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

TL;DR

This paper addresses the inverse problem of locating moving sources in wave fields by establishing theoretical uniqueness and stability results, and introduces a Bayesian inference framework with numerical validation.

Contribution

It provides new theoretical results on the uniqueness and stability of source localization and develops a Bayesian approach with Gaussian process priors for practical inference.

Findings

Proved uniqueness and stability for the inverse source problem.

Developed a Bayesian inference method using Gaussian process priors.

Numerically demonstrated the effectiveness of the proposed framework.

Abstract

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.