CN-115754896-B - Direction of arrival estimation method based on variable-fraction reasoning robust sparse Bayesian learning

Abstract

The invention provides a direction of arrival estimation method based on novel robust sparse Bayesian learning. The invention relates to a traditional sparse Bayesian learning method based on Gaussian noise assumption, which is characterized in that the performance of the traditional sparse Bayesian learning method is deteriorated in an impact noise environment, the problem of estimating the direction of arrival in array signal processing is converted into the problem of sparse reconstruction, a perception matrix formed by an array observation vector and an array guide vector is input, parameters are initialized, posterior distribution of the parameters and sparse signals is subjected to iterative updating, finally, the posterior approximation expectation of the sparse signals is taken as a reconstruction result of the posterior approximation of the sparse signals, and the result of estimating the direction of arrival is obtained according to a support set of the reconstructed sparse signals, wherein a robust sparse Bayesian learning algorithm of variational reasoning is designed, and the reconstruction and the result of estimating the direction of arrival with higher precision in a non-Gaussian noise environment are obtained through reasoning approximate posterior distribution. The invention has more robust estimation performance in the impact noise environment.

Inventors

• Rong Jiarui
• ZHANG JINGSHU
• DUAN HUIPING

Assignees

• 电子科技大学

Dates

Publication Date

20260505

Application Date

20221118

Claims (1)

1. 1. The DOA estimation method based on the variable-fraction reasoning robust sparse Bayesian learning is characterized by comprising the following steps: The input step comprises inputting a perception matrix A formed by an array observation vector y and an array guiding vector, determining the total number N of directions of arrival, the total number M of arrays and a direction of arrival set The method comprises the steps of initializing, namely, iteration times L, iteration threshold epsilon, super parameters alpha, beta 1 、β 2 、z、a、b、c 1 、d 1 、c 2 、d 2 , e and f, wherein alpha is the inverse variance of a support set estimated by the direction of arrival, each element of alpha is subjected to gamma distribution, z is a mark vector of whether an observed value is influenced by impact noise, each element of z is subjected to Bernoulli distribution, beta 1 is the accuracy of a conditional likelihood function of an array observed vector which is not influenced by the impact noise, beta 2 is the accuracy of a likelihood function of array observed data influenced by noise, and a, b, c 1 、d 1 、c 2 、d 2 , e and f are parameters used for iteratively updating posterior distribution of sparse signals; the iteration step is to update the posterior distribution of the super parameter and the sparse signal in an iteration way, and the iteration step is as follows: (1) Calculating sparse signals phi x ＝(A T DA+D α ) -1 by using the perception matrix A, the currently updated sign vector z and the inverse variance alpha of the support set of the direction of arrival estimation, wherein T represents matrix transposition, the matrix D＝<β 1 >D z +<β 2 >D 1-z ,D z ＝diag(<z>),D 1-z ＝I-D z ,diag represents extraction of diagonal matrix, and (a) represents an estimated value, D α =diag (< alpha >); (2) Calculating a reconstruction vector update value mu x ＝Φ x A T D y by using a sparse signal phi x , a perception matrix A and an array observation vector y, and updating a reconstruction vector x new estimated by the latest direction of arrival to mu x , wherein the reconstruction vector estimated by the direction of arrival updated last time is x old ; (3) Updating the estimated value corresponding to each element in alpha The direction of arrival number n=1, N; wherein the intermediate value X n is the nth element of the support set x of the direction of arrival estimation, x=x new ,Φ( n , n) is the nth row and column element of the sparse signal Φ x ; (4) Updating an estimate of beta 1 Wherein the intermediate value 〈(y-Ax) T D z (y-Ax)〉＝(y-Aμ x ) T D z (y-Aμ x )+tr(A T D z AΦ x )、 Tr denotes the trace of the matrix, m is the array number, z m is the mth element of the flag vector z; (5) Updating an estimate of beta 2 Wherein the intermediate value 〈(y-Ax) T D 1-z (y-Az)〉＝(y-Aμ x ) T D z (y-Aμ x )+tr(A T D z AΦ x )、 (6) Updating the estimated value for each element in z Where p is the probability density function ,p(z m ＝1)＝Cexp[-0.5<β 1 ><(y m -a m x) 2 >+<lnπ m >],π m , the m-th element of the probability pi for different noise distributions, a m is the m-th row ;p(z m ＝0)＝Cexp[-0.5<β 2 ><(y m -a m x) 2 >+<ln(1-π m )>],C of the array steering vector matrix A, is a constant, Y m is the m-th element of the array observation vector y; (7) Calculating an I x new -x old || 2 , if the I x new -x old || 2 is less than or equal to epsilon or the current iteration number k=L, entering a lower output step, if the I x new -x old || 2 is epsilon and k < L, updating the value of x old to x new , and returning to the step 1; The output step is that the binarization vector is obtained through the threshold processing of x new , so as to obtain the estimated support set I of the direction of arrival, and the angle of the direction of arrival set p corresponding to each element in the I is used for forming the estimated vector of the direction of arrival And output.

