Identification of advection-diffusion equation from a limited number of spatial locations

This paper presents an instrumental variable method for identifying advection-diffusion equation models in presence of output measurement noise. This partial differential equation is commonly used to describe the transport and dispersion of a solute in a river channel. The realistic measurement situation where spatial data are limited and non-uniformly distributed is considered. A refined instrumental variable method involving adaptive data filtering is proposed to handle the non-uniformly spatial data distribution. The performance of the proposed approach are illustrated by a numerical example.