Sensitivity of TLS and minimum norm methods of DOA estimation to errors due to either finite data or sensor gain and phase perturbations

Abstract

In the DOA (direction of arrival) estimation problem, we encounter either finite data or insufficient knowledge in array characterisation or both. It is therefore important to study how the subspace-based methods perform under these conditions. In this paper, we first consider the finite data case and establish two results: (i) the total least-squares approach to the linear prediction method (which we refer to as TLS-FLP method) is equivalent to the minimum norm (min. norm), method and (ii) the TLS-FBLP method yields a 3 dB lower mean-square error (mse) in the DOA estimates as compared to the TLS-FLP method. Next, we consider the asymptotic performance of the min. norm method in the presence of sensor gain and phase perturbations, and derive the expressions for themse in the DOA estimates assuming an uniform linear array. For the special case of a single source, we also obtain a simple and explicit expression for themse which, when compared with the corresponding result for the music algorithm, shows that the min. norm method is more sensitive than the music when the number of sensors exceeds 2. Computer simulations are included to support the the oretical predictions.