A Novel Subspace Fitting Method for DOA Estimation Based on Bayesian Compressive Sensing

The application of conventional Weighted Subspace Fitting (WSF) algorithm, which involves multidimensional nonlinear optimization, is limited for its huge computational burden and difficult initial parameter setting. Combing compressive sensing theory, a novel WSF algorithm for narrowband DOA estimation based on modified Bayesian Compressive Sensing (BCS) is proposed in this paper. The Projection Approximation Subspace Tracking deflation (PASTd) algorithm is utilized to efficiently estimate both the signal eigenvalues and corresponding eigenvectors, which significantly reducing the computation burden compares to the singular value decomposition of the sample covariance matrix. Exploiting the prior knowledge of spatial sparsity, we reformulate the WSF to a sparse signal reconstruct problem in the context of the multiple measurement vectors. Furthermore, a basis pruning mechanism via iterative relative thresholding is presented to speed up the convergence rate and avoid the matrix singular drawback during the original BCS iteration. Computer simulation results are presented and analyzed, demonstrating a number of advantages of the proposed method, including increased spatial resolution with low SNR and limited number of snapshots compared with MUSIC and l1SVD, improved robustness to the source number estimation error and can be directly applied to the scenarios where highly correlated or coherent sources are presented without any preprocessing.