## 2 Materials and Methods
### Precise Point Positioning (PPP) Technique  
The use of PPP in GNSS research is growing in interest since it has a high accuracy and the benefit of not needing base stations. The basis of the PPP technique was established with the publication by [PERSON] [37]. The first study on using PPP with GPS technology was conducted by [PERSON] et al. in 1997 [38]. The PPP technique has been widely used in agriculture [39], seismic [40; 41; 42], structural health monitoring [43], atmospheric [44], and so on. The PPP technique is also used in areas where atmospheric and environmental conditions are challenging for studies, such as the polar regions [45]. Worldwide positioning is made possible by this technique, which does not require additional GNSS infrastructure (Figure 1). Utilizing a single receiver, the PPP technique uses single or multifrequency GNSS data to estimate 3D coordinates, precise satellite orbit, clock products, and code/phase biases in real-time or post-process. The raw pseudo-range and carrier phase observation equations can be expressed as [46]  
\[P_{r,f}^{s}=\rho_{r}^{s}+dt_{r}-dt^{s}+dT+a_{f}\cdot dI_{r,1}^{s}+D_{r,f}-D_{f} ^{s}+\varepsilon_{P_{f}} \tag{5}\]  
\[\Phi_{r,f}^{s}=\rho_{r}^{s}+dt_{r}-dt^{s}+dT-a_{f}\cdot dI_{r,1}^{s}+\lambda_{ f}\Big{(}N_{r,f}^{s}+B_{r,f}-B_{f}^{s}\Big{)}+\varepsilon_{\Phi_{f}} \tag{6}\]  
\[\rho_{r}^{s}=\sqrt{\big{(}x^{s}-x_{r}\big{)}^{2}+\big{(}y^{s}-y_{r}\big{)}^{2} +\big{(}z^{s}-z_{r}\big{)}^{2}} \tag{7}\]  
where the subscript \(f=(1,\,2,\,3,\cdots)\) relates to a specific carrier frequency, superscript \(s\) refers to satellites; \(\rho_{r}^{s}\) indicates the geometric distance between the satellite \((x^{s},y^{s},z^{s})\) and receiver \((x_{r},y_{r},z_{r})\); \(dt_{r}\) and \(dt^{s}\) are the clock errors of receiver and satellite; \(dT\) is the slant tropospheric delay; \(dI_{r,1}^{s}\) is the slant ionospheric delay on the first carrier frequency and \(a_{f}=\lambda_{f}^{2}/\lambda_{1}^{2}\) is the carrier frequency-dependent factor; \(D_{r,f}\) and \(D_{f}^{s}\) are the receiver and satellite-specific code hardware delays; \(\lambda_{f}\) and \(N_{r,f}^{s}\) are the wavelength in meter and integer ambiguity in cycle; \(B_{r,f}\) and \(B_{f}^{s}\) are the receiver-dependent and satellite-dependent uncalibrated phase delays; \(\varepsilon_{P_{f}}\) and \(\varepsilon_{\Phi_{f}}\) are the pseudo-range and carrier phase measurement noise, respectively [47]. Figure 1: The basis of globally operating PPP. The ionospheric-free combination is commonly employed in GNSS dual-frequency PPP in order to remove the impact of the first-order ionospheric delay. \[ \begin{split} P^{s}_{r,IF}=\rho^{s}_{r}+dt_{r}-dt^{s}+dT+D_{r,IF}-D^{ s}_{IF}+\varepsilon_{P_{IF}}\\ \Phi^{s}_{r,IF}=\rho^{s}_{r}+dt_{r}-dt^{s}+dT+\lambda_{IF}\Big{(}N ^{s}_{r,IF}+B_{r,IF}-B^{s}_{IF}\Big{)}+\varepsilon_{\Phi_{IF}}\end{split}  \tag{8}\]  
It is conventional to utilize precise orbit \((x^{s},y^{s},z^{s})\) and \(\left(dt^{s}+D^{s}_{IF}\right)\) clock products from the IGS analysis center for the purpose of resolving satellite orbit and clock errors. Furthermore, the uncalibrated phase delays are inseparably associated with integer ambiguity. Equation (8) is consequently re-parameterized, and the error equation is expressed as follows:  
\[ \begin{split} r_{P_{IF}}=\rho^{s}_{r}+\overline{d}t_{r}+\left(dt ^{s}+D^{s}_{IF}\right)+dT-P^{s}_{r,IF}\\ r_{\Phi_{IF}}=\rho^{s}_{r}+\overline{d}t_{r}+\left(dt^{s}+D^{s}_{IF} \right)+dT+\lambda_{IF}\overline{N}^{s}_{r,IF}-\Phi^{s}_{r,IF}\end{split}  \tag{9}\]  
Estimable parameters include receiver position \((x_{r},y_{r},z_{r})\), clock error \(\overline{d}t_{r}\), tropospheric delay \(dT\), and ambiguity \(\overline{N}^{s}_{r,IF}\).