Learning the Unscented Kalman Filter

An implementation of Unscented Kalman Filter for nonlinear state estimation.

Nonlinear state estimation is a challenge problem. The well-known Kalman Filter is only suitable for linear systems. The Extended Kalman Filter (EKF) has become a standarded formulation for nonlinear state estimation. However, it may cause significant error for highly nonlinear systems because of the propagation of uncertainty through the nonlinear system.

The Unscented Kalman Filter (UKF) is a novel development in the field. The idea is to produce several sampling points (Sigma points) around the current state estimate based on its covariance. Then, propagating these points through the nonlinear map to get more accurate estimation of the mean and covariance of the mapping results. In this way, it avoids the need to calculate the Jacobian, hence incurs only the similar computation load as the EKF.

For tutorial purpose, this code implements a simplified version of UKF formulation, where we assume both the process and measurement noises are additive to avoid augment of state and also to simplify the assumption on nonlinear maps.

The code is heavily commented with an example to use the function. Hence, it is sutiable for beginners to learn the UKF. For comparison, the EKF code can be found from https://www.mathworks.com/matlabcentral/fileexchange/18189-learning-the-extended-kalman-filter