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In this paper, we introduce a general proximity-based formulation for moving horizon estimation (MHE) of constrained discrete-time linear systems. The cost function of the underlying optimization problem consists of convex stage costs as well as Bregman distances centered around the a priori estimates. The Bregman term allows to incorporate constraints into the cost function by means of relaxed barrier functions and to formulate the moving horizon estimator as an unconstrained optimization problem. The stability properties of the proposed estimator are investigated and the obtained results are illustrated by means of a numerical example.
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Gharbi et al. (2019) studied this question.
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