A Probabilistic Framework for Moving-Horizon Estimation: Stability and Privacy Guarantees
Vishaal Krishnan, Sonia Martı́nez · IEEE Transactions on Automatic Control · 2020
This article proposes a probabilistic framework for the design of robustly asymptotically stable moving-horizon estimators (MHE) for discrete-time nonlinear systems, and a mechanism to incorporate differential privacy in moving-horizon estimation. We formulate the moving-horizon estimator as an iterative proximal descent scheme in the space of probability measures with respect to the L2-Wasserstein metric, which we name W2-MHE. We then investigate asymptotic stability and robustness properties of the W2-MHE against the backdrop of the classical notion of strong local observability. Motivated by applications where the measurement data used by the estimator is to be kept private, we then propose a mechanism to incorporate differential privacy in the estimation method, based on an entropy regularization of the MHE objective functional. In particular, we find sufficient bounds on the regularization parameter to achieve the desired level of differential privacy. We then demonstrate the performance of the W2-MHE in numerical simulations.