CN-121998109-A - Programmable super-surface two-dimensional off-grid DOA estimation based on sparse Bayesian learning

CN121998109ACN 121998109 ACN121998109 ACN 121998109ACN-121998109-A

Abstract

The application discloses a programmable super-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning, and relates to the field of signal processing. The DOA estimation mathematical model is built according to a data measurement mechanism of the programmable hypersurface, the DOA estimation mathematical model is converted into a two-dimensional off-grid sparse model by utilizing Newton binomial expansion and two-dimensional linear Taylor expansion, and the two-dimensional off-grid sparse model is subjected to Bayesian inference by adopting an expected maximization technology through the sparse Bayesian probability model to obtain a predicted value of the DOA. According to the method, the DOA estimation problem is converted into the off-grid sparse signal recovery problem through the derived two-dimensional off-grid sparse model, and the Sparse Bayesian Learning (SBL) is adopted for solving. The Bayesian probability model is constructed according to the SBL basic framework, and iteration is carried out through Bayesian inference, so that DOA estimation efficiency and DOA estimation precision are greatly improved, and a theoretical template is provided for a sparse signal recovery estimation algorithm under a compressed sensing framework.

Inventors

FENG WEIKE
DU QIANQIAN
LI NINGHUI
LI JIAHAO
GUO YIDUO
LI HONGBING
XU HEXIU
HU XIAOWEI
PU TAO
MA JIAJUN

Assignees

中国人民解放军空军工程大学

Dates

Publication Date: 20260508
Application Date: 20251225

Claims (10)

