Resilient Distributed Estimation: Sensor Attacks

This paper studies multi-agent distributed estimation under sensor attacks. Individual agents make sensor measurements of an unknown parameter belonging to a compact set, and, at every time step, a fraction of the agents’ sensor measurements may fall under attack and take arbitrary values. We present the Saturated Innovation Update ($\mathcal{S}\mathcal{I}\mathcal{U}$) algorithm for distributed estimation resilient to sensor attacks. Under the iterative $\mathcal{S}\mathcal{I}\mathcal{U}$ algorithm, if less than one half of the agent sensors fall under attack, then, all of the agents’ estimates converge at a polynomial rate (with respect to the number of iterations) to the true parameter. The resilience of $\mathcal{S}\mathcal{I}\mathcal{U}$ to sensor attacks does not depend on the topology of the inter-agent communication network, as long as it remains connected. We demonstrate the performance of $\mathcal{S}\mathcal{I}\mathcal{U}$ with numerical examples.