Localization of Moving Sources: Uniqueness, Stability, and Bayesian Inference
Sára Wang, Mirza Karamehmedović, Faouzi Triki · SIAM Journal on Applied Mathematics · 2023
Abstract. We consider the subsonic moving point source problem for the scalar wave equation in [Formula: see text], proving a regularity result for the direct problem and uniqueness and stability results for the inverse problem. We then present and investigate numerically a Bayesian framework for the inference of the source trajectory and intensity from wave field measurements. The framework employs Gaussian process priors, the preconditioned Crank–Nicolson scheme with Markov chain Monte Carlo sampling, and conditioning on functionals to include prior information on the source trajectory.