On source-term parameter estimation for linear advection-diffusion equations with uncertain coefficients

Abstract

In this paper, we propose an algorithm for 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 in order to reduce uncertainty introduced by the coefficients. Then we design a source localization algorithm 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 uncertainty in advection coefficients. The localization algorithm is sequential; that is, it updates both the state estimate and the 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 advectiondominated transport of a nonreactive pollutant emanating from a point source.