A deterministic-statistical approach to reconstruct moving sources using sparse partial data

Abstract We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In first step, an approximate direct sampling method developed to obtain locations at different times. Such information coded in priors, which critical for success Bayesian second step. The well-posedness posterior measure analyzed sense Hellinger distance. Both steps are based on same physical model and use set combined inherits merits deterministic inversion as demonstrated by numerical examples.