Robust estimation of DOA from array data at low SNR

Abstract

We consider direction of arrival (DOA) estimation for a plane wave hidden in additive circularly symmetric noise at low signal to noise ratio. Starting point is the maximum-likelihood DOA estimator for a deterministic signal carried by a plane wave in noise with a Laplace-like distribution. This leads to the formulation of a DOA estimator based on the Least Absolute Deviation (LAD) criterion. The phase-only beamformer (which ignores the magnitude of the observed array data) turns out to be an approximation to the LAD-based DOA estimator. We show that the phase-only beamformer is a well performing DOA estimator at low SNR for additive homoscedastic and heteroscedastic Gaussian noise, as well as Laplace-like noise. We compare the root mean squared error of several different DOA estimators versus SNR in a simulation study: the conventional beamformer, the phase-only beamformer, and the weighted phase-only beamformer. The simulations indicate that the phase-only DOA estimator has desirable properties when the additive noise deviates from the Laplace-like assumption. The qualitative robustness of these DOA estimators is investigated by comparing the empirical influence functions. Finally, the estimators are applied to passive sonar measurements acquired with a horizontal array in the Baltic Sea.