Description

Direction of arrival estimation method based on variable-fraction reasoning robust sparse Bayesian learning Technical Field The invention relates to an array signal processing technology, in particular to a direction of arrival estimation technology for communication, radar and other systems in an impact noise environment. Technical Field Direction of arrival estimation is an important research topic in the field of array signal processing, and is widely focused and intensively studied in the fields of radar, communication and the like. In order to avoid the main defects of the traditional subspace method in the aspects of sampling quantity, coherent information sources and the like, researches on a direction-of-arrival estimation method based on sparse reconstruction have been developed gradually. The existing sparse reconstruction algorithm can better process Gaussian noise, but impact noise has a characteristic of obvious energy in a short time, and global influence on an observed value can be caused under a traditional compressed sensing frame, so that the reconstruction effect of the traditional sparse reconstruction algorithm is poor. The robust algorithm based on the traditional sparse Bayesian learning framework assumes that all observed values are affected by impact noise, but in an actual environment, the impact noise tends to have a short duration and only affects part of the observed values. The robust sparse Bayesian learning algorithm based on variational reasoning is used for indicating whether an observed value is influenced by impact noise or not by setting a flag variable, and further different conditional distribution models are established for different types of measured data, wherein the BP-RBCS (Beta-Bernoulli Prior model-based Robust Bayesian Compressed Sensing) eliminates the identified abnormal value from the observed vector, the model is simpler, but partial observed data ,Q.Wan,H.P.Duan,J.Fang,H.B.Li,Z.L.Xing.Robust Bayesian compressed sensing with outliers[J].Signal Processing,2017,5(17):104-109.;Mix-RSBL algorithm (Robust Sparse Bayesian Learning using Mixture model) is lost, the prior probability distribution assumption is carried out on the impact component in the noise, the observed data influenced by the impact noise is identified and processed, and then the observed data is applied to reconstruction and estimation, so that the observed data is utilized more fully, the estimation accuracy is improved, the resource waste is avoided, but the number of parameters needing to be updated is greatly increased, and therefore, the calculated amount is larger ,R.Zheng,X.Xu,Z.F.Ye,et al.Robust sparse Bayesian learning for DOA estimation in impulsive noise environments[J].Signal Processing,2020,171(5):1-6. Disclosure of Invention The invention aims to solve the technical problem of providing a method for estimating the direction of arrival by obtaining a sparse reconstruction result with higher precision under the condition of no obvious increase of calculated amount under the influence of impact noise. The invention adopts the technical scheme that the method for estimating the direction of arrival based on the variational reasoning robust sparse Bayesian learning comprises the following steps: 1. the DOA estimation method based on the variable-fraction reasoning robust sparse Bayesian learning is characterized by comprising the following steps: The input step comprises inputting a perception matrix A formed by an array observation vector y and an array guiding vector, determining the total number N of directions of arrival, the total number M of arrays and a direction of arrival set The method comprises the steps of initializing, namely, iteration times L, iteration threshold epsilon, super parameters alpha, beta 1、β2、z、a、b、c1、d1、c2、d2, e and f, wherein alpha is the reciprocal variance of a support set estimated by the direction of arrival, each element of alpha is subjected to gamma distribution, z is a mark vector of whether an observed value is influenced by impact noise, each element of z is subjected to Bernoulli distribution, beta 1 is the reciprocal variance of a conditional likelihood function of an array observed vector which is not influenced by the impact noise, beta 2 is the reciprocal variance of a likelihood function of array observed data influenced by noise, and a, b, c 1、d1、c2、d2, e and f are parameters used for iteratively updating posterior distribution of sparse signals; the iteration step is to update the posterior distribution of the super parameter and the sparse signal in an iteration way, and the iteration step is as follows: (1) Calculating a covariance matrix phi x＝(ATDA+Dα)-1;T of the sparse signal by using the perception matrix A, the currently updated sign vector z and the inverse variance alpha of the support set of the direction of arrival estimation to represent a matrix transpose, wherein the matrix D＝<β1>Dz+<β2>D1-z,Dz＝diag(<z>),D1-z＝I-Dz,diag repres