Nonlinear filters for chaotic oscillatory systems

Abstract This paper examines and contrasts the feasi-bility of joint state and parameter estimation of noise-driven chaotic systems using the extended Kalman fil-ter (EKF), ensemble Kalman filter (EnKF), and parti-cle filter (PF). In particular, we consider the chaotic vibration of a noisy Duffing oscillator perturbed by combined harmonic and random inputs ensuing a tran-sition probability density function (pdf) of motion which displays strongly non-Gaussian features. This system offers computational simplicity while exhibit-ing a kaleidoscope of dynamical behavior with a slight change of input and system parameters. An extensive numerical study is undertaken to contrast the perfor-mance of various nonlinear filtering algorithms with respect to sparsity of observational data and strength of model and measurement noise. In general, the per-formance of EnKF is better than PF for smaller ensem-ble size, while for larger ensembles PF outperforms EnKF. For moderate measurement noise and frequent measurement data, EKF is able to correctly track the dynamics of the system. However, EKF performanc