Research On DOA Estimation Methods Based On Low Rank Recovery And Sparse Reconstruction

The Direction of Arrival?DOA?is estimated to be one of the research hotspots in the field of array signal processing.It has a wide range of applications in radar,sonar,navigation,wireless communication,speech processing,and radio astronomy.At present,most of the conventional high-resolution subspace-based and sparse reconstruction-based DOA estimation algorithms are based on Gaussian white noise whose background noise is known statistically,the sampling covariance matrix is known,and the spatial source is exactly in the pre-divided space on the grid.However,in practical applications,due to the limited number of sampling times and the preset discrete grid points,it is impossible to know the sampling covariance matrix,and the source azimuth may not completely fall on the preset finite search grid.Such problems will As a result,the performance of the algorithm decreases or even fails,which limits the practical application of various DOA estimation algorithms.Aiming at the existing problems,this article studies the DOA estimation method under different conditions.The specific content is as follows:1.Focusing on the problem of rather large estimation error in the traditional Direction of Arrival?DOA?estimation algorithm induced by finite subsampling,a robust DOA estimation method based on low rank recovery is proposed in this paper.Following the low-rank matrix decomposition method,the received signal covariance matrix is firstly modeled as the sum of the low-rank noise-free covariance matrix and sparse noise covariance one.After that,the convex optimization problem associated with the signal and noise covariance matrix is constructed on the basis of the low rank recovery theory.Subsequently,a convex model of the estimation error of the sampling covariance matrix can be formulated,and this convex set is explicitly included into the convex optimization problem to improve the estimation performance of signal covariance matrix such that the estimation accuracy and robustness of DOA can be enhanced.Finally,with the obtained optimal noiseless covariance matrix,the DOA estimation can be implemented by employing the Minimum Variance Distortionless Response?MVDR?method.In addition,exploiting the statistical characteristics of the sampling covariance matrix estimation error subjecting to the asymptotic normal distribution,an error parameter factor selection criterion is deduced to reconstruct the noise-free covariance matrix preferably.Compared with the traditional Conventional BeamForming?CBF?,Minimum Variance Distortionless Response?MVDR?,MUltiple SIgnal Classification?MUSIC?and Sparse and Low-rank Decomposition based Augmented Lagrange Multiplier?SLD-ALM?algorithms,numerical simulations show that the proposed algorithm has higher DOA estimation accuracy and better robustness performance under finite sampling snapshot.2.Focusing on the problem of large estimation error caused by traditional DOA estimation algorithm due to grid mismatch in sparse reconstruction method,a discrete-off-grid DOA estimation method based on covariance matrix reconstruction is proposed.First,construct a spatial discrete grid,model the offset between the actual DOA and the grid points into the off-grid model,and build a uniform linear array receiving data model;then construct a sparse reconstruction based on the covariance matrix reconstruction method Convex optimization problem of signal;construct a convex model about sampling covariance matrix estimation error,and include this convex set into the convex optimization problem to improve the performance of sparse signal reconstruction and DOA estimation accuracy.Finally,a stepwise iterative method is used.Solve sparse signals and grid offset parameters to achieve DOA estimation.Numerical simulations show that,compared with the traditional conventional MUltiple SIgnal Classification?MUSIC?,l₁-SVD,Sparse and Low-Rank Decomposition based Robust MVDR?SLRD-RMVDR?,the proposed algorithm has higher angular resolution and DOA estimation accuracy.