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

Chen Qian, Chengying Song, Sheng Li*, Qingwei Chen, and Jian Guo
International Journal of Control, Automation, and Systems, vol. 19, no. 8, pp.2830-2841, 2021

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.

Keyword : Gaussian sum filter, non-Gaussian, nonlinear system, sparse grid quadrature filter.

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