Kalman Filter Variants for Nonlinear Systems: Applications to Synchronization of Chaotic Systems

Abstract : The problem of estimation of state of a stochastic nonlinear dynamical system in a noisy environment is of central importance in engineering. Furthermore it has a wide range of applications such as control system and chaotic synchronization. The process to obtain the state estimations is called filtering. Kalman Filter (KF) is the optimal Bayesian estimator for linear systems. However, the application of the KF to nonlinear systems can be difficult. Consequently, most existing methods rely on simplifying assumptions to obtain a tractable but approximate solution. This chapter presents and analyses the best known Kalman Filters variants for nonlinear systems, such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) respectively, which has been concluded in synchronization of chaotic systems.