Stochastic localization of sources with convergence guarantees

We establish convergence guarantees for a recently proposed Markov Chain Monte Carlo (MCMC) method to locate source(s) of a certain concentration field. Our method utilizes a Markovian controller to control the motion of autonomous vehicles on a compact search domain. The distribution of the resulting discrete-time Markov chain is used to estimate the locations of the sources. To guarantee the correctness of the localization, we prove that the existing invariant measure for the Markov chain is unique. The chain is shown to be uniform ergodic and will converge to its stationary distribution. The theoretically derived convergence rate is compared to results from numerical simulations.