Resilient Distributed Parameter Estimation With Heterogeneous Data

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.

Resilient Distributed Recovery of Large Fields

“…Second, the following result comes as a consequence of Lemma 3 in [12] and studies the convergence of scalar time-varying systems of the form wt+1 = 1 − r1(t)c3 (|wt| + c5) (t + 1) δ 3 wt + r1(t)c4 (t + 1) δ 4 ,…”

“…Prior work in resilient computation has focused on settings where all devices or agents share a common processing objective. For example, in resilient consensus, agents attempt to reach agreement on a decision or value in the presence of adversaries [7][8][9] and in resilient parameter estimation, agents attempt to recover a common unknown parameter from local measurements while coping with malicious data [10][11][12]. In contrast, in resilient field recovery, agents have different, heterogeneous processing objectives.…”

“…In distributed field recovery, each agent is interested in recovering a subset of components of θ * . This contrasts with the setup of distributed parameter estimation [11,12], where each agent is interested in estimating all components of θ * . In the context of robotic navigation, for example, each robot may only be interested in estimating its local surroundings instead of the entirety of the (large) unknown environment.…”

Resilient Distributed Estimation: Sensor Attacks

“…Summary of Contributions. Unlike the existing work in resilient consensus [1,10,12,[24][25][26], centralized and decentralized inference [2,11,18,27,29,31,33,34], distributed parameter estimation [6][7][8] and optimization [30,35], which all study setups with a common processing objective, in this paper, we consider the case when agents have different heterogeneous estimation goals. In particular, we study resilient distributed field estimation, where each agent seeks to estimate only a few components of a high-dimensional spatially distributed field parameter while under measurement attacks.…”

“…We consider a setup that is similar to the setup of our previous work [8]: a team of agents each makes noisy measurements (over time) of a fraction of an unknown field parameter, and an adversary arbitrarily manipulates some of these measurements. The goal in this paper, however, is different than the goal in [8]. In [8], each agent attempts to estimate the entire unknown parameter, while, here, each agent attempts, in collaboration with nearby neighbors, to estimate only a portion of the unknown parameter in which it is interested.…”