Comparison of Unscented Kalman Filters

Unscented Kalman filter (UKF) has been proven to be a superior alternative to the extended Kalman filter (EKF) when solving the nonlinear system in previous literatures. In order to accelerate the application of UKF in the actual system, a new simplified UKF is proposed in this paper. It is called Rao-Blackwellised additive unscented Kalman filter (RBAUKF), and is specially designed for the dynamic system with the additive noise, the nonlinear state equation and the linear measurement equation. Furthermore, three kinds of UKF are introduced at the same time for the purpose of comparing their advantage and disadvantage. The three filters are general UKF, additive unscented Kalman filter (AUKF), and Rao-Blackwellised unscented Kalman filter (RBUKF). In fact, the AUKF and RBUKF are the improved filters of the general UKF, and RBAUKF proposed in this paper is the upgraded version, which synthesizes the feature of AUKF and RBUKF. Finally, the simulation and analysis of the above UKF algorithms are done. The simulation results indicate that the computational complexity of RBAUKF is nearly half of UKF. The computational complexities of AUKF and RBUKF are in between UKF and RBAUKF. Moreover, the estimation accuracies of RBAUKF, AUKF and RBUKF are the same, while that of UKF is lower than theirs. It suggests that the performance of RBAUKF is best following by AUKF and RBUKF, and it is better than the general UKF.