# Distributed Design of Robust Kalman Filters over Corrupted Channels

## TL;DR

This paper introduces a distributed robust Kalman filter designed for uncertain systems over corrupted channels, with online error bounds and a switching fusion scheme to enhance performance in large networks.

## Contribution

It proposes a novel distributed robust Kalman filter with stochastic gains and a switching fusion scheme, along with a new collective observability condition for corrupted channels.

## Key findings

- The filter's mean square error is uniformly upper bounded under certain conditions.
- The switching fusion scheme reduces the upper bound of estimation error.
- Numerical simulations confirm scalability and effectiveness in large networks.

## Abstract

We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation errors are calculated online. We present a robust collective observability condition, under which the mean square error of the distributed filter is proved to be uniformly upper bounded if the network is strongly connected. For better performance, we modify the filer by introducing a switching fusion scheme based on a sliding window. It provides a smaller upper bound of the conditional mean square error. Numerical simulations are provided to validate the theoretical results and show that the filter scales to large networks.