GPS/BDS triple-frequency cycle slip detection and repair based on moving window global search method

Cycle slip detection and repair are crucial steps in achieving high accuracy in Global Navigation Satellite System (GNSS) data processing. The use of Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) triple frequency observations allows for more accurate detection and repair of cycle slips compared to single or dual frequency. This study presents a moving window global search method by selecting three sets of combined coefficients to construct geometry-free (GF) models to minimize the influence of the ionosphere, using a moving window to update the standard deviation of cycle slip estimation, applying the "3 sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upsigma$$\end{document}" criterion to constrain the range, and utilizing a global search method to detect and repair triple-frequency cycle slips. Through five sets of 1 Hz GNSS data experiments, the results demonstrate the effectiveness of this method in determining the position and size of triple-frequency cycle slips while avoiding multi-value problems. The detection success rate for GPS ranges from 98.0 to 100.0%, while BDS ranges from 92.0 to 100.0%. On average, GPS achieves a detection rate of 99.2%, and BDS reaches 96.7%, which is 0.8% and 1.8% higher than the direct rounding method, respectively. Compared to existing methods, it is also effective for the vast majority of small cycle slips within 2 cycles.