Multi-rank processing for passive ranging in underwater acoustic environments subject to spatial coherence loss

In this work we derive the maximum likelihood estimator for passive wavefront curvature ranging systems operating in environments subject to a spatial coherence loss. As a consequence of the spatial coherence loss, the optimum processor is no longer a rank-1 matched filter and now instead involves a multi-rank weighted combination of the data based on the coherence matrix eigenvectors and eigenvalues. We also establish an interesting connection of our proposed multi-rank processor to the conventional rank-1 processor, and to the non-coherence sub-array processor, under different operating conditions. A comparative study is carried out in evaluating the performance of the proposed processors.