An optimal sequential filter for the linear system with correlated noises

The sequential filter is a kind of useful estimate fusion algorithm. Traditional sequential filters are mainly utilized for the linear systems with the assumption of uncorrelated noises. Recently, some effective algorithms have been presented for the linear system with multiple sensors and correlated noises. Unfortunately, they can´t perfectly solve the optimal filtering estimate in linear minimum mean square error (LMMSE) for the systems with correlative measurement noises which are also cross-correlated with the process noise one time step apart and seldom discussed in present researches. And a novel sequential filter, which is optimal in LMMSE, is proposed in this paper for the linear dynamic system with correlative measurement noises which are also cross-correlated with the process noise one time step apart. The kernel of the novel optimal sequential filter is to decorrelate these correlations by use of the equivalent measurement function. Synchronously, the computer simulations are also presented to illustrate its performance.