Consensus-Based Distributed Filtering with Fusion Step Analysis

TL;DR

This paper analyzes the performance of consensus-based distributed filtering with limited fusion steps, providing a theoretical framework for understanding the trade-offs between filtering accuracy and communication costs in sensor networks.

Contribution

It introduces a novel analysis of finite fusion steps in distributed filtering, deriving explicit relations between performance degradation and fusion frequency.

Findings

Performance degradation can be quantified in closed form.

Steady-state covariance converges exponentially to centralized optimal.

Trade-off between communication cost and filtering accuracy is established.

Abstract

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 matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments.