High resolution bearing estimation without eigen decomposition

Abstract

We consider the bearing estimation problem as a matrix approximation problem. The columns of a matrix X are embedded with the snapshot vectors from an N element array. The matrix X is approximated by a matrix X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</inf> in the least square sense. The rank, as well as the structure of the space spanned by columns of X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</inf> , are prespecified. After X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</inf> is computed, the bearings of the sources, the spatial correlation of the source signals can be estimated. Our technique is then compared with other methods such as MUSIC and SVD processing. When the number of snapshot vectors available for processing is large a simpler adaptive algorithm is suggested.