Unscented Kalman Filter for Nonlinear Systems with Colored Measurement Noise

Abstract

Traditional unscented Kalman filter (UKF) calls for that noise should be Gaussian white one, and can not solve nonlinear filtering problem with colored noise. For this reason, a new UKF filtering algorithm with colored measurement noise is proposed. Firstly, optimal filtering framework for a class of nonlinear discrete-time systems with colored measurement noise is derived on the basis of augmented measurement information and minimum mean square error estimation. Secondly, filtering recursive formula of UKF with colored noise is proposed through applying unscented transformation (UT) to calculation the posterior mean and covariance of the nonlinear state in this optimal framework. The proposed UKF can effectively deal with the issue that traditional UKF is failure under the condition that measurement noise is colored. A numerical simulation example also shows its feasibility and effectiveness.