Finite-Time Guarantees for Byzantine-Resilient Distributed State Estimation With Noisy Measurements

This article considers resilient cooperative state estimation in unreliable multiagent networks. A network of agents aim to collaboratively estimate the value of an unknown vector parameter, while an unknown subset of agents suffer Byzantine faults. We refer to the faulty agents as Byzantine agents. Byzantine agents malfunction arbitrarily and may send out highly unstructured messages to other agents in the network. As opposed to fault-free networks, reaching agreement in the presence of Byzantine agents is far from trivial. In this article, we propose a computationally efficient algorithm that is provably robust to Byzantine agents. At each iteration of the algorithm, a good agent performs a gradient descent update based on noisy local measurements, exchanges its update with other agents in its neighborhood, and robustly aggregates the received messages using coordinate-wise trimmed means. Under mild technical assumptions, we establish that good agents learn the true parameter asymptotically in almost sure sense. We further complement our analysis by proving (high probability) finite-time convergence rate, encapsulating network characteristics.