid Coordinates and method for producing the same The partial derivative matrix obtained by the coordinate derivation, Is that A matrix of offset values for the direction, Is that A matrix of offset values for directions, wherein Represent the first Of a grid of Offset value sum of directions A directional offset value; 、 To observe a signal set and a sparse signal set, Is a noise set, superscript Representing a transpose; Due to And Are independent of each other, for The above formula can be rewritten as: ; Wherein the method comprises the steps of , Can be obtained by maximizing the expected likelihood function, namely: ; Parameters (parameters) And The expression of (2) is: ; ; Wherein the matrix subscripts Representing taking the first of the matrices Columns, e.g. Representation posterior mean matrix Conjugate of (2) The number of columns in a row, 、 Representing the observed signal Posterior mean matrix Is the first of (2) Columns.
5. The grid refinement-based off-grid sparse reconstruction direct positioning method according to claim 1, wherein performing the refinement splitting of the preliminary grid on the preliminary grid through iteration based on the offset value matrix of each coordinate direction comprises: When obtaining Offset value matrix of direction And Offset value matrix of direction After that, set up the first Personal grid Is the coordinates of (a) Each iteration of the grid refinement process proceeds according to the following rules: ; ; ; The first can be obtained by the above formula Personal grid Split into two new grids, one new grid Its coordinates are Another new grid is the first Personal grid Splitting a new grid Remaining grid after Wherein, the method comprises the steps of, And Is a new grid And remaining grid Corresponding space power; And (3) finishing the splitting process of the new grid by iterating for a plurality of times until the preset condition of the minimum grid interval is reached.
6. The grid refinement-based off-grid sparse reconstruction direct positioning method according to claim 1, wherein the step of further searching the grid corresponding to the preliminary positioning result by using a maximum likelihood criterion according to the grid refinement splitting result and the space power of each new grid after iteration to determine the position of the new grid where the radiation source is located comprises the following steps: first of the results of preliminary positioning of the radiation source Multiple grids, array output covariance matrix Matrix with signal components in two adjacent directions removed It can be defined as: ; Wherein, e.g. 、 Representing an overcomplete dictionary set Covariance matrix Corresponds to the first Portions of the maximum peak grid: ; ; Wherein, the Represent the first Maximum peak grid Comprises the first The location of the new grid is determined, Representing an overcomplete dictionary set In (a) The corresponding portion of the first and second metal layers, Representing variance vectors In (a) Corresponding space power; Corrected array output covariance matrix Expressed as: ; Wherein the method comprises the steps of For complete dictionary set In (a) The corresponding portion of the first and second metal layers, Is the first The spatial power of the maximum peak grid; constructing a maximum likelihood function As logarithm of joint distribution, namely: ; by maximising The position of the new grid where the radiation source is located is obtained.
7. The grid refinement-based outlier sparse reconstruction direct localization method of claim 6, wherein the maximizing The process of (1) comprises: defining an auxiliary quantity: ; ; substituting auxiliary variables into maximum likelihood functions And remove and connect with And Uncorrelated terms, get: ; Order the To obtain a given Optimum in time The expression: ; based on the true position of the radiation source Is positioned at 、 Searching for new grids in the range through a preset step length, thereby maximizing : ; Wherein, the Represent the first The position coordinates of the individual radiation sources, Represent the first Maximum peak grid Comprises the first Position coordinates of the new grid; Namely the first Final position estimation results of the individual radiation sources.
8. A terminal device comprising a processor, a memory and a computer program stored in the memory, characterized in that the processor, when executing the computer program, implements the grid refinement based method for direct localization of outlier sparse reconstruction of any one of claims 1-7.
9. A computer readable storage medium, in which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the grid refinement based outlier sparse reconstruction direct localization method according to any one of claims 1-7.

Description

Grid refinement-based off-grid sparse reconstruction direct positioning method Technical Field The invention relates to the technical field of passive positioning, in particular to a grid refinement-based method for directly positioning a radiation source through sparse reconstruction, which can be used for positioning a radiation source through satellites. Background The direct positioning technology is used as an optimal positioning framework, and global optimal solutions are generally obtained through grid exhaustive search of a positioning parameter space. However, the real radiation source is not precisely located in the position parameter grid, and the resulting grid mismatch (off-grid) tends to cause positioning errors, i.e. a departure problem. The learner combines the traditional two-step positioning method and the direct positioning method, combines the advantages of low complexity of the traditional method and high positioning precision of the direct positioning method, and introduces partial disadvantages of the two-step method into the direct positioning method although the scope of global search can be reduced. The direct positioning algorithm of the self-adaptive grid refinement can perform coarse estimation on the radiation source first and then perform fine estimation around the position and the angle, so that the calculated amount of the direct positioning algorithm is effectively reduced. However, the increase in the number of grids simply increases the probability that the radiation source will be covered by the grids and does not fundamentally solve the direct localization departure problem. In the direct positioning, the Hao et al introduce the idea of sparse Bayesian derivation from the grid into indoor direct positioning, establish a sparse Bayesian direct positioning model of the dynamic grid from the grid, and effectively reduce grid quantization errors. She Hongzhen aims at the grid-off problem, the grid-off quantity and the channel attenuation deviation are considered, the real overcomplete dictionary is approximated through first-order taylor expansion, the estimation of the grid-off and the channel attenuation is achieved, however, under the condition of a large initial grid, the accuracy of the first-order taylor expansion is low, and the grid-off positioning error is large. Therefore, how to further improve the positioning accuracy and robustness of the outlier under the condition of smaller computational complexity is a technical problem to be solved in the field. In the existing direct positioning algorithm, discrete grid division is needed to be carried out on the interested area, global optimal points are searched at each grid position to achieve positioning, and the discrete area is liable to cause a grid separation problem, namely the real position of the radiation source is not located on a preset grid, so that parameter grid quantization errors exist. Disclosure of Invention The invention aims to provide a grid refinement-based method for directly positioning through grid-free sparse reconstruction, which is used for further improving grid-free positioning accuracy and robustness under the condition of smaller calculation complexity. In order to realize the tasks, the invention adopts the following technical scheme: a grid refinement-based off-grid sparse reconstruction direct positioning method comprises the following steps: Preliminary meshing is carried out on the region of interest, and a sparse representation model of the observation signal is constructed; Performing sparse Bayesian reasoning on the basis of a sparse representation model of an observation signal to obtain a preliminary positioning result of a radiation source, performing formal different characterization on the sparse representation model based on Taylor expansion of an overcomplete dictionary and by utilizing offset value matrixes in different coordinate directions, and performing new grid refinement and splitting on the preliminary grid through iteration based on the offset value matrixes in each coordinate direction; and further searching the grids corresponding to the preliminary positioning result by using a maximum likelihood criterion according to the grid refinement splitting result and the space power of each new grid after iteration, and determining the position of the new grid where the radiation source is positioned so as to realize fine searching. Further, the method comprises a moving observation station and a plurality of fixed radiation sources, wherein the observation station performs a plurality of array snapshot samples in each observation time slot; the sparse representation model of the observed signal is as follows: Wherein 、Is thatA set of snapshot observation signals and a set of sparse signals,Represented as a set of overcomplete dictionaries sparsely represented under different observation time slots,Is a noise set. Further, performing sparse Bayesian inference on the b