[1] In the analyses of geodetic very long baseline interferometry (VLBI) and GPS data the analytic form used for mapping of the atmosphere delay from zenith to the line of site is most often a three-parameter continued fraction in 1/sin(elevation). Using the 40 years reanalysis (ERA-40) data of the European Centre for Medium-Range Weather Forecasts for the year 2001, the b and c coefficients of the continued fraction form for the hydrostatic mapping functions have been redetermined. Unlike previous mapping functions based on data from numerical weather models (isobaric mapping functions (Niell, 2000) and Vienna mapping functions (VMF) (Boehm and Schuh, 2004)), the new c coefficients are dependent on the day of the year, and unlike the Niell mapping functions (Niell, 1996) they are no longer symmetric with respect to the equator (apart from the opposite phase for the two hemispheres). Compared to VMF, this causes an effect on the VLBI or GPS station heights that is constant and as large as 2 mm at the equator and that varies seasonally between 4 mm and 0 mm at the poles. The updated VMF, based on these new coefficients and called VMF1 hereinafter, yields slightly better baseline length repeatabilities for VLBI data.

Troposphere mapping functions are used in the analyses of Global Positioning System and Very Long Baseline Interferometry observations to map a priori zenith hydrostatic and wet delays to any elevation angle. Most analysts use the Niell Mapping Function (NMF) whose coefficients are determined from site coordinates and the day of year. Here we present the Global Mapping Function (GMF), based on data from the global ECMWF numerical weather model. The coefficients of the GMF were obtained from an expansion of the Vienna Mapping Function (VMF1) parameters into spherical harmonics on a global grid. Similar to NMF, the values of the coefficients require only the station coordinates and the day of year as input parameters. Compared to the 6‐hourly values of the VMF1 a slight degradation in short‐term precision occurs using the empirical GMF. However, the regional height biases and annual errors of NMF are significantly reduced with GMF.

Abstract:In this contribution, we present a GPS+GLONASS+BeiDou+Galileo four-system model to 10 fully exploit the observations of all these four navigation satellite systems for real-time precise orbit 11 determination, clock estimation and positioning. A rigorous multi-GNSS analysis is performed to achieve

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The world of satellite navigation is undergoing dramatic changes with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSSs). At the moment more than 70 satellites are already in view, and about 120 satellites will be available once all four systems (BeiDou + Galileo + GLONASS + GPS) are fully deployed in the next few years. This will bring great opportunities and challenges for both scientific and engineering applications. In this paper we develop a four-system positioning model to make full use of all available observations from different GNSSs. The significant improvement of satellite visibility, spatial geometry, dilution of precision, convergence, accuracy, continuity and reliability that a combining utilization of multi-GNSS brings to precise positioning are carefully analyzed and evaluated, especially in constrained environments.