Space-time processing of multisensor time delay data in bearing estimation

The present paper derives the statistical measures on the bearing estimates (bias, variance, Cramer-Rao Bound) for unequally separated clusters of hydrophones and also unequal variances on the time delay estimates. The present results reduce to those found in the literature for direction finding systems that presume equally separated clusters of hydrophones and equal time delay variances. The derivation takes into account those differences in spatial and temporal characteristics in the direction finding system to design an optimum weighting filter. When applied, the filter is shown to lead to improved direction finding estimates through reduction of both bias and variance. The relative influence of the various approaches on the quality of the bearing estimates is identified. Finally, it is shown that merging without weighting of the available time delay data may deteriorate the bearing estimate instead of improving it.