Remote Estimation for Markov Jump Linear Systems: A Distributionally Robust Approach

This paper considers the problem of remote state estimation for Markov jump linear systems in the presence of uncertainty in the posterior mode probabilities. Such uncertainty may arise when the estimator receives noisy or incomplete measurements over an unreliable communication network. To address this challenge, the estimation problem is formulated within a distributionally robust framework, where the true posterior is assumed to lie within a total variation distance ball centered at the nominal posterior. The resulting minimax formulation yields an estimator that extends the classical MMSE solution with additional terms that account for mode uncertainty. A tractable implementation is developed using a distributionally robust variant of the first-order generalized pseudo-Bayesian algorithm. A numerical example is provided to illustrate the applicability and effectiveness of the approach.