Subspace-based adaptive method for estimating direction-of-arrival with luenberger observer

In this paper, we propose a computationally simple and efficient subspace-based adaptive method for estimating directions-of-arrival (AMEND) for multiple coherent narrowband signals impinging on a uniform linear array (ULA), where the previously proposed QR-based method is modified for the number determination, a new recursive least-squares (RLS) algorithm is proposed for null space updating, and a dynamic model and the Luenberger state observer are employed to solve the estimate association of directions automatically. The statistical performance of the RLS algorithm in stationary environment is analyzed in the mean and mean-squares senses, and the mean-square-error (MSE) and mean-square derivation (MSD) learning curves are derived explicitly. Furthermore, an analytical study of the RLS algorithm is carried out to quantitatively compare the performance between the RLS and least-mean-square (LMS) algorithms in the steady-state. The theoretical analyses and effectiveness of the proposed RLS algorithm are substantiated through numerical examples.