Reinitialized partial moments for the identification of the heat equation parameters

This paper presents a new method for identifying partial differential equation (PDE). The goal is to exploit the interesting properties of the reinitialized partial moments (RPM) for PDE parameter estimation. This approach consists in applying integrals to find a partial derivative approximation. The obtained RPM model gives a direct continuous-time system identification and is linear with respect to the unknown parameters. In order to illustrate the application of this technique, we focus in the identification of the heat equation which represents a PDE with two variables.