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On estimation of nonlinear functionals from discrete noisy measurements

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  • Control Theory and Applications
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Abstract

The principal objective of this paper is to estimate a nonlinear functional of state vector (NFS) in dynamical system. The NFS represents a multivariate functional of state variables which carries useful information of a target system for control. The paper focuses on estimation of the NFS in linear continuous-discrete systems. The optimal nonlinear estimator based on the minimum mean square error approach is derived. The estimator depends on the Kalman estimate of a state vector and its error covariance. Some challenging computational aspects of the optimal nonlinear estimator are solved by usage of the unscented transformation for implementation of the nonlinear estimator. The special quadratic functional of state vector (QFS) is studied in detail. We derive effective matrix formulas for the optimal quadratic estimator and mean square error. The quadratic estimator has a simple closed-form calculation procedure and it is easy to implement in practice. The obtained results we demonstrate on theoretical and practical examples with different types of an nonlinear functionals. Comparison analysis of the optimal and suboptimal estimators is presented. The subsequent application of the proposed optimal nonlinear and quadratic estimators demonstrates their effectiveness.

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Author information

Authors and Affiliations

  1. Department of Sensor Systems, Hanwha Corporation R&D Center, 52-1 Oesam-dong, Yuseong-gu, Daejeon, 305-106, Korea

    Il Young Song

  2. Department of Information and Statistics, Research Institute of Natural Science, Gyeongsang National University, 501 Jinjudaero, Jinju, Gyeongsangnam-do, 660-701, Korea

    Vladimir Shin

  3. Department of Mathematics, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon, 406-772, Korea

    Won Choi

Authors
  1. Il Young Song
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  2. Vladimir Shin
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  3. Won Choi
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Corresponding author

Correspondence to Won Choi.

Additional information

Recommended by Associate Editor Juhoon Back under the direction of Editor Duk-Sun Shim. This journal was supported by the Incheon National University Research Grant in 2014–2015.

Il Young Song received the B.S. degree from the Changwon National University, Korea, in 2007, and the M.S. degree from the Gwangju Institute of Science and Technology (GIST), Gwangju, in 2008. He received the Ph.D. degree from the GIST in 2012. He is currently a senior researcher in Hanwha Corporation R&D Center, Pangyo, Korea.

Vladimir Shin received the B.Sc. and M.Sc. degrees in applied mathematics from Moscow State Aviation Institute in 1977 and 1979, respectively. In 1985, he received the Ph.D. degree in mathematics from the Institute of Control Science, Russian Academy of Sciences. He is currently a professor in Gyeongsang National University, Korea. His research interests include estimation, filtering, tracking, and data fusion.

Won Choi received his Ph.D from Sung Kyun Kwan University under the direction of Yeong Don Kim. Since 1993 he has been at the University of Incheon. In 1996 and 2003, he was in Steklov Mathematical Institute of Russia and University of Iowa, respectively. His research interests center on stochastic processes and biomathematics.

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Song, I.Y., Shin, V. & Choi, W. On estimation of nonlinear functionals from discrete noisy measurements. Int. J. Control Autom. Syst. 15, 2109–2117 (2017). https://doi.org/10.1007/s12555-016-0382-2

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  • DOI: https://doi.org/10.1007/s12555-016-0382-2

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