In this contribution we address the issue of estimating parameters of a process, which is described by a set of first order, quasi-linear partial differential equations (PDEs) from a set of measurements. The parameters are found by minimizing the sum of the square of the errors over a finite set of measurement data. The errors are defined as the differences between the model Outputs and corresponding measurements. Since the assumption of constant model parameters may not be realistic in many practical applications, the estimation is carried out using a moving and fixed-size window of data. When a new measurement becomes available, the oldest measurement is discarded and the new one is added. (C) 2009 Elsevier Ltd. All rights reserved.