联邦滤波器理论研究

Study on the Theory of Federated Filter

应用矩阵理论和信息分配原理导出集中卡尔曼滤波、分散化滤波和联邦滤波之间的等价关系,证明联邦滤波器的全局滤波精度和集中卡尔曼滤波的滤波精度相同,并用信号流程图直观清晰地说明联邦滤波比分散化滤波结构更简单,计算量小。提出一种动态最优信息分配系数确定的方法,该方法使联邦滤波局部滤波器的设计也成为最优,并从理论上证明其具有最高的软故障检测灵敏度。

Based on the matrix theory and information sharing principle, this paper deduces the equivalent relations among the centralized Kalman filtering, decentralized filtering and federated filtering. It is proved that the global filtering accuracy of the federated filter is the same as the filtering accuracy of the centralized Kalman filter. Signal flow diagram is given to illustrate the filtering architecture visually and clearly. Compared with the decentralized filter, the federated filter has simpler architecture and less computation load. The determination of dynamically optimal information sharing coefficients is proposed in this paper. It also makes the design of local filters optimal. Besides, it is proved in theory that the optimal local filters have top soft-fault detecting sensitivity.