Design of UKF with correlative noises based on minimum mean square error estimation

Unscented Kalman filter (UKF) for a class of nonlinear discrete-time systems with correlative noises is designed to overcome the limitation that the conventional UKF calls for system noise and measurement to be irrelative. Recursive filtering equations of UKF with correlative noises are given based on minimum mean square error estimation and orthogonal transformation, and unscented transformation (UT) is applied to calculation the posterior distribution of the nonlinear system state. The proposed UKF solves the problem of nonlinear filtering failure in conventional UKF when system noise is correlated with measurement noise, so it expands the applications of the conventional UKF. A simulation example shows the effectiveness of the designed UKF.