Expected likelihood support for deterministic maximum likelihood DOA estimation

In this paper, the “expected likelihood” approach, previously introduced for the stochastic (unconditional) Gaussian case, is extended over the so-called deterministic (conditional) Gaussian case. Direction of arrival (DOA) estimation when arbitrary temporally correlated waveforms transmitted by point sources of interest impinge onto a uniformly spaced linear array is examined. Specifically, we introduce a normalized likelihood ratio that for the true DOAs have p.d.fs that (for practical purposes) have weak enough dependence on these DOAs to be used in the expected likelihood approach. The utility of this approach is demonstrated by examples on DOA estimation in the so-called “threshold” region.