Computation of Optimal Weights for Solving the Atmospheric Source Term Estimation Problem

Abstract

AbstractIn case of a release of a hazardous material (e.g., a chemical or a biological agent) in the atmosphere, estimation of the source from concentration observations (provided by a network of sensors) is a challenging inverse problem known as the atmospheric source term estimation (STE) problem. This study emphasizes a method, known in the literature as the renormalization inversion technique, for addressing this problem. This method provides a solution that has been interpreted as a weighted minimal norm solution and can be computed in terms of a generalized inverse of the sensitivity matrix of the sensors. This inverse is constructed by using an appropriate diagonal weight matrix whose components fulfill the so-called renormalizing conditions. The main contribution of this paper is that it proposes a new compact algorithm (it requires less than 15 lines of MATLAB code) to obtain, in a fast and efficient way, those optimal weights. To show that the algorithm, based on the properties of the resolution matrix, matches the requirements of emergency situations, analysis of the computational complexity and memory requirements is included. Some numerical experiments are also reported to show the efficiency of the algorithm.