Globally optimal distributed and sequential state fusion filters for multi-sensor systems with correlated noises✩

The problem concerning the multi-sensor fusion filtering for systems with correlated system and measurement noises is studied in this paper. Each sensor produces a local predictor by using its own measurements and then sends it to a fusion center. In the fusion center, by applying the projection theory and difference technology, the globally optimal distributed state fusion filter without feedback and sequential state fusion filter with recursive estimators of noises are presented in the sense of linear minimum variance by using all received local predictors, respectively. Under the condition that local prediction gain matrices are of full column rank, the proposed distributed and sequential state fusion filters can achieve the same estimation accuracy as the centralized fusion filter, i.e., they both have global optimality. The optimality is strictly proved. The corresponding steady-state fusion filters are also explored. A sufficient condition for the convergence of the proposed fusion filters is given. A target tracking example verifies the effectiveness of the proposed algorithms.