Global Optimality for Generalized Federated Filter

Based on the matrix theory and the information sharing principle, the analytic relation among centralized Kalman filtering, decentralized filtering, and federated filtering is derived. It is proved that the global filtering of federated filters is optimal only when the dimensions of the master filter and the local filters are totally equal. If the dimensions of the master filter and the local filters are different, then only suboptimal solution can be obtained. The structure of a generalized federated filter is proposed. In terms of the information sharing principle, the information matrix of the one-step prediction state error and the one-step prediction state are reset to obtain the suboptimal solution of the global filtering. Furthermore, the suboptimal solution of the global filtering is used as observation feedback to correct the one-step prediction state and yield the optimal solution of the global filtering. The optimal feedback gain matrix is mathematically derived, so the filtering result is theoretically proved to be equivalent to the centralized Kalman filtering. The result of the simulation experiments with a dual-SINS/GPS integrated navigation system demonstrates the validity of the algorithm.