For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence of the estimation error covariance matrix of each sensor is guaranteed under a collective observability condition. In particular, the steady-state covariance matrix can be simplified as the solution to a discrete-time Lyapunov equation. Moreover, the performance degradation induced by reduced fusion frequency is obtained in closed form, which establishes an analytical relation between the performance of the CMDF with finite fusion steps and that of centralized filtering. Meanwhile, it provides a trade-off between the filtering performance and the communication cost. Furthermore, it is shown that the steady-state estimation error covariance matrix exponentially converges to the centralized optimal steady-state covariance matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments.

对于基于测量的分布式过滤（CMDF）的共识，通过在每个采​​样间隔内进行无限的共识融合操作，传感器网络中的每个节点都可以通过集中过滤实现最优的过滤性能。然而，由于物理系统中的通信资源有限，融合步骤的数量不可能是无限的。为了解决这个问题，本文分析了 CMDF 在有限共识融合操作下的性能。首先，通过引入修正的离散时间代数Riccati方程和几种新技术，保证了每个传感器的估计误差协方差矩阵在集体可观测性下的收敛性。健康）状况。特别是，稳态协方差矩阵可以简化为离散时间李雅普诺夫方程的解。此外，以封闭形式获得了由降低融合频率引起的性能下降，这建立了具有有限融合步骤的CMDF性能与集中滤波性能之间的解析关系。同时，它提供了过滤性能和通信成本之间的权衡。此外，结果表明稳态估计误差协方差矩阵以指数方式收敛到集中式最优稳态协方差矩阵，融合操作在每个采样间隔内趋于无穷大。最后，通过说明性数值实验验证了理论结果。