LAUSR

The ways of estimating the inter-system bias (ISB) have an important influence on BDS/GPS combined precise point positioning (PPP). Ordinarily, in data processing, the precise ephemeris and clock offset from the Center for Orbit Determination in Europe (CODE), Deutsches GeoForschungsZentrum (GFZ), and Wuhan University (WHU), respectively, are applied to obtain the ISB products (ISBCOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{COD}}$$\end{document}, ISBGFZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{GFZ}}$$\end{document}, and ISBWHU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{WHU}}$$\end{document}). Currently, in the case of BDS/GPS PPP, the ISB is generally considered to be a stable value in a given day and estimated as a constant. To better understand the mechanism underlying the generation of ISB in combined PPP, we deduce and establish the ISB estimation formulas and mathematical models and collect and process data from 19 multi-GNSS experimental stations. The results show that the ranges of ISBCOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{COD}}$$\end{document} and ISBWHU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{WHU}}$$\end{document} at different times are within 0.3 m, while ISBGFZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{GFZ}}$$\end{document} can change up to 6.5 m. An interesting phenomenon is that the ISBGFZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{GFZ}}$$\end{document} for different stations has a similar variation trend in a day, and in some days, the ISBs of all stations show a linear trend which may mainly be influenced by satellite clock offset. In addition, the temporal stability of ISB is independent of receiver software version number and antenna type, while the receiver type has little influence on the stability of ISB. Therefore, it is reasonable to estimate ISBCOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{COD}}$$\end{document} and ISBWHU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{WHU}}$$\end{document} as constant in a day and use a random walk to obtain ISBGFZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{GFZ}}$$\end{document}. The results show that the convergence speed and accuracy of BDS/GPS PPP obtained by the random walk method are higher than those using the constant method, no matter whether ISBGFZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{GFZ}}$$\end{document}, ISBCOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{COD}}$$\end{document}, or ISBWHU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ISB}}_{\text{WHU}}$$\end{document} is used.