An Improved Weight Adaptive Gaussian Sum Algorithm Based on Sparse-Grid Quadrature Filter for Non-Gaussian Models

Abstract

Nonlinear filtering algorithm is the key technology for dealing with complex systems in sensor data processing. To improve the filtering accuracy of the nonlinear filtering algorithm in the non-Gaussian case, an improved version of the Gaussian sum algorithm, the Gaussian sum adaptive sparse grid quadrature filter (GSASQF), is proposed. The proposed algorithm overcomes the challenges by introducing the Gaussian sum principle, which converts the non-Gaussian state and noise in the system into the form of weighted sum of Gaussian components. Based on the Bayesian filtering framework, a three-level sparse grid sampling rule is introduced, with the sparse grid orthogonal filtering algorithm serving as the sub-filter. By determining the sampling point parameters, the filtering process for each combination of Gaussian components is implemented, thereby ensuring the filtering accuracy of each group. In addition, in combination with the ideal of data-driven, the weight of each Gaussian component combination is adaptively updated inversely by the values of the sensor measurement, which improves the global filtering accuracy of nonlinear system under non-Gaussian noise. The combination of these three improvements enables high-precision filtering of non-Gaussian non-linear systems. Theoretical analysis and simulation confirm that the proposed GSASQF algorithm provides advantages in filtering accuracy for nonlinear non-Gaussian filtering problems.