Environmentally and statistically robust matched-field source localization based on information geometry principles

Matched-field processing (MFP) achieves underwater source localization by measuring the correlation between the array and replica signals, with traditional MFP being equivalent to estimating the Euclidean distance between the data cross-spectral density matrix (CSDM) and replica matrices. However, in practical applications, random inhomogeneities in the marine environment and inaccurate estimation of CSDM reduce MFP performance. The traditional minimum variance matched-field processor with environmental perturbation constraints perturbs a priori environment parameters to obtain linear constraints and yields the optimal weight vectors as the replica vectors. In this paper, within the framework of information geometry, the geometric properties of CSDMs as semi-positive definite and Hermitian enable CSDMs to be described as points in a Riemannian manifold. Source localization can be achieved by quantifying the similarity between the CSDMs as the geodesic distance between the points on the manifold. This paper introduces a constrained replica CSDM composed of perturbed replica vectors and proposes a robust matched-field processor based on two non-Euclidean distances: the Riemannian distance and the modified Jensen-Shannon distance. Simulations and experimental results demonstrate that the proposed processors are more robust against environmental and statistical mismatches than traditional processors and can also reduce sidelobe level and improve the resolution.