Based on the standard Unscented Kalman Filter (UKF), the modified UKF is presented for nonlinear stochastic systems with correlated noises. The modified UKF consists of the prediction equations and the measurement equations, and holds the sigma points chosen by Unscented Transformation (UT). The stability of the modified UKF for the nonlinear stochastic system with correlated noises is analyzed. It is proved that under certain conditions, the estimation error of the UKF remains bounded. These results are verified by using Matlab simulations on two numerical example systems.
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