  We address the problem of maximizing privacy of stochastic dynamical systems
whose state information is released through quantized sensor data. In
particular, we consider the setting where information about the system state is
obtained using noisy sensor measurements. This data is quantized and
transmitted to a remote station through a public/unsecured communication
network. We aim at keeping the state of the system private; however, because
the network is not secure, adversaries might have access to sensor data, which
can be used to estimate the system state. To prevent such adversaries from
obtaining an accurate state estimate, before transmission, we randomize
quantized sensor data using additive random vectors, and send the corrupted
data to the remote station instead. We design the joint probability
distribution of these additive vectors (over a time window) to minimize the
mutual information (our privacy metric) between some linear function of the
system state (a desired private output) and the randomized sensor data for a
desired level of distortion--how different quantized sensor measurements and
distorted data are allowed to be. We pose the problem of synthesizing the joint
probability distribution of the additive vectors as a convex program subject to
linear constraints. Simulation experiments are presented to illustrate our
privacy scheme.
