Estimation of differential code biases for Beidou navigation system using multi-GNSS observations: How stable are the differential satellite and receiver code biases?

Differential code biases (DCBs) are important parameters that must be estimated accurately and reliably for high-precision GNSS applications. For optimal operational service performance of the Beidou navigation system (BDS), continuous monitoring and constant quality assessment of the BDS satellite DCBs are crucial. In this study, a global ionospheric model was constructed based on a dual system BDS/GPS combination. Daily BDS DCBs were estimated together with the total electron content from 23 months’ multi-GNSS observations. The stability of the resulting BDS DCB estimates was analyzed in detail. It was found that over a long period, the standard deviations (STDs) for all satellite B1–B2 DCBs were within 0.3 ns (average: 0.19 ns) and for all satellite B1–B3 DCBs, the STDs were within 0.36 ns (average: 0.22 ns). For BDS receivers, the STDs were greater than for the satellites, with most values <\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 ns. The DCBs of different receiver families are different. Comparison of the statistics of the short-term stability of satellite DCBs over different time intervals revealed that the difference in STD between 28- and 7-day intervals was small, with a maximum not exceeding 0.06 ns. In almost all cases, the difference in BDS satellite DCBs between two consecutive days was <\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<$$\end{document}0.8 ns. The main conclusion is that because of the stability of the BDS DCBs, they only require occasional estimation or calibration. Furthermore, the 30-day averaged satellite DCBs can be used reliably for the most demanding BDS applications.