A Hierarchical Bayesian Detector for Weak Underwater Acoustic Signal Detection Under Environmental Mismatch

Weak underwater acoustic signal detection is fundamentally challenged by low signal-to-noise ratio (SNR), colored ocean noise, multipath distortion, and environmental mismatch. Existing weak-signal detectors have mainly focused on spectral enhancement, time-frequency tracking, or fixed-environment model matching, while environmentally robust Bayesian methods have been developed primarily for localization, matched-field processing, and channel estimation rather than weak passive detection itself. To bridge this gap, this paper proposes a hierarchical Bayesian detector for weak underwater acoustic signal detection under environmental mismatch. The received observation is modeled by jointly incorporating structured weak-signal coefficients, target-related parameters, and uncertain environmental parameters into a unified Bayesian hypothesis-testing framework. In particular, the acoustic environment is treated as a latent random variable rather than a fixed nominal condition so that robustness can be achieved through environmental marginalization. Since the resulting marginal likelihood is analytically intractable, a variational Bayesian approximation is developed to derive a tractable evidence-based detection statistic. Numerical simulations under low-SNR, multipath-distorted, and environmentally uncertain underwater conditions demonstrate that the proposed detector achieves consistently strong performance under both matched and mismatched scenarios. Ablation results in controlled simulations further indicate that environmental marginalization provides the largest observed robustness gain, whereas the structured weak-signal prior offers an additional improvement in weak-signal discrimination. These results provide controlled simulation-based evidence for the potential of hierarchical Bayesian inference in robust passive underwater acoustic detection under prescribed environmental uncertainty models.