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Unscented Kalman Filtering for Nonlinear State Estimation with Correlated Noises and Missing Measurements

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  • Control Theory and Applications
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Abstract

The unscented Kalman filtering problem is investigated for a class of nonlinear discrete stochastic systems subject to correlated noises and missing measurements. Here, a random variable obeying Bernoulli distribution with known conditional probability is introduced to depict the phenomenon of missing measurements occurring in a stochastic way. Due to taking the correlation of noises into account, a one-step predictor is designed by applying the innovative analysis and unscented transformation approach. And then, based on one-step predictor and the minimum mean square error principle, a new unscented Kalman filtering algorithm is proposed such that, for the correlated noises and missing measurements, the filtering error is minimized. By solving the recursive matrix equation, the filter gain matrices and the error covariance matrices can be obtained and the proposed results can be easily verified by using the standard numerical software. We finally provide a numerical example to show the performance of the proposed approach.

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Author information

Authors and Affiliations

  1. Department of Control Science and Engineering, Control and Simulation Center, Harbin Institute of Technology, Harbin, China

    Long Xu, Kemao Ma & Hongxia Fan

  2. School of Basic Science, Harbin University of Commerce, Harbin, China

    Hongxia Fan

Authors
  1. Long Xu
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  2. Kemao Ma
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  3. Hongxia Fan
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Corresponding author

Correspondence to Kemao Ma.

Additional information

Recommended by Associate Editor Young Soo Suh under the direction of Editor PooGyeon Park. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 61174001 and 61321062.

Long Xu received his B.Sc. degree in Applied Mathematics from Harbin University, Harbin, China, in 2011, and his M.Sc. degree in Applied Mathematics from Harbin University of Science and Technology, Harbin, China, in 2015. He is currently a Ph.D. candidate with Control Science and Engineering, Harbin Institute of Technology, Harbin, China. His current research interests include nonlinear control and filtering, time-varying systems and stochastic systems.

Kemao Ma received his Bachelor degree in engineering from the Department of Information and Control Engineering, Xi’an Jiaotong University, China, in 1992, and his Ph.D. degree from Harbin Institute of Technology, China, in 1998. Since 2006, he has been a professor at the Control and Simulation Center, School of Astronautics, Harbin Institute of Technology, China. His current research interest includes nonlinear control, non-smooth analysis and control, robust control and their applications to guidance and control of flight vehicles.

Hongxia Fan received her Bachelor and Master degrees in science from the School of Mathematics and Computer Science, Harbin Normal University, China, in 2002 and 2005. Since 2005, she has been a teacher at School of basic sciences, Harbin University of Commerce, China. Now she is a Ph.D. student and her current research interest includes nonlinear control, sliding mode control and neural network adaptive control.

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Xu, L., Ma, K. & Fan, H. Unscented Kalman Filtering for Nonlinear State Estimation with Correlated Noises and Missing Measurements. Int. J. Control Autom. Syst. 16, 1011–1020 (2018). https://doi.org/10.1007/s12555-017-0495-2

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  • DOI: https://doi.org/10.1007/s12555-017-0495-2

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