A nonlinear filter based on Fokker-Planck equation

Author

Kumar, M. ; Chakravorty, Suman

Author_Institution

Dept. of Aerosp. Eng., Texas A & M Univ., College Station, TX, USA

fYear

2010

fDate

June 30 2010-July 2 2010

Firstpage

3136

Lastpage

3141

Abstract

In this paper, a nonlinear filter based on Fokker-Planck equation (FPE) is presented for applications involving long time durations in between measurement updates. A previously developed semianalytical meshless algorithm is used to obtain the transient FPE response of nonlinear systems in near real time. Use of eigenfunctions of the discretized FP operator as basis functions causes equation error in FPE to reduce with time, implying that the algorithm is especially suited to problems with sparse measurements. The measurement update is implemented via weak form of the Bayes rule. An alternative based on function approximation of the posterior density is suggested to speed up this process. Filtering examples for up to 4-state systems are considered and compared with the extended Kalman filter (EKF).

Keywords

Fokker-Planck equation; Kalman filters; nonlinear control systems; nonlinear filters; transient response; Fokker-Planck equation; extended Kalman filter; long time durations; nonlinear filter; nonlinear systems; semianalytical meshless algorithm; transient FPE response; Eigenvalues and eigenfunctions; Filtering; Function approximation; Nonlinear equations; Nonlinear filters; Nonlinear systems; Real time systems; Robustness; State estimation; Time measurement;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2010

Conference_Location

Baltimore, MD

ISSN

0743-1619

Print_ISBN

978-1-4244-7426-4

Type

conf

DOI

10.1109/ACC.2010.5531029

Filename

5531029