Geometry-Constrained Joint Multipath Exploitation for Single-Transceiver Underwater Acoustic Localization

Boundary reflections are usually treated as interference in underwater acoustic localization, yet their position-dependent delays can form a virtual aperture for a single transceiver. This paper develops a geometry-constrained method for exploiting that information without calibrated reflection amplitudes or phases. Reciprocal direct, surface, and bottom echoes are described by image-source delays, while their complex gains remain nuisance parameters. Variable projection yields a position-dependent joint multipath exploitation (JME) objective. The equivalent Fisher information relates local accuracy to bandwidth, path energy, resolvability, and delay-gradient geometry. Grid-search initialization (GSI) and delay-geometric initialization (DGI) feed a common safeguarded Newton-like refinement (JME-NR). Simulations include a coherent matched-field processing baseline and environmental mismatch tests. Among the JME routes, GSI is more reliable at very low signal-to-noise ratio (SNR), whereas DGI becomes more effective with reliable delay extraction and path association. For a fixed target at 0dB, GSI-JME-NR achieves an all-trial root-mean-square error (RMSE) of 0.128m, close to the exact position error bound of 0.127m. In finite-tank tests with a separated transmitter and receiver, three two-dimensional configurations with 20 measurements each yield refined RMSEs of 11.14–39.76mm relative to the target’s geometric center. Three-dimensional tests show that improved waveform fitting does not necessarily reduce the error relative to this center.