A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

This letter presents a closed-form solution to estimate space-dependent transport parameters of a linear one dimensional diffusion-transport-reaction equation. The infinite dimensional problem is approximated by a finite dimensional model by 1) taking a frequency domain approach, 2) linear parameterization of the unknown parameters, and 3) using a semi-discretization. Assuming full state knowledge, the commonly used output error criterion is rewritten as the equation error criterion such that the problem results in linear least squares. The optimum is then given by a closed-form solution, avoiding computational expensive optimization methods. Functioning of the proposed method is illustrated by means of simulation.