Ensemble Kalman and Particle Filter for Noise-Driven Oscillatory Systems

Abstract

Combined state and parameter estimation of dynamical systems plays an important role in many branches of applied science and engineering. A wide variety of methods have been developed to tackle the joint state and parameter estimation problem. The Extended Kalman Filter (EKF) method is a popular approach which combines the traditional Kalman filtering and linearisation techniques to effectively tackle weakly nonlinear and non-Gaussian problems. Its mathematical formulation is based on the assumption that the probability density function (PDF) of the state vector can be reasonably approximated to be Gaussian. Recent investigations have been focused on Monte Carlo based sampling algorithms in dealing with strongly nonlinear and non-Gaussian models. Of particular interest is the Ensemble Kalman Filter (EnKF) and the Particle Filter (PF). These methods are robust in handling general forms of nonlinearities and non-Gaussian models, albeit with higher computational costs. In this paper we report the joint state and parameter estimation of noise-driven oscillatory systems undergoing limit cycle oscillation using EKF, EnKF and PF.