Simultaneous input and state filtering: An ensemble approach

This paper presents a study of simultaneous input and state estimation for nonlinear dynamic systems. The problem considers both unknown input and state variables, where the inputs represent unknown signals driving or existing in a system, e.g., disturbances, system uncertainties or unmodeled dynamics. To deal with the problem, we will develop a set of ensemble-based filtering approaches in a Bayesian statistical framework. The fundamental notion is to approximate the probability distributions of the unknown input and state variables by ensembles of samples, propagate the ensembles to track the evolving probability distributions, and then translate the ensembles into input and state estimates. The proposed methods is an extension of the ensemble Kalman filtering and applicable to high-dimensional systems. Simulation results will be presented to verify their effectiveness.