# GPS/BDS Medium/Long-Range RTK Constrained with Topospheric Delay Parameters from NWP Model
## 1 Introduction
Different from the ionosphere, the troposphere is a non-dispersive medium and includes hydrostatic (dry) delay and non-hydrostatic or wet delay [12]. The hydrostatic delay typically reaches about 2.3 m in the zenith direction at sea level [13] and can be accurately modeled [14; 15]. Although the wet part only contributes about 10% of the total tropospheric delay, it is very difficult to model adequately using only surface measurements. The accuracy of conventional wet delay models, i.e., the Hopfield model, Ifadis model [16] and Meddes model [17], can be over 5 cm vertically, which can cause positioning errors of more than 1.5 m [18]. Double difference can be used to reduce the tropospheric delay, but it is not suitable for the long-range baseline RTK. High-precision tropospheric delay can also be estimated by GNSS carrier-phase measurements, together with position, ionospheric delay, and ambiguity [19; 20]. This technique has been widely used for water vapor estimation and high-precision differential positioning [21]. However, this method requires a period of time for the accurate estimation of the tropospheric delay parameters. Another method to eliminate the effect of wet tropospheric delay is to measure it directly with instruments: radiosonde, infrared spectral hygrometer and water vapor radiometer (WVR). WVR is the most commonly used instrument, and its accuracy can reach about 1 cm [22]. However, the cost of these instruments is too high to install them at each reference and rover station. As a result, tropospheric delay is the most significant error that affects the performance of the RTK, especially over the long-rang RTK. Apart from the methods mentioned above, the numerical weather prediction (NWP) model can also be used to estimate the tropospheric delay. The meteorological parameters can be derived at any location and at any time within the area by using the required information from NWP models for describing the neutral atmosphere. Using these meteorological parameters, tropospheric delays of the area can be estimated. Many researchers have applied zenith tropospheric delay (ZTD) measured by GPS to validate the ZTD derived from meteorological data and concluded that they basically agreed with each other [23; 24; 25; 26]. Research demonstrated that the ZTD derived from the NWP model-global data acquisition system (GDAS) agreed with the IGS ZTD solutions at a 3.0 cm root mean square difference (RMSD) level with biases of up to 4.5 cm over a 1.5-year period at 18 globally distributed IGS stations [27]. The test results of [28] showed that the RMSD of the ZTD calculated by the European Centre for Medium-Range Weather Forecasts (ECMWF), reanalyzed data with a horizontal resolution of 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) in China, was 3.54 cm and that of the National Centers for Environmental Prediction (NCEP), with a horizontal resolution of 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\), was 5.36 cm. However, the tropospheric delay estimated by the reanalyzed data cannot be used in real-time positioning. Experimental results showed that the RMSD of the ZTD derived from NCEP surface forecast data was 10 cm over China [28]. Research also demonstrated that although independent observation showed good accuracy of the zenith hydrostatic delay (ZHD) derived from the NWP models, the accuracy of the zenith wet delay (ZWD) derived from these models was usually far less than that of the ZHD, especially in low-altitude regions [29]. A few studies have been done to investigate the possible use of ray-tracing using raw NWP models to improve GPS RTK processing [30; 31; 32; 33]. The effectiveness of the network RTK initialization was improved by 19% using the National Oceanic and Atmospheric Administration (NOAA) model compared with the Hopfield model [30]. Although an improvement of about 60% in the vertical coordinate bias was found, the absolute accuracy cannot be expected to be better than 10 cm owing to the remaining mis-modeling of the troposphere [31].