# Resilient Distributed Parameter Estimation with Heterogeneous Data

## TL;DR

This paper introduces SAGE, a resilient distributed estimator that guarantees convergence to the true parameter despite measurement attacks, even with heterogeneous and partially unobservable local models.

## Contribution

The paper proposes SAGE, a novel distributed estimator resilient to measurement attacks, effective with heterogeneous data and independent of network topology.

## Key findings

- SAGE guarantees convergence under a bound on compromised streams.
- Resilience does not depend on communication network topology.
- Numerical examples demonstrate SAGE's effectiveness.

## Abstract

This paper studies resilient distributed estimation under measurement attacks. A set of agents each makes successive local, linear, noisy measurements of an unknown vector field collected in a vector parameter. The local measurement models are heterogeneous across agents and may be locally unobservable for the unknown parameter. An adversary compromises some of the measurement streams and changes their values arbitrarily. The agents' goal is to cooperate over a peer-to-peer communication network to process their (possibly compromised) local measurements and estimate the value of the unknown vector parameter. We present SAGE, the Saturating Adaptive Gain Estimator, a distributed, recursive, consensus+innovations estimator that is resilient to measurement attacks. We demonstrate that, as long as the number of compromised measurement streams is below a particular bound, then, SAGE guarantees that all of the agents' local estimates converge almost surely to the value of the parameter. The resilience of the estimator -- i.e., the number of compromised measurement streams it can tolerate -- does not depend on the topology of the inter-agent communication network. Finally, we illustrate the performance of SAGE through numerical examples.