On DOA estimation in unknown colored noise-fields using an imperfect estimate of the noise covariance

Most algorithms for direction-of-arrival (DOA) estimation require the noise covariance matrix to be known or to possess a known structure. In many cases the noise covariance is in fact estimated from separate measurements. This paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present. It is assumed that a batch of signal-free samples is available in addition to the signal-containing samples. No assumption is made on the structure of the noise covariance. In this work the asymptotical covariance of weighted subspace fitting (WSF) is derived for the case when the data are whitened using an estimated noise covariance. The obtained expression suggests an optimal weighting that improves performance compared to the standard choice. In addition, a new method based on covariance matching is proposed. The proposed method is by construction asymptotically efficient. Monte Carlo simulations show promising small sample performance for the two new methods and confirm the asymptotical results. The CRB for the data model is included in the numerical evaluations and it is found to coincide with the WSF asymptotical covariance derived.