Correlation-based passive localization: Linear system modeling and sparsity-aware optimization

In underwater passive localization, matched field processing has faced mismatch challenges for many years. To overcome the mismatch, data-derived replicas have gained increasing popularity due to their better localization performance than parameter-based ones, among which the cross correlation–based replicas showed enhanced robustness against the spectral differences between the library and target vessels. However, cross correlation–based matching localizations result in high sidelobes and require enough frequency samples to eliminate grating lobes. This issue has been widely reported in the previous literature but has yet to be theoretically analyzed. In this work, we revisit the conventional correlation-based matching procedures and formulate the ambiguity surface as a least-norm solution of an underdetermined linear system. This formulation permits understanding the sidelobes from an optimization perspective. Based on this view, the high sidelobe challenge and requirement of measurements are systematically tackled by recasting the matching problem as a sparsity-aware optimization problem. The superiority of the proposed optimization approach is showcased through simulated data in the waveguide, microphone data in the air, and SWellEx-96 data. The linear system modeling is also extended to a distributed sensor network, profiting from the spatial gain brought by various azimuthal directions with respect to the source.