Brief paper: Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

Authors:
Benjamin L. Pence;Hosam K. Fathy;Jeffrey L. Stein
Affiliations:
Mechanical Engineering Department, The University of Michigan, Ann Arbor, MI 48109-2125, United States;Mechanical and Nuclear Engineering Department, Pennsylvania State University, University Park, PA 16802, United States;Mechanical Engineering Department, The University of Michigan, Ann Arbor, MI 48109-2125, United States
Venue:
Automatica (Journal of IFAC)
Year:
2011

Citing 6
Cited 0

Stochastic finite elements: a spectral approach

Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

SIAM Journal on Scientific Computing
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches

Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Stochastic spectral methods for efficient Bayesian solution of inverse problems

Journal of Computational Physics
A generalized polynomial chaos based ensemble Kalman filter with high accuracy

Journal of Computational Physics
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	22.14

Visualization

Abstract

This paper combines polynomial chaos theory with maximum likelihood estimation for a novel approach to recursive parameter estimation in state-space systems. A simulation study compares the proposed approach with the extended Kalman filter to estimate the value of an unknown damping coefficient of a nonlinear Van der Pol oscillator. The results of the simulation study suggest that the proposed polynomial chaos estimator gives comparable results to the filtering method but may be less sensitive to user-defined tuning parameters. Because this recursive estimator is applicable to linear and nonlinear dynamic systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.