Decentralization of the Gaussian maximum likelihood estimator and its applications to passive array processing

In radar and sonar the trajectory of a radiating source can be estimated by measuring the relative travel time of the signal to several spatially separated receivers. A minimum variance estimate is achieved by simultaneous coherent processing of all receiver outputs. A considerable simplification in estimator structure, and therefore in processor complexity, is obtained by pairwise processing of the receiver outputs. In this paper we determine the performance degradation incurred by decoupling the estimation procedure in such a fashion. We show that if the individual in-band signal-to-noise ratio at each receiver output is much greater than unity, pairwise processing is nearly optimal. If the individual in-band signal-to-noise ratio falls below unity, but the post-beam-forming signal-to-noise ratio (i.e., the product of the individual signal-to-noise ratio and the number of receivers) is large, simultaneous coherent processing yields a level of performance equal to that of pairwise processing with unit signal-to-noise ratio. If the post-beam-forming signal-to-noise ratio does not exceed unity even in the signal frequency band, pairwise processing seriously degrades performance. Finally, we note that decentralizing estimator structure is a powerful technique that may be used to simplify processor complexity whenever large data vectors and/or large parameter sets must be processed.