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This work considers resilient, cooperative state estimation in unreliablemulti-agent networks. A network of agents aims to collaboratively estimate thevalue of an unknown vector parameter, while an {\em unknown} subset of agentssuffer Byzantine faults. Faulty agents malfunction arbitrarily and may send out{\em highly unstructured} messages to other agents in the network. As opposedto fault-free networks, reaching agreement in the presence of Byzantine faultsis far from trivial. In this paper, we propose a computationally-efficientalgorithm that is provably robust to Byzantine faults. At each iteration of thealgorithm, a good agent (1) performs a gradient descent update based on noisylocal measurements, (2) exchanges its update with other agents in itsneighborhood, and (3) robustly aggregates the received messages usingcoordinate-wise trimmed means. Under mild technical assumptions, we establishthat good agents learn the true parameter asymptotically in almost sure sense.We further complement our analysis by proving (high probability) {\emfinite-time} convergence rate, encapsulating network characteristics.

Finite-time Guarantees for Byzantine-Resilient Distributed State Estimation with Noisy Measurements