Unscented Kalman Filters and Particle Filter Methods for Nonlinear State Estimation

For nonlinear state space models to resolve the state estimation problem is difficult or these problems usually do not admit analytic solution. The Extended Kalman Filter (EKF) algorithm is the widely used method for solving nonlinear state estimation applications. This method applies the standard linear Kalman filter algorithm with linearization of the nonlinear system. This algorithm requires that the process and observation noises are Gaussian distributed. The Unscented Kalman Filter (UKF) is a derivative-free alternative method, and it is using one statistical linearization technique. The Particle Filter (PF) methods are recursive implementations of Monte-Carlo based statistical signal processing. The PF algorithm does not require either of the noises to be Gaussian and the posterior probabilities are represented by a set of randomly chosen weighted samples.