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Gain-Constrained Extended Kalman Filtering with Stochastic Nonlinearities and Randomly Occurring Measurement Delays

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Abstract

In this paper, the gain-constrained extended Kalman filtering problem is studied for discrete time-varying nonlinear system with stochastic nonlinearities and randomly occurring measurement delays. Both deterministic and stochastic nonlinearities are simultaneously present in the model, where the stochastic nonlinearities are described by first moment and can encompass several classes of well-studied stochastic nonlinear functions. A diagonal matrix composed of mutually independent Bernoulli random variables is introduced to reflect the phenomenon of randomly occurring measurement delays caused by unfavorable network conditions. The aim of the addressed filtering problem is to design a finite-horizon recursive filter such that, for all stochastic nonlinearities, randomly occurring measurement delays and gain constraint, the upper bound of the cost function involving filtering error is minimized at each sampling time. It is shown that the filter gain is obtained by solving matrix equations. A numerical simulation example is provided to illustrate the effectiveness of the proposed algorithm.

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Acknowledgments

This work was supported in part by the Natural Science Foundation of China under Grant 61233005 and National 973 Project under Grant 2014CB744200. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers and editors.

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Authors and Affiliations

  1. School of Instrumentation Science and Optoelectronic Engineering, Beihang University, Beijing, 100191, China

    Shuo Zhang, Jianhui Zhao, Yan Zhao & Gaoliang Li

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  1. Shuo Zhang
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  2. Jianhui Zhao
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  3. Yan Zhao
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  4. Gaoliang Li
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Correspondence to Yan Zhao.

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Zhang, S., Zhao, J., Zhao, Y. et al. Gain-Constrained Extended Kalman Filtering with Stochastic Nonlinearities and Randomly Occurring Measurement Delays. Circuits Syst Signal Process 35, 3957–3980 (2016). https://doi.org/10.1007/s00034-016-0244-4

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