Underwater Doppler-bearing pulse source tracking based on an outlier-tolerant variational Bayesian adaptive Kalman filter

Tracking underwater non-cooperative targets with Doppler-bearing target motion analysis relies on pulse signal parameters estimated via sonar arrays. However, successfully implementing a Kalman filter for this purpose requires key parameters, including the noise covariance matrices, which cannot be known a priori in practical scenarios. A more critical challenge is that uncertainties in the marine environment and target-array geometry corrupt the parameter estimates with measurement outliers. Existing nonlinear variational Bayesian (VB) filters are not robust to this issue, as their fundamental reliance on Gaussian models and deterministic sampling degrades their convergence rate and tracking accuracy. For high-precision tracking under these conditions, this paper proposes an outlier-tolerant nonlinear VB adaptive Kalman filter that utilizes a hierarchical inverse-Wishart-gamma mixture distribution model to robustly identify outliers and more accurately approximate the measurement noise covariance matrix, while also employing the adaptive high-order cubature sampling method to improve the estimation accuracy of the expectation. The validity of this combined method is verified via rigorous numerical simulations and sea trials. Simulation results highlight the performance superiority of the proposed filter over traditional approaches utilizing inverse Wishart noise modeling and deterministic integral sampling. Furthermore, superior performance on sea trial data confirmed the filter's effectiveness and robustness.