Globally optimal sequential and distributed fusion state estimation for multi-sensor systems with cross-correlated noises

This paper is concerned with globally optimal sequential and distributed fusion estimation algorithms in the linear minimum variance (LMV) sense for multi-sensor systems with cross-correlated noises, where the measurement noises from different sensors are cross-correlated with each other at the same time step and correlated with the system noise at the previous time step. First, a globally optimal sequential fusion filter is proposed by considering the estimators for measurement noises. The equivalence on estimation accuracy of the proposed sequential fusion filter and centralized fusion filter is proven. It has reduced computational cost since it avoids the measurement augmentation. Then, a distributed fusion filter is also proposed by considering the prior fusion estimator and feedback from the fusion center. Under the condition that local gain matrices are full column rank, the proposed distributed fusion filter has the same estimation accuracy as the centralized fusion filter, that is, it also has global optimality. Their equivalence on estimation accuracy is proven. Stability and steady-state properties of the proposed algorithms are analyzed. A sufficient condition for the existence of steady-state filters is given. Finally, simulation results for a target tracking system show the effectiveness of the proposed algorithms.