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Novel Simplex Kalman Filters

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Abstract

In this paper, a new class of nonlinear Kalman filter is proposed to further improve filtering accuracy and efficiency for high-dimensional state estimation, which is named simplex Kalman filter (SKF). In the proposed SKF, the simplex rules of different numerical accuracy are utilized to generate two sets of sigma points that are applied to numerically compute multivariate moment integrals encountered in nonlinear Kalman filter (NKF). The proposed SKFs can achieve improvement of computational efficiency in state estimation. With the increase in the state dimension, the computational complexity of the new SKFs is lower than that of traditional NKF, which can mitigate the curse of dimension issue in high-dimensional systems. Simulations on nonlinear high-dimensional problem and bearings only tracking demonstrate that in comparison with different NKFs, the new SKFs can improve the filtering performance efficiently.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 61101232), Fundamental and Frontier Research Project of Chongqing (Grant No. cstc2014jcyjA40020) and the Fundamental Research Funds for the Central Universities (Grant No. XDJK2014B001).

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Wen-Jie Zhang, Shi-Yuan Wang & Ya-Li Feng

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  1. Wen-Jie Zhang
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  2. Shi-Yuan Wang
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  3. Ya-Li Feng
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Correspondence to Shi-Yuan Wang.

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Zhang, WJ., Wang, SY. & Feng, YL. Novel Simplex Kalman Filters. Circuits Syst Signal Process 36, 879–893 (2017). https://doi.org/10.1007/s00034-016-0323-6

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  • DOI: https://doi.org/10.1007/s00034-016-0323-6

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