Non-Gaussian Filters for Nonlinear Continuous-Discrete Models

Abstract

In this paper, we propose using an ensemble Kalman filter (EnKF) and particle filters (PFs) to obtain superior state estimation accuracy for nonlinear continuous-discrete models. We discretize the Ito-type stochastic differential system model by means of the usual procedure and suppress the approximation error by using small discrete times. We then simply apply the EnKF and PFs originally developed for nonlinear discrete-time models to the discretized system models, yielding the non-Gaussian filtering algorithms. Since the nonlinear problems generally make the states non-Gaussian as time proceeds, these non-Gaussian filters are promising for improving estimation accuracy. Their filtering performance is evaluated using two benchmark simulation models and compared with the performance of existing Gaussian filters, such as extended and unscented Kalman filters, and with that estimated by using the recursive Cramér-Rao lower bounds.

Keywords

• nonlinear continuous-discrete model
• non-gaussian filter
• importance selection
• simulations
• recursive cramér-rao lower bounds