Design of a Sequential Filtering Method Fully Equivalent to the Centralized Filter with Cross-Correlated Noise

This paper investigates the optimal fusion estimation problem for a class of multi-sensor systems, in which the measurement noises of distinct sensors are mutually cross-correlated and each measurement noise is correlated with the system process noise at the previous time step. First, based on the Gram-Schmidt orthogonalization principle, the innovation of each arriving measurement is recursively projected onto the span of all previous random innovations, and these projections are subtracted to obtain a mutually orthogonal sequential innovation sequence. Second, a sequential fusion Kalman filter is established using this sequential innovation sequence. It is rigorously proved that the proposed sequential fusion Kalman filter is equivalent to the centralized fusion Kalman filter in estimation performance. Finally, a simulation example of a target tracking system is presented to demonstrate the effectiveness of the proposed algorithm.