Localization of Point Sources for Poisson Equation using State Observers

A method based on iterative observer design is presented to solve point source localization problem for Poisson equation with given boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain.