Multirate multisensor distributed data fusion algorithm for state estimation with cross-correlated noises

This paper is concerned with the optimal state estimation problem under linear dynamic systems when the sampling rates of different sensors are different. For simplicity, we consider two sensors where one´s sampling rate is three times as much as the other´s. The noises of different sensors are cross-correlated and are also coupled with the system noise of the previous step. By use of the projection theorem and induction hypothesis repeatedly, a distributed fusion estimation algorithm is derived. The algorithm is proven to be distributed optimal in the sense of Linear Minimum Mean Square Error (LMMSE) and can effectively reduces the oscillation existed in the sequential algorithm. Finally, a numerical example is shown to illustrate the effectiveness of the proposed algorithm.