An iteration scheme with stability guarantees for proximity moving horizon estimation

In this paper, we propose and investigate an iteration scheme for proximity moving horizon state estimation of discrete-time linear systems subject to polytopic constraints. Based on a relaxed barrier function formulation of the underlying optimization problem, the state estimate is computed at each time instant after a limited number of optimization iterations. We establish sufficient conditions for the stability of the resulting estimation error. A simulation example demonstrates the computational efficiency of the proposed scheme and illustrates its satisfactory performance in comparison with fully converged proximity moving horizon estimators.