AN ITERATIVE PROPER ORTHOGONAL DECOMPOSITION (I-POD) TECHNIQUE WITH APPLICATION TO THE FILTERING OF PARTIAL DIFFERENTIAL EQUATIONS

摘要

In this paper, we consider the filtering of systems governed by partial differentialrnequations (PDE). We adopt a reduced order model (ROM) based strategyrnto solve the problem. We propose an iterative version of the snapshot properrnorthogonal decomposition (POD) technique, termed I-POD, to construct ROMsrnfor PDEs that is capable of capturing their global behaviour. Further, the techniquernis entirely data based, and is applicable to forced as well as unforcedrnsystems. We apply the ROM generated using the I-POD technique to constructrnreduced order Kalman filters to solve the filtering problem. The methodologyrnis tested on several 1-dimensional PDEs of interest including the heat equation,rnthe wave equation and 2-dimensional pollutant transport equation.