Adaptive minimax robust M-beamforming for multiple moving sources and impulse noise

The windowed multiple source M-beamforming and M-estimates of the direction-of-arrival (DOA) are developed for source visualization and nonparametric high-resolution tracking of rapidly moving sources. These M-beamforming and M-estimates are robust with respect to impulse random errors having a unknown heavy-tailed distribution. The beamforming and estimates are defined by minimizing a nonquadratic residual loss function derived from the Huber minimax robust estimation theory. Based on the linear local polynomial approximation (LPA) of DOA the method gives estimates of instantaneous values of the directions as well as their first derivatives. Marginal beamformers are proposed for estimation and moving source visualization in two-dimensional space θ-θ. These marginal beamformers are able to localize and track every source individually nulling signals from all other moving sources. Recursive implementation of estimation algorithms are developed