On Source-Term Parameter Estimation for Linear Advection-Diffusion Equations with Uncertain Coefficients

In this paper, we propose an algorithm estimating parameters of a source term of a linear advection-diffusion equation with an uncertain advection-velocity field. First, we apply a minimax state estimation technique order to reduce uncertainty introduced by the coefficients. Then we design a source localization algoritm which uses the state estimator as a model and estimates the parameters of the source term given incomplete and noisy data. The principal novelty of the proposed algorithm is in that it is robust with respect to the uncertainty in advection coefficients, i.e. wind fields. The localization algorithm is sequential, that is it updates both state estimate and source estimate once a new observation arrives. To demonstrate the efficacy of the proposed algorithm, we present a numerical example of source localization in two spatial dimensions for the advection-dominated transport of a non-reactive pollutant emanating from a point-source.