  For large-scale cyber-physical systems, the collaboration of spatially
distributed sensors is often needed to perform the state estimation process.
Privacy concerns naturally arise from disclosing sensitive measurement signals
to a cloud estimator that predicts the system state. To solve this issue, we
propose a differentially private set-based estimation protocol that preserves
the privacy of the measurement signals. Compared to existing research, our
approach achieves less privacy loss and utility loss using a numerically
optimized truncated noise distribution. The proposed estimator is perturbed by
weaker noise than the analytical approaches in the literature to guarantee the
same level of privacy, therefore improving the estimation utility. Numerical
and comparison experiments with truncated Laplace noise are presented to
support our approach. Zonotopes, a less conservative form of set
representation, are used to represent estimation sets, giving set operations a
computational advantage. The privacy-preserving noise anonymizes the centers of
these estimated zonotopes, concealing the precise positions of the estimated
zonotopes.
