A Nonlinear Filter Using Pseudo-Formal Linearization Based on Chebyshev Interpolation

Abstract

In this paper, we consider a design method of a nonlinear filter using a pseudo-formal linearization based on Chebyshev interpolation. The aims of this design method are the easy synthesis of a nonlinear filter, and the reduction of the computational burden in both linearization and estimation processes. First we divide the given region of state space into some subdomains considering the nonlinearity of the given nonlinear system. Next we piecewisely linearize given nonlinear dynamic and measurement systems by a formal linearization method of Chebyshev interpolation. Then we can apply the steady-state Kalman filter for each linearized system on a subdomain, and smoothly unite each Kalman filter on a subdomain by an automatic choosing function into a single filter on a whole domain. To verify the effectiveness of the presented method, we demonstrate numerical experiments of a nonlinear filter for an electric power system.