Journal
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
Volume 19, Issue 8, Pages 2830-2841Publisher
INST CONTROL ROBOTICS & SYSTEMS, KOREAN INST ELECTRICAL ENGINEERS
DOI: 10.1007/s12555-020-0490-x
Keywords
Gaussian sum filter; non-Gaussian; nonlinear system; sparse grid quadrature filter
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Funding
- Natural Science Foundation of China [61673217, 61333008, 61673219]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province [KYCX19_0300]
- National defense basic scientific research program [JCKY2019606D001]
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The study introduces the Gaussian sum technique to develop the Gaussian sum sparse grid quadrature filter for improving the filtering effect under non-Gaussian conditions. The algorithm approximates non-Gaussian probability densities and utilizes SGQF for filter updates, demonstrating better accuracy in solving nonlinear non-Gaussian filtering problems.
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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