Robust iterative observer for source localization for Poisson equation

Abstract

Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.