Fast sequential source localization using the Projected Companion Matrix approach

The sequential forms of the spectral MUSIC algorithm, such as the sequential MUSIC (S-MUSIC) and the recursively applied and projected MUSIC (RAP-MUSIC) algorithms, use the previously estimated DOA (direction of arrival) to form an intermediate array gain matrix and project both the array manifold and the signal subspace estimate into its orthogonal complement. By doing this, these methods avoid the delicate search of multiple maxima and yield a more accurate DOA estimation in difficult scenarios. However, these high-resolution algorithms adapted to a general array geometry suffer from a high computational cost. On the other hand, for linear equispaced sensor array, the root-MUSIC algorithm is a fast and accurate high-resolution scheme which also avoids the delicate search of multiple maxima but a sequential scheme based on the root-MUSIC algorithm does not exist. This paper fills this need. Thus, we present a new sequential high-resolution estimation method, called the Projected Companion Matrix MUSIC (PCM-MUSIC) method, in the context of source localisation in the case of linear equispaced sensor array. Remark that the proposed algorithm can be used without modification in the context of spectral analysis.