Abstract
This paper deals with the analysis of a class of offline state estimators for LTI discrete-time systems in the presence of an arbitrary measurement noise which can potentially take any value. The considered class of estimators is defined as the solution of an optimization problem involving a performance function which can be interpreted as a generalization of cost functions used in the Maximum Correntropy Criterion. The conclusion of the analysis is that if the system is observable enough, then the considered class of estimators is resilient, which means that the obtained estimation error is independent from the highest values of the measurement noise. In the case of systems with a bounded process noise, the considered class of estimators provides a bounded estimation error under the appropriate conditions despite not being designed for this scenario.
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