An improved resampling particle filter algorithm based on digital twin

The problem of weight degradation is inevitable in particle filtering algorithms, and the resampling approach is an important method to reduce the particle degradation phenomenon. To solve the problem of particle diversity loss in existing resampling methods, this paper proposes a new digital twin-based resampling algorithm to improve the accuracy of particle filter estimation based on the traditional resampling algorithm. The digital twin-based resampling algorithm continuously improves the resampling process through the data interaction between the data model and the physical model, and realizes the real-time correction capability of particle weights that traditional resampling methods do not have. The new algorithm calibration rules are divided according to the size of particle weights, with particles of large weights retained and particles of small weights selectively processed. Compared with the traditional resampling algorithm, the new resampling algorithm reduces the mean square error of the particle filter estimation results by 16.62%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, 16.49%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, and 13.86%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, and improves the computing speed by 7.67%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, 2.25%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, and 7.54%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, respectively, in the simulation experiments of nonlinear systems with univariate unsteady state growth model. The algorithm is experimentally demonstrated to accurately track a person in motion in an indoor building in a non-rigid target tracking application, which illustrates the effectiveness and reasonableness of the digital twin-based resampling algorithm.