## 2 BDS/GNSS for Earth Observations
### GNSS Positioning
Additionally, two distinct tropospheric models were evaluated: the estimated ZTD (Zenith Topospheric Delay) model and the traditional Saastamoinen model. The findings indicated a significant improvement in the performance of GNSS combinations (including single systems such as Galileo-only, GLONASS-only, and GPS-only, as well as dual combinations like GLONASS + GPS, Galileo + GPS, Galileo + GLONASS, and the triple combination of Galileo + GLONASS + GPS) relative to single-GNSS scenarios [12]. Some comparisons between NRTK, PPP, and static surveys (using the latter as a reference), using some benchmark points, were presented in [13]. NRTK positioning was achieved by different methods (VRS and FKP), while PPP solutions were computed with two types of software (CSRS, version 3 and RTKLib). A thorough statistical analysis was conducted to determine whether the frequency distribution of the residuals of the coordinates aligned with a normal distribution across all tested pairs. The findings indicated that the normal distribution hypothesis was supported in the majority of comparisons. Specifically, the Static-versus-NRTK pairs exhibited the highest level of consistency, while the pairs generated with the CSRS software demonstrated better consistency when compared to those derived from the RTKLIB software, based on the PPP solutions [13; 14; 15]. GNSS PPP is commonly utilized because of its affordability and the possibility of quick implementation. Currently, the observation models commonly used in PPP can generally be separated into two main sections: combined and non-combined models. Combined models include the ionosphere-free combination model and the UofC model, while non-combined models are based on original GNSS observations. The conventional ionosphere-free (IF) synthesis of dual-frequency measurements effectively eliminates the first-order ionospheric delay, thereby greatly minimizing the effect of ionospheric delay on GNSS measurements. As a result, this synthesis is widely utilized in PPP for positioning solutions. The observation equation can be articulated as follows [16; 17]. \[\mathrm{P}^{\mathrm{s}}_{r,j}=\frac{{\mathrm{f_{1}}}^{2}}{{\mathrm{f_{1}}}^{2 }-{\mathrm{f_{2}}}^{2}}\mathrm{P}_{1}-\frac{{\mathrm{f_{2}}}^{2}}{{\mathrm{f_{1 }}}^{2}-{\mathrm{f_{2}}}^{2}}\mathrm{P}_{2}=\rho^{\mathrm{s}}_{r,j}+\mathrm{c} (\mathrm{dt}_{\mathrm{r}}-\mathrm{dt}_{\mathrm{s}})+t^{\mathrm{s}}_{r,j}+ \mathrm{\varepsilon}^{\mathrm{s}}_{\mathrm{p},j} \tag{3}\]  
\[\mathcal{O}^{\mathrm{s}}_{r,j}=\frac{{\mathrm{f_{1}}}^{2}}{{\mathrm{f_{1}}}^{ 2}-{\mathrm{f_{2}}}^{2}}\mathcal{O}_{1}-\frac{{\mathrm{f_{2}}}^{2}}{{\mathrm{f _{1}}}^{2}-{\mathrm{f_{2}}}^{2}}\mathcal{O}_{2}=\rho+\mathrm{c}(\mathrm{dt}_ {\mathrm{r}}-\mathrm{dt}_{\mathrm{s}})+t^{\mathrm{s}}_{r,j}+\lambda_{j}\cdot N ^{\mathrm{s}}_{r,j}+\mathrm{\varepsilon}^{\mathrm{s}}_{\mathcal{O}j} \tag{4}\]  
where \(\mathrm{P}^{\mathrm{s}}_{r,j}\) is the pseudorange measurement, \(\mathcal{O}^{\mathrm{s}}_{r,j}\) refers to the carrier-phase measurement, c is the speed of light in a vacuum, \(\rho^{\mathrm{s}}_{r,j}\) represents the distance between the receiver and the satellite, \(t^{\mathrm{s}}_{r,j}\) refers to tropospheric delay, \(dt_{\mathrm{r}}\) is the receiver clock error, \(dt_{s}\) is the satellite clock error, \(\lambda_{j}\) is the carrier wavelength, and \(N^{\mathrm{s}}_{r,j}\) is the integer ambiguity. The frequencies associated with the L1 and L2 carrier-phase measurements are \(f_{1}\) and \(f_{2}\). Finally, \(\mathrm{\varepsilon}^{\mathrm{s}}_{\mathrm{p},j}\) and \(\mathrm{\varepsilon}^{\mathrm{s}}_{\mathcal{O}j}\) represent the noise in both the pseudorange and carrier-phase observations. In recent years, with the processing of GNSS, both the ionosphere-free model and the UofC model have been expanded to handle multi-frequency signals with achieving excellent results. The UofC model is another type of observation that eliminates ionospheric effects through a combination-based method, as proposed by the University of Calgary, Canada [18].