# Resilient Distributed Field Estimation

## TL;DR

This paper introduces SAFE, a resilient distributed estimator that enables agents in a network to accurately estimate specific field components despite measurement attacks, by leveraging consensus and adaptive techniques.

## Contribution

The paper proposes SAFE, a novel resilient distributed estimation algorithm that guarantees convergence under attack conditions, improving robustness in networked physical field estimation.

## Key findings

- SAFE guarantees almost sure convergence to true values under attack conditions
- The estimator is resilient to measurement manipulations by adversaries
- Numerical examples demonstrate the effectiveness of SAFE

## Abstract

We study resilient distributed field estimation under measurement attacks. A network of agents or devices measures a large, spatially distributed physical field parameter. An adversary arbitrarily manipulates the measurements of some of the agents. Each agent's goal is to process its measurements and information received from its neighbors to estimate only a few specific components of the field. We present $\mathbf{SAFE}$, the Saturating Adaptive Field Estimator, a consensus+innovations distributed field estimator that is resilient to measurement attacks. Under sufficient conditions on the compromised measurement streams, the physical coupling between the field and the agents' measurements, and the connectivity of the cyber communication network, $\mathbf{SAFE}$ guarantees that each agent's estimate converges almost surely to the true value of the components of the parameter in which the agent is interested. Finally, we illustrate the performance of $\mathbf{SAFE}$ through numerical examples.