An extended Perron-Frobenius operator filter for nonlinear state estimation

Abstract

We propose an extended Perron--Frobenius Operator Filter (PFOF) for nonlinear state estimation. The method learns the Perron--Frobenius operator, an infinite-dimensional linear operator fully preserving properties of a nonlinear dynamical system, using the extended Dynamic Mode Decomposition (eDMD). This enables us to explicitly account for non-Gaussian distributions exhibited by the nonlinear system within a linear-operator representation, while retaining the freedom to choose basis functions in eDMD. Through two numerical examples, we show that the extended PFOF achieves high computational efficiency and high estimation accuracy by exploiting the flexibility in the choice of basis functions in eDMD.