Fusion algorithm of correlated local estimates.

*(English)*Zbl 1125.93483Summary: Three algorithms for fusing local estimates are compared. The first one (algorithm A) is the well known Federated filtering algorithm proposed by N. A. Carlson [Federated filter for fault-tolerant integrated navigation systems, in: Proc. IEEE Position, Location and Navigation Symposium, Oriando, FL, 110–119 (1988); IEEE Trans. Aerospace Electron. Syst. 26, No. 3, 517–525 (1990)], 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, 1428–1433 (2000)].

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.

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, 1428–1433 (2000)].

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.

##### MSC:

93E11 | Filtering in stochastic control theory |

93E10 | Estimation and detection in stochastic control theory |

93C95 | Application models in control theory |