1. The programmable ultra-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning is characterized by comprising the following steps of: Establishing a DOA estimation mathematical model according to a data measurement mechanism of the programmable subsurface; Converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model by utilizing Newton binomial expansion and two-dimensional linear Taylor expansion; and carrying out Bayesian inference on the two-dimensional off-grid sparse model by adopting a expectation maximization technology through the sparse Bayesian probability model to obtain the estimated value of the DOA.
2. The programmable ultra-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning as set forth in claim 1, wherein the process of establishing the DOA estimation mathematical model comprises: collecting signals irradiated to the programmable super surface, wherein the signals are expressed as ; Wherein S K is the kth signal, k=1, 2,..k, M, N is the number of array elements of the programmable subsurface rows and columns, respectively, Representing the phase of the kth signal at the time of the kth snapshot, Representing the reflection coefficient of the mth row and n column of the supersurface, The coding matrix is represented by a representation of the code, Representing the position of the mth row and n column of the subsurface, And The projection of the kth signal on the x-axis and the y-axis respectively, For the position of the receiver, λ is the center wavelength, For the noise of the t-th snapshot, j represents the imaginary part; Collecting measurement data of a periodic incident signal, and establishing a DOA estimation mathematical model: ; Wherein, the In order to receive the matrix of signals, For spreading the coding matrix, L is the number of coding matrices, In order to guide the vector matrix, Representing a matrix of the incident signals, A white noise matrix representing a complex Gaussian distribution, T is the number of snapshot cycles, and C represents the complex set.
3. The method for estimating the DOA on the basis of the sparse Bayesian learning by using the programmable super surface two-dimensional off-grid DOA according to claim 1, wherein the process of converting the DOA estimated mathematical model into the two-dimensional off-grid sparse model by utilizing Newton's binomial expansion and two-dimensional linear Taylor expansion comprises the following steps: Based on Newton binomial expansion, the method is applied to expansion of square root term of receiver position, and the coupled guide matrix is decomposed into two independent guide matrices; Adopting two-dimensional Taylor expansion, and approximating a target guide vector corresponding to the real DOA through a guide vector of an adjacent grid and an off-grid error; and converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model based on the target steering vector matrix.
4. A programmable ultra-surface two-dimensional off-grid DOA estimation method based on sparse bayesian learning as recited in claim 3, wherein the process based on newton's binomial expansion comprises: Based on Newton's binomial expansion, the expansion applied to the square root term of the receiver position: ; Wherein, the For the location of the receiver(s), Positions of the m-th row and the n-th column of the super surface; decomposing the coupled steering matrix into two independent steering matrices: ; Wherein, the 、 Is a steering matrix, lambda is the center wavelength, Is Khatri-Rao product, K is total number of signals, And Respectively the first Projection of the individual signals on the x-axis and y-axis, 、 Representing the corresponding steering vectors M, N as array elements of the programmable subsurface rows and columns, respectively, C representing the complex set and j representing the imaginary part.
5. A programmable subsurface two-dimensional off-grid DOA estimation method based on sparse bayesian learning as recited in claim 3, wherein the two-dimensional taylor expansion process comprises: dividing the signal projection into uniform grid sets, and if the signal is an off-grid signal, approximating the representation based on the guide vector pairs and the off-grid error pairs of adjacent grids: ; ; And The projection of the kth signal on the x-axis and the y-axis respectively, 、 The corresponding steering vector is represented by a vector, 、 Respectively is And The nearest-neighbor grid of the grid is selected, Is that With respect to Is used for the purpose of determining the derivative of (c), Is that With respect to Is used for the purpose of determining the derivative of (c), , Is the grid number; Synthesizing a two-dimensional target guide vector: Wherein, the Representing the corresponding two-dimensional steering vector, Representing the kronecker product.
6. A programmable ultra-surface two-dimensional off-grid DOA estimation method based on sparse bayesian learning as recited in claim 3, wherein the process of converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model based on a target-oriented vector matrix comprises: Constructing a two-dimensional sparse representation based on the target steering vector: ; Wherein, the Representing the corresponding two-dimensional steering vector, Representing the kronecker product of the two, , , In the form of a grid number, 、 Respectively is And The nearest-neighbor grid of the grid is selected, 、 The corresponding steering vector is represented by a vector, , In order to be an off-grid error, Representing a transpose of the matrix; constructing a target steering vector matrix based on two-dimensional sparse representation of each target steering vector: ; Wherein, the M, N are the number of array elements in the programmable subsurface rows and columns, respectively, C represents the complex set, , , , 。 Is a vector with all of the elements being 1, Representing a real set; Converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model through a target steering vector matrix: ; Wherein, the In a sparse form of rows of the incident signal matrix, For expanding the coding matrix, L is the number of coding matrices, T is the number of snapshot periods, A white noise matrix representing a complex gaussian distribution.
7. The programmable ultra-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning according to claim 1, wherein the process of performing Bayesian inference on the two-dimensional off-grid sparse model by using a expectation maximization technique through the sparse Bayesian probability model comprises the following steps: taking a two-dimensional off-grid sparse model as an input variable, constructing a Bayesian framework with layered prior to obtain a joint probability density function: fixing other variables and super parameters, and calculating mathematical expectations about posterior probability of the input variables; And obtaining the optimal estimation of the input variable and the super-parameters by maximizing the posterior probability.
8. The method for estimating the DOA of the programmable subsurface two-dimensional off-grid based on sparse Bayesian learning according to claim 7, wherein the Bayesian framework construction process comprises: Assuming that the measured noise is complex gaussian white noise, a likelihood estimate is obtained: ; Wherein, the In the sparse form of the rows of the incident signal matrix, Y is a two-dimensional off-grid sparse model, , In order to be an off-grid error, For the purpose of the noise energy estimation, Is that Is used for the matrix of units of (a), Is the inverse of the noise energy estimate, In the form of a vector matrix, 、 Respectively being the T column of X, Y matrix, T being the number of snapshot cycles; The gaussian prior of the incident signal variable is: ; Wherein, the , Is the variance vector of the incident signal variable X, R represents the real set, , In the form of a grid number, Is a 0 vector of length P, Representing a transpose of the matrix; gamma a priori is expressed as: ; ; wherein ρ is a super-parameter, Representing gamma distribution with shape parameter a and scale parameter b , Representing gamma distribution with shape parameter 1 and scale parameter ρ ; Assume that the off-grid error obeys a uniform prior: wherein r is a grid interval; the posterior probability of the incident signal variable obeys a multi-element complex gaussian distribution: ; Wherein, the , ; Integrating each stage of the layered Bayesian framework to obtain a joint probability density function: ; Wherein Z is the expansion of X at X 0 .
9. The method for estimating the DOA of the programmable subsurface two-dimensional off-grid based on sparse Bayesian learning according to claim 8, wherein the mathematical expectation for calculating the posterior probability of the input variable is: ; ; ; wherein T is a middle diagonal matrix, Is a vector matrix Is a complex matrix of the matrix.
10. The method for estimating the DOA on the two-dimensional off-grid of the programmable subsurface based on sparse Bayesian learning as recited in claim 9, wherein the process of obtaining the optimal estimate of the input variable and the super-parameters by maximizing the posterior probability comprises the steps of: Independent super-parameter variables are integrated into constants, derivatives of the super-parameter variables are solved, and extreme points of the super-parameters are calculated: ; wherein T is the number of snapshot cycles, Representing the transpose of the matrix, L being the number of encoding matrices, In order to take the F-norm operation, For row p of matrix U, 1 P 、1 L are all 1 vectors of length P, L, 、 Respectively as a matrix 、 Is used to determine the conjugate transpose of (a), 、 The conjugate transpose of matrix U, Z, Z is a variable introduced, and is the expansion of X; and reversely calculating DOA estimated values based on each super-parameter extreme point.

