Abstract
The length of the convergence time in Precise Point Positioning (PPP) is a result of unmodeled errors. The tropospheric delay error is considered a major error source that affects the PPP solution accuracy and convergence time, especially in the height coordinates. Recent research showed that Numerical Weather Models (NWM)-based tropospheric correction models are superior to traditional empirical tropospheric models. We investigate the tropospheric delay difference between the ray-traced NWM and the final troposphere estimates from the International GNSS Service (IGS). Long time series of about 5 years of tropospheric delay are obtained from the European Centre for Medium-Range Weather Forecast and compared with the final IGS tropospheric delay time series for 30 globally distributed IGS stations. It is shown that the ray-traced tropospheric delay differences depend on time and experience seasonal variations with a non-zero mean. The mean is found to be 0.47 cm and the standard deviation is 1.40 cm. To model such differences, the least-squares spectral analysis approach is used to estimate the deterministic part of the tropospheric residuals (linear trend and periodic signals). The remaining tropospheric differences are estimated as a random walk process with 5 mm/root h random noise. To study the effect of the developed model on both station position and tropospheric delay estimate, we implement our model in GPS processing software, and the data from 15 IGS stations are processed. These stations are divided into two groups. The first group consists of nine IGS stations from the same network used to estimate the model, and their corresponding model values are extrapolated to the test epochs in 2018. However, the second group consists of six IGS stations, and their corresponding values are interpolated from the nearby stations. It is shown that the root means square error (RMSE) of station position in both groups can be improved by 5.68%, 0.76%, and 11.88% in Easting, Northing, and Up directions, respectively. In addition to the improvement in the RMSE of station positions, an improvement of 7.91% is obtained for total tropospheric delay estimates.