Passive localization of acoustic sources is treated within a geometric framework where non-Euclidean distance measures are computed between a cross-spectral density estimate of received data on a vertical array and a set of stochastic replica steering matrices, rather than traditional replica steering vectors. A processing scheme involving matrix-matrix comparisons where steering matrices, as functions of the replica source coordinates, naturally incorporate environmental variability or uncertainty provides a general framework for considering the acoustic inverse source problem in an ocean waveguide. Within this context a subset of matched-field processors is examined, based on recent advances in the application of non-Euclidean geometry to statistical classification of data feature clusters. The matrices are interpreted abstractly as points in a Riemannian manifold, and an appropriately defined distance measure between pairs of matrices on this manifold defines a matched-field processor for estimating source location. Acoustic simulations are performed for a waveguide comprising both a depth-dependent sound-speed profile perturbed by linear internal gravity waves and a depth-correlated surface noise field, providing an example of the viability of this approach to passive source localization in the presence of sound-speed variability.
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