State Estimation with Secrecy against Eavesdroppers
This addresses confidentiality in state estimation for systems like networked control, but it is incremental as it builds on existing secrecy frameworks.
The paper tackles the problem of remote state estimation in the presence of an eavesdropper by introducing a control-theoretic definition of perfect secrecy, where the user's error remains bounded while the eavesdropper's error grows unbounded, and proposes a mechanism using random withholding of sensor information under specific rate conditions.
We study the problem of remote state estimation, in the presence of an eavesdropper. An authorized user estimates the state of a linear plant, based on the data received from a sensor, while the data may also be intercepted by the eavesdropper. To maintain confidentiality with respect to state, we introduce a novel control-theoretic definition of perfect secrecy requiring that the user's expected error remains bounded while the eavesdropper's expected error grows unbounded. We propose a secrecy mechanism which guarantees perfect secrecy by randomly withholding sensor information, under the condition that the user's packet reception rate is larger than the eavesdropper's interception rate. Given this mechanism, we also explore the tradeoff between user's utility and confidentiality with respect to the eavesdropper, via an optimization problem. Finally, some examples are studied to provide insights about this tradeoff.