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

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Abstract

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.

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The computation data are available upon request.

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Acknowledgements

This work was supported by the Italian Ministry of Education, University, and Research, and the Consejo Nacional de Ciencia y Tecnología of Mexico under Grant 250611.

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Authors and Affiliations

  1. Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125, Naples, Italy

    Laura Celentano

  2. Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon, 66450, San Nicolás de los Garza, Mexico

    Michael V. Basin

  3. International Laboratory of Informational and Navigation Systems, ITMO University, 197101, Saint Petersburg, Russia

    Michael V. Basin

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  1. Laura Celentano
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  2. Michael V. Basin
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Correspondence to Michael V. Basin.

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Celentano, L., Basin, M.V. Optimal Estimator Design for LTI Systems with Bounded Noises, Disturbances, and Nonlinearities. Circuits Syst Signal Process 40, 3266–3285 (2021). https://doi.org/10.1007/s00034-020-01635-z

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