Secure distributed estimation of linear systems

Abstract

A two-dimensional linear time-invariant system is considered. The two dimensions of its states are observed by one sensor each. Every sensor quantizes its observations into a finite number of messages, using also the other sensor's past decisions. The combined sensor outputs should allow for a bounded estimation error (reliability). For a natural quantizer, we identify the cases where a price in the quantizer sum rate has to be paid for the fact that observations are distributed. At the same time, an eavesdropper should not be able to track the system state (security). Using the same quantizer as before, security is shown to be possible if the eavesdropper has less information than the estimator in that it for each sensor message pair obtains a larger set of indistinguishable message pairs.