## 2 Materials and Methods
### Five-System Integrated PPP Time Transfer Model
\begin{array}{l}{{p}_{IF,r}^{s,G}={\mu}_{r}^{s,G}\cdot x+cd{\overline{ t}}_{r}^{G}+{m}_{r}^{s,G}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,G}={\mu}_{r}^{s,G}\cdot x+cd{\overline{t}}_{r}^{G}+{m}_{r}^{s,G} \cdot Z_{r}+{\overline{N}}_{IF,r}^{s,G}}\\ {{p}_{IF,r}^{s,R}={\mu}_{r}^{s,R}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{IF,r }^{s,R}+{m}_{r}^{s,R}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,R}={\mu}_{r}^{s,R}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,R}+{m}_{r}^{s,R}\cdot Z_{r}+{\overline{N}}_{IF,r}^{s,R}}\\ {{p}_{IF,r}^{s,E}={\mu}_{r}^{s,E}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,E}+{m}_{r}^{s,E}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,C2}={\mu}_{r}^{s,C2}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,C2}+{m}_{r}^{s,C2}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,C2}={\mu}_{r}^{s,C2}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,C2}+{m}_{r}^{s,C2}\cdot Z_{r}+{\overline{N}}_{IF,r}^{s,C2}}\\ {{p}_{IF,r}^{s,C3}={\mu}_{r}^{s,C3}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,C3}+{m}_{r}^{s,C3}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,C3}={\mu}_{r}^{s,C3}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,C3}+{m}_{r}^{s,C3}\cdot Z_{r}+{\overline{N}}_{IF,r}^{s,C3}}\\ {{p}_{IF,r}^{s,I}={\mu}_{r}^{s,I}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,I}+{m}_{r}^{s,I}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,I}={\mu}_{r}^{s,I}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,J}+{m}_{r}^{s,I}\cdot Z_{r}}\\ {{p}_{IF,r}^{s,I}={\mu}_{r}^{s,I}\cdot x+cd{\overline{t}}_{r}^{G}+IS{p}_{r}^{ G,J}+{m}_{r}^{s,I}\cdot Z_{r}+{\overline{N}}_{IF,r}^{s,J}}\\ \end{array} \right. \tag{3}\]  
\[\left\{ \begin{array}{l}cd{\overline{t}}_{r}^{G}=cd{t}_{r}^{G}+{b}_{r,IF}^{G} +d{D}^{AC,G}\\ {IS{p}_{F}^{G,Q}=cd{t}_{r}^{G}-cd{t}_{r}^{G}+{b}_{r,IF}^{G}-{b}_{r,IF}^{G}+d{D} ^{AC,Q}-d{D}^{AC,G}}\\ {{\overline{N}}_{IF,r}^{s,Q}={N}_{IF,r}^{s,Q}+{B}_{r,IF}^{Q}+{B}_{IF}^{s,Q}-{b}_ {r,IF}^{Q}-{b}_{IF}^{s,Q}}\\ \end{array} \right. \tag{4}\]  
where \(G\), \(R\), \(E\), \(C2\), \(C3\), and \(J\) denote the GPS, GLONASS, Galileo, BDS-2, BDS-3, and QZSS, respectively, \(p\) and \(l\) denote the observed-minus-computed (OMC) values of code and phase observations, respectively, \(\mu\) denotes the unit vector in the direction from the receiver to the satellite, \(x\) represents the three-dimensional (3D) coordinates of the receiver, \(cd{t}_{r}^{G}\) is the receiver clock estimate including the receiver-dependent code hardware delay as well as the satellite clock datum of GPS, \(IS{B}_{r}^{G,Q}\) denotes the ISB between GPS and other satellite systems, \({\overline{N}}_{IF,r}^{s,Q}\) is the phase ambiguity that loses its integer character after being mixed with various hardware delays, \(m\) indicates the wet mapping function, and \(Z\) denotes the tropospheric zenith wet delay (ZWD). To enhance the PPP time transfer, the station coordinates in the Solution Independent Exchange (SINEX) weekly solution files provided by the International GNSS Service (IGS) can be used as a priori constraints. The following pseudo-observation equation can be introduced into the observation model of PPP time transfer:  
\[x_{SNX}=x \tag{5}\]  
where \(x_{SNX}\) denotes the a priori receiver coordinates in three dimensions. The parameters that need to be estimated include the 3D coordinates of the receiver, receiver clock offset, ISB, tropospheric ZWD, and phase ambiguity, which can be expressed as:  
\[O=[x,cd{\overline{t}}_{r}^{G},IS{B}_{r}^{G,R},IS{B}_{r}^{G,E},IS{B}_{r}^{G,C2 },IS{B}_{r}^{G,C3},IS{B}_{r}^{G,J},Z_{r}, \tag{6}\]  
where \(O\) denotes the vector of estimates. In addition to a rigorous functional model, a suitable stochastic model is also crucial for high-accuracy PPP time transfer.