# Consensus-Based Distributed Filtering with Fusion Step Analysis

arXiv: https://arxiv.org/abs/2112.06395 · HTML: https://mlsanity.com/paper/2112.06395/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Distributed Bayesian Learning of Dynamic States](https://mlsanity.com/paper/2212.02565/) (2022)

## Abstract (arXiv)

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.