This paper studies multiagent 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 (SIU) algorithm for distributed estimation resilient to sensor attacks. Under the iterative SIU 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 SIU to sensor attacks does not depend on the topology of the interagent communication network, as long as it remains connected. We demonstrate the performance of SIU with numerical examples.