Localization of moving sources: uniqueness, stability, and Bayesian inference

Sára Wang (1) , Mirza Karamehmedović (1) , Faouzi Triki (2)

1 DTU - Danmarks Tekniske Universitet = Technical University of Denmark
2 EDP - Equations aux Dérivées Partielles

We consider the subsonic moving point source problem for the scalar wave equation in $\pmb{R}^3$, 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 pre-conditioned Crank-Nicholson scheme with Markov Chain Monte Carlo sampling, and conditioning on functionals to include prior information on the source trajectory.

Domaines: Equations aux dérivées partielles [math.AP]

Sára Wang, Mirza Karamehmedović, Faouzi Triki. Localization of moving sources: uniqueness, stability, and Bayesian inference. 2022. ⟨hal-03639458⟩