Passive Sonar Frequency Estimation Using System-Informed Neural Networks With Ensemble-Based Uncertainty Quantification

Abstract

Accurate and high-resolution frequency estimation is essential for underwater surveillance with passive sonar systems. Recently, system-informed neural networks (SINNs) have been introduced to address the limitations of conventional methods by providing improved generalization, fast inference, and outputs consistent with system models. Prior work has extended SINN with multiple measurements to leverage consistency across them, yet some frequency components remain weak or masked by noise. In this study, we enhance SINN performance using a deep ensemble with uncertainty quantification (UQ), leveraging the temporal continuity of frequency components. Multiple SINNs are trained with distinct initializations on separate training sets, producing diverse predictions for the same test sample. The resulting UQ provides insights into the prediction uncertainty associated with specific frequency bin components. Consequently, we unify adjacent UQs in time to refine the estimated frequency spectrum by further suppressing residual noise. Simulations demonstrate improved noise reduction, though at the cost of occasionally missing minor components. In-situ evaluations using two acoustic data confirm that the proposed scheme surpasses nominal SINN and approaches sparse recovery methods, achieving clearer detection of major components under low signal-to-noise ratio, long-range conditions, albeit at the cost of weakened estimation of minor components.