## 2 Methods
After fixing the satellite orbits with precise satellite orbit products, correcting the satellite clock offsets with precise satellite clock products, and correcting the tropospheric dry delay with a priori model, the linearized observation model of five-system integrated PPP can be described as:  
\[\left\{ \begin{array}{l}p_{IF,r}^{\rm S,G}=\mu_{r}^{\rm S,G}\quad x+cdt_{r}^{ \rm G}+m_{r}^{\rm S,G}\ Z_{r}\\ l_{IF,r}^{\rm S,G}=\mu_{r}^{\rm S,G}\quad x+cdt_{r}^{\rm S}+m_{r}^{\rm S,G}\ Z_{r}+ \end{array} \right.\]where \(p_{IF}\) and \(I_{IF}\) denote the observed-minus-computed (OMC) IF-based code and phase observables, respectively, \(\mu\) denotes the unit vector in the line-of-sight direction, \(x\) denotes the three-dimensional (3D) receiver coordinates, \(cdf^{G}_{r}\) denotes the estimated receiver clock offsets grouped with the receiver UCDs of GPS, \(m\) is the wet mapping function, \(Z\) is the tropospheric zenith wet delay (ZWD), and \(ISB^{G,O}_{r}\) denotes the ISB between the satellite systems \(Q(O\
otin G)\) and \(G\). The estimated parameters include receiver coordinates, receiver clocks, ISB, ZWD and phase ambiguities, that is:  
\[O=\left[x,cdf^{G}_{r},ISB^{G,R}_{r},ISB^{G,E}_{r},ISB^{G,C}_{r},ISB^{G,J}_{r}, Z_{r},\overline{N}^{s,G}_{IF,r},\overline{N}^{s,R}_{IF,r},\overline{N}^{s,E}_{IF,r}, \overline{N}^{s,C}_{IF,r},\overline{N}^{s,J}_{IF,r}\right] \tag{5}\]  
where \(O\) is the vector of estimates. In addition to the rigorous functional model, a proper stochastic model also plays a very important role in the data processing of PPP. It is assumed that the observations of different types (i.e., code and phase observations), from different satellites, or on different frequencies are independent. The variance of observations from a GNSS/RNSS satellite on a single frequency can be computed as follows:  
\[\sigma^{2}(ele)=k_{1}^{2}+k_{2}^{2}/\left(\sin(ele)\right)^{2} \tag{6}\]  
where \(ele\) is the satellite elevation angles, and the two terms \(k_{1}\) and \(k_{2}\) are constants, which are both set to 3 mm for phase observations. As for code observations, the ratio between the standard deviation (STD) of them and the phase observations is chosen as 100:1 for GPS, Galileo and OZSS satellites, 150:1 for GLONASS satellites, and 500:1 for BDS satellites [26]. It is important to notice that the observations of BDS geostationary orbit (GEO) satellites are further down weighted by a factor of ten times compared with the observations from other BDS satellites. For further analysis, we compare the positioning performance between the BDS-only static PPP (long-term performance of PPP) with a ratio of 100:1 and 500:1 based on the GFZ final precise products. The convergence time of BDS-only static PPP with a ratio of 100:1 can be increased by several minutes over the case with a ratio of 500:1, indicating that the code observations of BDS are poor, and thus the latter one is employed. According to the support of code observation types by the ground tracking stations, the code observations \"C1C\" and \"C2W\" on L1 and L2 frequencies for GPS, \"C1P\" and \"C2P\" on G1 and G2 frequencies for GLONASS, \"C1C\" and \"C5C\" (or \"C1X\" and \"C5X\") on E1 and ESA frequencies for Galileo, \"C2I\" and \"C6I\" on B1 and B3 frequencies for BDS, and \"C1C\" and \"C2L\" (or \"C1C\" and \"C2X\") on L1 and L2 frequencies for QZSS are adopted in this study, respectively. The above code observation types are defined in Receiver Independent Exchange (RINEX) version 3.04. It should be noted that the setting for the variance of code observations shown in Equation (6) for the five satellite systems is rough, and a precise setting should be further investigated. [PERSON] [27] proposed a method about the precise setting for the variance of code observations, which may be used to further refine the stochastic model.