Optimal fusion estimation for stochastic systems with cross-correlated sensor noises

This paper is concerned with the optimal fusion of sensors with cross-correlated sensor noises. By taking linear transformations to the measurements and the related parameters, new measurement models are established, where the sensor noises are decoupled. The centralized fusion with raw data, the centralized fusion with transformed data, and a distributed fusion estimation algorithm are introduced, which are shown to be equivalent to each other in estimation precision, and therefore are globally optimal in the sense of linear minimum mean square error (LMMSE). It is shown that the centralized fusion with transformed data needs lower communication requirements compared to the centralized fusion using raw data directly, and the distributed fusion algorithm has the best flexibility and robustness and proper communication requirements and computation complexity among the three algorithms (less communication and computation complexity compared to the existed distributed Kalman filtering fusion algorithms). An example is shown to illustrate the effectiveness of the proposed algorithms.