Research On DOA Estimation Based On Low-rank Matrix Reconstruction Theory

Direction of arrival(DOA)estimation is a significant investigation topic at array signal processing.Its main principle is that the direction of the source of interest can be estimated according to the observed signal and the array manifold of the corresponding array.Generally speaking,the covariance matrix of noiseless observation incoming wave is a low rank matrix.Because the rank of the source matrix is the number of sources,and the array manifold matrix is a full rank matrix.When calculating the covariance matrix,we get it by the product of the array manifold matrix,the source matrix and the conjugate transpose of the array manifold matrix.Therefore,the rank of covariance matrix is still the same as that of source matrix,that is,the number of sources is also the same.However,in some real scenes,different signal models,noise models and array models will destory the ideal circumstance.The covariance matrix of incoming wave is no longer a low rank matrix at above condition.If we decompose the covariance matrix into the noise subspace and the signal subspace,the covariance is a full rank matrix and the minimum eigenvalue is not zero at all,so we can not distinguish the two subspaces accurately.By doing so,the capability of the traditional subspace based DOA estimation method is significantly degraded.For the sake of deal with these issues,this article puts forward several low rank matrix fill methods to recover the low rank characteristic of observed matrix,so as to improve the DOA estimation performance in different scenarios.The principal details and novelty of this article can be seen as:(1)This paper presents a method of DOA estimation for coprime array in coherent source based on low rank matrix reconsitution.For the sake of deal with the issue that the traditional coprime array direction finding algorithm can not validly find direction when the sources are correlated to each other,the higher dimension covariance matrix is structured by array interpolation method,and the corresponding Toeplitz matrix is constructed by using the relevant information of the matrix.Then,this algorithm is used to restore the constructed Toeplitz matrix.The reconstructed matrix has the property of decoherence,so as to realize the DOA estimation of sparse matrix under coherent source.(2)Two methods based on low rank matrix reconstruction are put forward to enhance the DOA estimation capability of differential virtual array at high SNR.For the sake of deal with the issue that the capability of DOA estimation of difference coarray tends to be flat at high SNR region,the expression of the second-order statistics is acquired via inferring the distribution of the calculation bias of the augmented covariance matrix of coarray.On the one hand,combining the corresponding relationship between the augmented covariance matrix and the interpolation augmented covariance matrix,we can construct the corresponding low rank matrix reconstruction problem;on the other hand,we can use the cost function of covariance fitting to construct the optimization problem.The estimation performance of the reconstructed matrix at high SNR is significantly improved compared with the previous methods.(3)A low rank matrix reconsitution based direction finding algorithm for coprime array in non-uniform noise is come up with.For the sake of deal with the issue of poor capability of the previous coprime array DOA estimation in non-uniform noise,the linear prediction method and low rank matrix reconsitution method are combined to reconstruct the matrix of the linear prediction model by using low rank matrix reconstruction method,so as to restore the value of the diagonal elements of the augmented covariance matrix and the zero value caused by interpolation,and enhance the capability of coprime array direction finding in non-uniform noise.