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Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models

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  • Control Theory and Applications
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Abstract

To improve the filtering effect of the sparse grid quadrature filter (SGQF) under non-Gaussian conditions, the Gaussian sum technique is introduced, and the Gaussian sum sparse grid quadrature filter (GSSGQF) is developed. We present a systematic formulation of the SGQF and extend it to the discrete-time nonlinear system with the non-Gaussian noise. The proposed algorithm approximates the non-Gaussian probability densities by a finite number of weighted sums of Gaussian densities, and takes the SGQF as the Gaussian sub-filter to conduct the time and measurement update for each Gaussian component. An application in the discrete-time nonlinear system with the non-Gaussian noise has been shown to demonstrate the accuracy of the GSSGQF. It outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the GSSGQF provides significant performance improvement in the calculation accuracy for nonlinear non-Gaussian filtering problems.

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Nanjing, Jiangsu Province, 210094, China

    Chen Qian, Chengying Song, Sheng Li, Qingwei Chen & Jian Guo

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  1. Chen Qian
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  2. Chengying Song
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  3. Sheng Li
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  4. Qingwei Chen
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  5. Jian Guo
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Corresponding author

Correspondence to Sheng Li.

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This work is supported by the Natural Science Foundation of China (No. 61673217, No. 61333008, and No. 61673219), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX19_0300) and National defense basic scientific research program(JCKY2019606D001).

Chen Qian is a Ph.D. student in the School of Automation, Nanjing University of Science & Technology. His research interests include adaptive control, Kalman filter, integrated navigation, and nonlinear system filtering.

Chengying Song is a Ph.D. student in the School of Automation, Nanjing University of Science & Technology. Her research interests include integrated navigation, starlight navigation, nonlinear system control, and multi-sensor fusion.

Sheng Li is an Assocciate Professor in School of Automation, Nanjing University of Science & Technology. His research interests include nonlinear system control, robot control, and process control.

Qingwei Chen is a Professor in the School of Automation, Nanjing University of Science & Technology. His research interests include servo system control, fuzzy control, integrated navigation, and nonlinear system control.

Jian Guo is a Professor in the School of Automation, Nanjing University of Science & Technology. His research interests include intelligent control and intelligent system, robot system, and high precision motor control.

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Qian, C., Song, C., Li, S. et al. Algorithm of Gaussian Sum Filter Based on SGQF for Nonlinear Non-Gaussian Models. Int. J. Control Autom. Syst. 19, 2830–2841 (2021). https://doi.org/10.1007/s12555-020-0490-x

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  • DOI: https://doi.org/10.1007/s12555-020-0490-x

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