Fusion algorithm of correlated local estimates

Three algorithms for fusing local estimates are compared. The first one (algorithm A) is the well known Federated filtering algorithm proposed by Carlson [Federated filter for fault-tolerant integrated navigation systems, in: Proceedings of IEEE Position, Location and Navigation Symposium, Oriando, FL, 1988 pp. 110–119; IEEE Trans. Aerospace and Electronic System 26 (3) (1990) 517–525], which needs an Upper Bound technique to eliminate the correlation between local estimates, and a reset procedure to make the global estimate optimal. The second one (algorithm B) proposed by Hong Jin and Hong Yue Zhang directly calculates the optimal global estimate as a weighted sum of correlated local estimates using general weighting matrices [Fusion algorithm of correlated local estimates for federated filter, in: Proceedings of the 3rd Asian Control Conference, Shanghai, 2000, pp. 1428–1433]. In this paper a simplified algorithm (algorithm C) is derived, which uses diagonal weighting matrices. The simplification leads to less computation as compared to that of algorithm B, but the global estimate is sub-optimal. Comparison between these three algorithms is conducted by theoretical analysis and extensive simulations as well. The comparison reveals that the algorithm C has moderate calculation load, strong fault tolerance and little loss in estimation accuracy. And the sensitivities to the values of covariance matrices of noises are similar for the three algorithms.