Physics-guided Bayesian matrix completion of replica libraries for underwater source localization

For matched field localization using ship radiated noise as sources of opportunity, replica libraries are often incomplete because vessel trajectories cannot fully cover the observation region. The completion problem can be formulated as recovering missing replica entries from partial observations, for which Bayesian matrix completion methods provide a probabilistic framework. However, the relatively high effective rank of replica libraries constructed from cross correlation functions requires more observations for reliable completion. To address this issue, a physics guided extension of Bayesian matrix completion with graphs (BMCG) is proposed. An envelope transform (ET) is applied to mitigate rapid propagation induced phase oscillations, thereby reducing the effective rank of the replica library. The circular structures revealed by ET are exploited to construct an initialization for BMCG. By incorporating ET-based rank reduction and circular-pattern initialization into BMCG, the proposed method enables reliable replica recovery. Simulations and experimental results demonstrate the effectiveness of the proposed method in localization, with observations of the sources of opportunity available only along a limited number of trajectories.