Optimal Estimator Design for LTI Systems with Bounded Noises, Disturbances, and Nonlinearities

This paper presents a new estimation technique for linear time-invariant (LTI) systems with bounded additional nonlinearities and/or disturbances, measurement noises, and initial states. A new direct methodology is developed to design an estimator optimizing the maximum estimation error of the system state or its linear function in a prefixed time interval. For some mechanical systems, both the parameters of the optimal estimator and the related maximum estimation error in a closed form are provided. The proposed method is illustrated through four simulation and experimental examples.