# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
###### Abstract  
Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution. multi-GNSS; zenith tropospheric delays; GNSS meteorology; radiosonde; ERA5 2023315457 1 2  
signals [11], and estimate coordinate, clock, and atmospheric products [12; 13]. Experiment results showed that positioning precision and convergence rate can be improved by the integration of multiple GNSS systems with more visible satellites and observations when compared to the single-GNSS system [14; 15]. For example, [PERSON] et al. [16] designed a four-system GNSS model, which resulted in a convergence time reduction of 70% and an accuracy improvement of 25% when compared to the single-GNSS system solution. With multi-GNSS combined processing, ZTD can be obtained with better accuracy within several millimeters [17]. [PERSON] et al. [18] collected dual-frequency observations of GPS and BDS from some regions of China and compared BDS ZTDs with those of GPS. In [19], the authors showed that the accuracy of precipitable water vapor could be increased by a few millimeters when utilizing a GPS + BDS combined solution. The real-time water vapor of a four-system solution (GPS + BDS + Galileo + GLONASS) was also studied in [20] and demonstrated greater accuracy and stronger ZTD reliability when compared to the single-system solutions. [PERSON] et al. [21] used GPS and GLONASS observations to develop a tomography model and showed great potential in the study of water vapor profiles. [PERSON] et al. [22] estimated real-time ZTD using real-time satellite orbit and clock products and the results were more reliable and accurate than that of the single-GNSS system. [PERSON] et al. [23] developed multi-GNSS PPP ambiguity resolution for real-time ZTD retrieval which proved a great improvement in accuracy with respect to the Center for Orbit Determination in Europe, U.S. Naval Observatory products, and ECMWF data when compared to a GPS-only solution. [PERSON] et al. [24] analyzed the PPP performances of single-system and multi-GNSS combined PPP solutions and obtained a great improvement of the positioning accuracy and convergence by adding BDS-3 observations. The ZTD accuracy was improved by 20.5% when compared to the BDS-2. [PERSON] et al. [25] obtained the station coordinates by GPS, GPS + GLONASS, and GPS + GLONASS + Galileo + BDS combined solutions and the results showed that the ZTD differences between the three solutions were less than 20 mm. [PERSON] et al. [26] used a network-based real-time kinematic approach to estimate ZTD by measurements of four constellations: GPS, Galileo, GLONASS, and BDS satellites.