Estimation of directions of arrival of multiple distributed sources for nested array

We consider the problem of estimating the nominal directions of arrival (DOA) of multiple distributed sources using nested array. In practical applications, angular spread of distributed source arises due to the multipath propagation and local scattering around the vicinity of a source. DOA estimation methods based on point-source assumption are known to severely degrade in the presence of the angular spread. To solve this problem, we develop a distributed source model based approach for a nested array. Based on the concept of difference co-array, redundancy averaging technique is applied to the sample covariance matrix. By exploiting the annihilating property of the redundancy averaged terms, an efficient method based on annihilating filter (AF) is proposed. This method can be applied to the case of more sources compared with the actual physical sensors without a priori knowledge of the spreading parameters. Whereas the sample covariance matrix is corrupted by either noise or estimation error due to finite snapshots, so an AF method with structured low rank approximation (SLRA) is further proposed, which results in a better estimate. Finally, numerical simulations demonstrate the effectiveness of the proposed methods.