Rao-Blackwellised Extended Kalman Filter with Correlated Noises

Abstract

Aiming at the adverse influence of correlation between measurement noise and process noise for filtering precision in nonlinear system estimation, Firstly, Rao-Blackwellised modeling technique is introduced to disassemble nonlinear and linear component of system state, and then Kalman filter and extended Kalman filter are used to realize estimation for them, respectively. On that basis, we construct the Rao-Blackwellised extended Kalman filter. Secondly, through rearrange the state transition function and make it independent between process noise and measurement noise, we give the decoupling method of correlated noises. Finally, combined with the Rao-Blackwellised extended Kalman filter and the decoupling method of correlated noises, a novel Rao-Blackwellised extended Kalman filter with correlated noises is proposed in this paper. The new method not only improves the filtering precision, but also decreases the calculated amount relative to standard extended Kalman filter, The theoretical analysis and experimental results show the efficiency of the proposed algorithm.