Robust State Estimation for Linear Systems Under Distributional Uncertainty

Abstract

Modeling uncertainties for real linear systems are unavoidable. These uncertainties can significantly degrade the performance of optimal state estimators designed for nominal system models. The challenge is quantifying such uncertainties and devising robust estimators that are insensitive to them. This paper is therefore concerned with distributionally robust state estimation for linear Markov systems. We propose a new modeling framework that describes uncertainties using a family of distributions so that the worst-case robust estimate in the state space is made over the least-favorable distribution. This framework uses only one or two scalars to express the uncertainty set and does not require the structural information of model uncertainties. Furthermore, the moment-based ambiguity set is suggested to embody the distributional uncertainty family. As a result, the estimation problem transforms into a nonlinear semidefinite program with linear constraints, which can be analytically and efficiently solved. Intensive experiments illustrate the advantages of the proposed framework over existing methods.