Global Navigation Satellite System (GNSS) ultra-rapid orbit is critical for geoscience and real-time engineering applications. To improve the computational efficiency and the accuracy of predicted orbit, a parallel approach for multi-GNSS ultra-rapid orbit determination is proposed based on Message Passing Interface (MPI)/Open Multi Processing (OpenMP). This approach, compared with earlier efficient methods, can improve the efficiency of multi-GNSS ultra-rapid orbit solution without changing the original observation data and retaining the continuity and consistency of the original parameters to be estimated. To obtain high efficiency, three steps are involved in the approach. First and foremost, the normal equation construction is optimized in parallel based on MPI. Second, equivalent reduction of the estimated parameters is optimized using OpenMP parallel method. Third, multithreading is used for parallel orbit extrapolation. Thus, GNSS ultra-rapid orbit determination is comprehensively optimized in parallel, and the computation efficiency is greatly improved. Based on the data from MGEX and IGS stations, experiments are carried out to analyze the performance of the proposed approach in computational efficiency, accuracy and stability. The results show that the approach greatly improves the efficiency of satellite orbit determination. It can realize 1-h update frequency for the multi-GNSS ultra-rapid orbit determination using 88 stations with four-system observations. The accuracy of the GPS, GLONASS, Galileo and BDS ultra-rapid orbit with 1-h update frequency using the parallel approach is approximately 33.4%,31.4%,40.1% and 32.8% higher than that of the original orbit, respectively. The root mean squares (RMS) of GPS, GLONASS, Galileo and BDS predicted orbit are about 3.2 cm, 5.1 cm, 5.6 cm and 11.8 cm. Moreover, the orbit provided by the proposed method has a better stability. The precision loss of all parallel optimization can be negligible and the original correlation between the parameters is fully preserved.

To obtain high-accuracy post and real-time precipitable water vapor (PWV) with simple process when the measured meteorological parameters are unavailable, a grid direct conversion model of zenith tropospheric delay (ZTD) and PWV in tropical regions (named CZP) is proposed with the consideration of the characteristics of spatiotemporal changes based on ERA5 reanalysis data from 2016 to 2019. The results show that the CZP model has good performance at each grid points compared with ERA5 PWV. The comparison results with the GNSS PWV of 61 IGS stations in tropical regions show that the mean bias and root mean square (RMS) of CZP GNSS PWW are no more than 1.1 mm and 1.4 mm, respectively. Furthermore, the CZP GNSS PWV at the co-located stations demonstrates a remarkable correlation with the radiosonde PWV (RS PWV) with the mean correlation coefficient of 0.93 and the bias and RMS of CZP GNSS PWV with respect to RS PWV are 1.61 mm and 3.11 mm, respectively. Additionally, the real-time CZP PWV is compared with the PWV based on GPT3 model with respect to RS PWV after the real-time GNSS ZTD are estimated by Precise Point Positioning (PPP). The results indicate that the real-time CZP PWV has higher accuracy with mean bias and RMS of -0.55 and 3.55 mm, respectively. The above results verify the high accuracy and feasibility of the CZP model for retrieving post and real-time PWV in the absence of measured meteorological data.