  In this paper we focus on the dynamic state estimation which harnesses a vast
amount of sensing data harvested by multiple parties and recognize that in many
applications, to improve collaborations between parties, the estimation
procedure must be designed with the awareness of protecting participants' data
and model privacy, where the latter refers to the privacy of key parameters of
observation models. We develop a state estimation paradigm for the scenario
where multiple parties with data and model privacy concerns are involved.
Multiple parties monitor a physical dynamic process by deploying their own
sensor networks and update the state estimate according to the average state
estimate of all the parties calculated by a cloud server and security module.
The paradigm taps additively homomorphic encryption which enables the cloud
server and security module to jointly fuse parties' data while preserving the
data privacy. Meanwhile, all the parties collaboratively develop a stable (or
optimal) fusion rule without divulging sensitive model information. For the
proposed filtering paradigm, we analyze the stabilization and the optimality.
First, to stabilize the multi-party state estimator while preserving
observation model privacy, two stabilization design methods are proposed. For
special scenarios, the parties directly design their estimator gains by the
matrix norm relaxation. For general scenarios, after transforming the original
design problem into a convex semi-definite programming problem, the parties
collaboratively derive suitable estimator gains based on the ADMM. Second, an
optimal collaborative gain design method with model privacy guarantees is
provided, which results in the asymptotic MMSE state estimation. Finally,
numerical examples are presented to illustrate our design and theoretical
findings.
