Title: An Information Matrix Approach for State Secrecy,
Abstract: This paper studies the problem of remote state estimation in the presence of
a passive eavesdropper. A sensor measures a linear plant's state and transmits
it to an authorized user over a packet-dropping channel, which is susceptible
to eavesdropping. Our goal is to design a coding scheme such that the
eavesdropper cannot infer the plant's current state, while the user
successfully decodes the sent messages. We employ a novel class of codes,
termed State-Secrecy Codes, which are fast and efficient for dynamical systems.
They apply linear time-varying transformations to the current and past states
received by the user. In this way, they force the eavesdropper's information
matrix to decrease with asymptotically the same rate as in the open-loop
prediction case, i.e. when the eavesdropper misses all messages. As a result,
the eavesdropper's minimum mean square error (mmse) for the unstable states
grows unbounded, while the respective error for the stable states converges to
the open-loop prediction one. These secrecy guarantees are achieved under
minimal conditions, which require that, at least once, the user receives the
corresponding packet while the eavesdropper fails to intercept it. Meanwhile,
the user's estimation performance remains optimal. The theoretical results are
illustrated in simulations.