Distributed Estimation Under Sensor Attacks
arXiv: Optimization and Control(2017)
摘要
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 agentsu0027 sensor measurements may fall under attack and take arbitrary values. The goal of this paper is to develop a distributed estimation algorithm to ensure that all, even those whose sensors are under attack, correctly estimate the parameter of interest. We assume a fully distributed setup; there is no fusion center and inter-agent collaboration is restricted to message exchanges between neighboring agents, the neighborhoods corresponding to a pre-specified, possibly parse, communication graph. We present two versions of the Saturated Innovation Update (SIU) algorithm for distributed estimation resilient to sensor attacks. The SIU algorithm is a consensus + innovations type estimator: agents iteratively estimate the parameter of interest by combining estimates of neighbors (consensus) and local sensing information (innovations). In the SIU algorithm, each agent applies a local, time-varying scalar gain to its innovation term to ensure that the energy of the scaled innovation lies below a threshold. Under the first version of SIU, which uses constant combination weights, if less than three tenths of agent sensors fall under attack, then, all of the agentsu0027 estimates converge exponentially fast to the true parameter. Under the second version, which uses time-decaying weights, if less than one half of the agent sensors fall under attack, then, all of the agentsu0027 estimates converge at a polynomial rate to the true parameter. We show that the resilience of SIU to sensor attacks does not depend on the topology of the inter-agent communication network, as long as it remains connected. Finally, we demonstrate the performance of SIU with numerical examples.
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