State estimation using an extended Kalman filter with privacy-protected observed inputs

In this paper, we focus on the parameter estimation of dynamic state-space models using privacy-protected data. We consider an scenario with two parties: on one side, the data owner, which provides privacy-protected observations to, on the other side, an algorithm owner, that processes them to learn the system's state vector. We combine additive homomorphic encryption and Secure Multiparty Computation protocols to develop secure functions (multiplication, division, matrix inversion) that keep all the intermediate values encrypted in order to effectively preserve the data privacy. As an application, we consider a tracking problem, in which a Extended Kalman Filter estimates the position, velocity and acceleration of a moving target in a collaborative environment where encrypted distance measurements are used.