Kriging Interpolation in Modelling Tropospheric Wet Delay

External Tropospheric Corrections by Using Kriging Interpolation for Improving PPP-RTK Positioning Solutions

With the availability of satellite carrier-phase delay corrections provided by a reference network or the International GNSS Service (IGS), the integer ambiguity resolution for a single receiver can be successfully achieved, which is the so-called PPP-RTK concept. Although PPP-RTK can significantly shorten the convergence time, it is still worthwhile to further investigate fast and high-precision GNSS parameter estimation to improve efficiency and productivity. In order to fully exploit the potential of GNSS for positioning applications, we herein introduce external troposphere corrections as constrained pseudo observables to the undifferenced and uncombined PPP-RTK model. Since the uncertainties of the corrections are considered in the data processing, the PPP-RTK model with the weighted tropospheric corrections is referred to as the tropospheric-weighted model. Kriging interpolation is applied to generate the tropospheric corrections, as well as the corresponding variances. The quality of the tropospheric-weighted model is assessed by the positioning Root Mean Square (RMS) errors and the convergence time to reach a 10 cm accuracy. The 90% 3D convergence time of the kinematic positioning mode of the tropospheric-weighted model is 43.5 min with the ambiguity-float solution and 21.5 min with the ambiguity-fixed solution, which are shortened by 4.5 min and 5.5 min as compared to those of the standard PPP-RTK model, respectively. As for the static positioning mode, the 90% 3D convergence time of the tropospheric-weighted model for the ambiguity-float and -fixed solutions is 25.5 min and 15 min, while the 3D convergence time is 31.5 min and 18.5 min for the standard PPP-RTK model, respectively. The results also show that the tropospheric-weighted model can still work well in a 5 cm convergence threshold.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.

HGPT2: An ERA5-Based Global Model to Estimate Relative Humidity

The neutral atmospheric delay is one of the major error sources in Space Geodesy techniques such as Global Navigation Satellite Systems (GNSS), and its modeling for high accuracy applications can be challenging. Improving the modeling of the atmospheric delays (hydrostatic and non-hydrostatic) also leads to a more accurate and precise precipitable water vapor estimation (PWV), mostly in real-time applications, where models play an important role, since numerical weather prediction models cannot be used for real-time processing or forecasting. This study developed an improved version of the Hourly Global Pressure and Temperature (HGPT) model, the HGPT2. It is based on 20 years of ERA5 reanalysis data at full spatial (0.25° × 0.25°) and temporal resolution (1-h). Apart from surface air temperature, surface pressure, zenith hydrostatic delay, and weighted mean temperature, the updated model also provides information regarding the relative humidity, zenith non-hydrostatic delay, and precipitable water vapor. The HGPT2 is based on the time-segmentation concept and uses the annual, semi-annual, and quarterly periodicities to calculate the relative humidity anywhere on the Earth’s surface. Data from 282 moisture sensors located close to GNSS stations during 1 year (2020) were used to assess the model coefficients. The HGPT2 meteorological parameters were used to process 35 GNSS sites belonging to the International GNSS Service (IGS) using the GAMIT/GLOBK software package. Results show a decreased root-mean-square error (RMSE) and bias values relative to the most used zenith delay models, with a significant impact on the height component. The HGPT2 was developed to be applied in the most diverse areas that can significantly benefit from an ERA5 full-resolution model.