Particle filtering with correlated measurement and process noise at the same time

Non-linear filter has been widely used in many applications, and particle filter (PF) is a promising approach because it can treat the non-linear and non-Gaussian system. If there are correlations between process noise and measurement noise in the non-linear system, the performance of general PF degenerates. The study addresses that there are correlated measurement and process noise at the same time in the non-linear system. Aiming at this problem, the authors decouple the correlation and rearrange the state transition equation to a new one, and remove the correlation. And then apply the general PF based on the new state transition equation and the original measurement equation. From the derivation, it is easy to know that the proposed method is equal to general PF when there are no correlated noises. Experimental results show that the proposed method outperforms the general PF when there are correlated noises.