# Secure distributed filtering for unstable dynamics under compromised observations

## TL;DR

This paper develops a secure distributed filtering method for linear systems with unstable dynamics, addressing the challenge of compromised observations by malicious agents, and establishes conditions for bounded estimation errors.

## Contribution

It introduces a recursive distributed filter with a saturation scheme and consensus step, linking boundedness conditions to network and system properties, including 2s-sparse observability.

## Key findings

- The proposed filter maintains bounded estimation error under certain conditions.
- Sufficient conditions depend on network topology, system structure, and compromised agent subset.
- Numerical simulations validate the effectiveness of the method.

## Abstract

In this paper, we consider a secure distributed filtering problem for linear time-invariant systems with bounded noises and unstable dynamics under compromised observations. A malicious attacker is able to compromise a subset of the agents and manipulate the observations arbitrarily. We first propose a recursive distributed filter consisting of two parts at each time. The first part employs a saturation-like scheme, which gives a small gain if the innovation is too large. The second part is a consensus operation of state estimates among neighboring agents. A sufficient condition is then established for the boundedness of estimation error, which is with respect to network topology, system structure, and the maximal compromised agent subset. We further provide an equivalent statement, which connects to 2s-sparse observability in the centralized framework in certain scenarios, such that the sufficient condition is feasible. Numerical simulations are finally provided to illustrate the developed results.