Minimax robust M-beamforming for moving sources and impulse noise environment

The minimax robust M — beamforming is developed for complex-valued array observations (snapshots) contaminated by impulse random errors having an unknown heavy-tailed error distribution. The beamformer as a robust estimator of the time-varying direction of arrival (DOA) and the waveform signal (envelope) is defined by minimizing a nonquadratic loss function of residuals. A tracking ability of the estimates is assured by using the local polynomial approximation (LPA) model of a source movement and a sliding window of observations. A proposed new beamformer has a two-dimensional power function. Maximum peaks of this power function are used for source separation and estimation of DOAs, their first derivatives and waveform signal. The asymptotic variance and bias of these estimates are obtained for a wide class of loss functions and probability distributions of the noise. These results justify using the minimax Huber's estimation theory for a selection of the loss function of the M — beamforming loss functions.