A novel uncertainty evaluation method based on the particle filter and beta distribution for data with unknown distribution

Zhenying Cheng; Xu Chen; Liying Liu; Dongxu Cheng; Qiangxian Huang; Ruijun Li

doi:10.1063/5.0164859

A novel uncertainty evaluation method based on the particle filter and beta distribution for data with unknown distribution

Rev Sci Instrum. 2023 Sep 1;94(9):095115. doi: 10.1063/5.0164859.

Authors

Zhenying Cheng^{1

2}, Xu Chen^{1

2}, Liying Liu^{1

2}, Dongxu Cheng³, Qiangxian Huang^{1

2}, Ruijun Li^{1

2}

Affiliations

¹ School of Instrument Science and Opto-Electronics Engineering, Hefei University of Technology, Hefei 230009, China.
² Anhui Province Key Laboratory of Measuring Theory and Precision Instrument, Hefei University of Technology, Hefei 230009, China.
³ Technology Center, China Tobacco Henan Industrial Co., Ltd., Zhengzhou 475000, China.

PMID: 37737702
DOI: 10.1063/5.0164859

Abstract

Uncertainty evaluation for unknown distribution data is a key problem to be solved in uncertainty evaluation theory. To evaluate the measurement uncertainty of data with unknown distributions, a novel uncertainty evaluation method based on the particle filter (PF) and beta distribution is proposed in this paper. A beta distribution with wide adaptability was adopted as the distribution type of measurement results, the parameters of the beta distribution were taken as the parameters to be estimated, and a state-space model was established. The PF method, suitable for non-Gaussian data, was utilized to obtain the estimates of the parameters of the beta distribution according to the measurement results. Finally, the best estimates of the measurement results and their uncertainty were calculated using the beta distribution parameters. Simulation results show that the proposed method is adaptive to accurately evaluate the measurement uncertainties of data, especially for non-Gaussian distribution data or asymmetrically distributed data. Multiple evaluation results show that the method has good robustness. The experimental results for the drift errors of a laser interferometer show that the uncertainty result of the proposed method is consistent with the Monte Carlo method. This method is suitable for a variety of distribution types that can be characterized through beta distribution and can solve the optimal estimation and uncertainty evaluation of most measurement results with unknown distribution types.