Frequency Domain Estimation of Spatially Varying Parameters in Heat and Mass Transport

This paper presents a frequency domain approach to estimate spatially varying physical parameters of a one dimensional diffusion-transport-reaction equation. A non-linear least squares optimization of a frequency relevant criterion is proposed on the basis of measurements from a limited number of sensors. Analytic expressions of the Jacobian of the criterion function are exploited in an efficient numerical scheme. The proposed method exploits the sparsity of the underlying discretized model for a fast computation of the system parameters. The performance of the proposed procedure is illustrated by a number of simulation results. We demonstrate that the proposed method is able to estimate a spatially varying profile of unknown physical parameters in a realistic scenario.