Maximum-likelihood wideband direction-of-arrival estimation

The specific problem that was addressed is one in which there is limited data in both the temporal and spatial dimensions, so that one cannot assume the use of ordinary Fourier transforms on the time domain outputs of each sensor. Rather, zero-mean Gaussian statistics were assumed, and the likelihood of the observed data was directly maximized with respect to the parameters which enter into the covariance matrix of the multivariate distribution. Two models were pursued. The first is a parametric model in which it is assumed that there are a fixed number of independent, wide-sense-stationary, plane-wave signals. The second model is one in which there is energy impinging upon the array from a spatial continuum. EM (expectation-maximization) algorithms appropriate for these two problems were derived