• underwater source localization
• finite element method
• Bayesian estimation
• acoustic source localization

This work addresses underwater source localization (USL) using a passive array system of acoustic sensors. This problem aims at detecting a radiating source and estimating its position in space by analyzing the acoustic field measured by an array of hydrophones. Due to the special characteristics and complexity of the underwater environment, USL using a passive array of acoustic sensors is a challenging task, attracting great interest within both the control and signal processing communities, especially in complex environments characterized by multipath and reverberation effects, irregular seabed geometry, and low signal-to-noise ratio (SNR). In such scenarios, underwater acoustic propagation and its effects can be exploited to enable passive localization. This work proposes a recursive Bayesian approach that propagates finite-element (FE) approximations of the wave equation to model the discretized space-time dynamics of the acoustic field conditioned on the position of the source, and sequentially estimates the field and the position of the radiating source directly from the acoustic measurements. FE models provide accurate predictions of the field dynamics, while retaining the advantage of general applicability over analytical and over-approximate solutions that are impractical for real-world scenarios. Specifically, two FEM-based discretization schemes are developed for acoustic field estimation, including a more computationally efficient spectral element method (SEM) formulation that exploits high-degree piecewise polynomials as basis functions, providing good accuracy with fewer degrees of freedom in comparison
with standard FEM. The proposed algorithms for USL implement a multiple-model (MM) state estimator where each filter runs a propagation model with a different source term associated to the hypothesis of the source being positioned in a specific element of the discretized domain. The decision on the propagation model that is more likely given the available acoustic measurements is taken based on the mode probabilities associated to each hypothesis. To handle the high dimension of the
large-scale field estimation problem and reduce the computational complexity, the
MM filter is implemented by using the ensemble Kalman filter (EnKF). Simulation experiments demonstrated the capability of the proposed MM-FE-EnKF in an underwater source tracking case-study with noisy measurements and model mismatch.
Finally, the effectiveness of a fast FMM-SE-EnKF exploiting computational advantages of SEM and an efficient implementation of MM, is demonstrated by means of simulation experiments in underwater acoustic environments with regular and irregular seabed geometry, and via comparison with standard USL algorithms.