Multi-sensor signal processing on a PSD matrix manifold

We propose to use the power spectral density (PSD) matrices of the received signals of a multi-sensor system as the feature of processing. PSD matrices have structural constraints and they form a manifold in signal space. We introduce two new Riemannian distance (RD) measures on the PSD matrix manifold and developed algorithms to locate the means and medians of PSD matrices in terms of these RD. These concepts are then applied to the detection of narrow-band sonar signals in noise and the results are encouraging.