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Range-coherent matched field processing (MFP) coherently combines snapshots to localize a moving, narrowband source. This approach differs from existing MFP approaches that treat each snapshot as having a random phase due to both unknown motion through the medium and imprecise knowledge of the source frequency. Range-coherent MFP requires determination of the source phase acquired between snapshots. With that information, MFP can be applied to the cross-spectrum of snapshots acquired at different times, since relative phase between snaps