Description

Programmable super-surface two-dimensional off-grid DOA estimation based on sparse Bayesian learning Technical Field The application relates to the technical field of signal processing, in particular to a programmable super-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning. Background Angle of arrival (DOA) estimation is a core technology in the fields of radar, sonar, navigation, etc. The appearance of programmable supersurfaces provides a new path for DOA estimation, and electromagnetic properties can be dynamically regulated in real time by integrating active elements such as PIN diodes into the superatoms. The DOA estimation method has the advantages of simple process, small section, low cost and high integration level, can finish DOA estimation by a single-channel architecture, effectively overcomes the defects of the traditional technology, and has great application potential in the fields of vehicle driving navigation, unmanned aerial vehicle information transmission and the like. Sparse signal recovery algorithm based on compressed sensing theory provides algorithm support for ultra-surface DOA estimation, and orthogonal matching pursuit, iterative soft threshold algorithm and the like are widely applied. However, the prior algorithm needs to perform discretization processing on the spatial domain, and inevitably has the problem of grid mismatch, namely, the space grid gap between the discrete grid and the real incidence angle of the signal can generate quantization error, and the estimation performance is seriously affected. Although error correction algorithms such as off-grid sparse Bayesian inference (OGSBI) and the like are developed in the traditional phased array system, the algorithms cannot be directly sleeved on the programmable super-surface based on the design of a phased array data measurement model. Therefore, the off-grid observation model adapting to the programmable subsurface is established, a targeted error correction scheme is developed, the key for improving the DOA estimation actual performance of the programmable subsurface is provided, and the method has important significance for promoting the industrialized application of the programmable subsurface in the DOA estimation field. Disclosure of Invention In view of the above, the application provides a programmable super-surface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning, which can improve DOA estimation accuracy and has lower calculation time consumption. In order to achieve the above object, the following schemes are proposed: the programmable subsurface two-dimensional off-grid DOA estimation method based on sparse Bayesian learning comprises the following steps: Establishing a DOA estimation mathematical model according to a data measurement mechanism of the programmable subsurface; Converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model by utilizing Newton binomial expansion and two-dimensional linear Taylor expansion; and carrying out Bayesian inference on the two-dimensional off-grid sparse model by adopting a expectation maximization technology through the sparse Bayesian probability model to obtain the estimated value of the DOA. According to the specific embodiment provided by the application, the application discloses the following technical effects: The application provides a sparse Bayesian learning-based programmable hypersurface two-dimensional off-grid DOA estimation method, which is characterized by establishing a DOA estimation mathematical model according to a data measurement mechanism of a programmable hypersurface, converting the DOA estimation mathematical model into a two-dimensional off-grid sparse model by utilizing Newton binomial expansion and two-dimensional linear Taylor expansion, and carrying out Bayesian inference on the two-dimensional off-grid sparse model by adopting a desired maximization technology through a sparse Bayesian probability model to obtain a predicted value of the DOA. According to the method, the DOA estimation problem is equivalent to the off-grid Sparse Signal Recovery (SSR) problem through the derived two-dimensional off-grid sparse model, and the Sparse Bayesian Learning (SBL) is adopted for solving. And the Bayesian probability model is constructed according to the SBL basic framework, and iteration is carried out through Bayesian inference, so that DOA estimation efficiency and accuracy are greatly improved. Drawings In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present application, and that other drawings can be obtained according to the provided drawings withou