## 3 Results
### Performance of Multi-System PPP with Precise Products from Different Analysis Centers
#### 3.4.2 Static Position Solutions  
In order to show more details of the position solutions, we select the static positioning results at the station KIR0 on 17 May 2020 (DOY 138 of 2020) using ESA final products as an example, and the epoch-wise position errors for the four single-system cases and the five-system combination case are illustrated in Figure 10. The static GRECJ-PPP can achieve a centimeter-level positioning accuracy within only several minutes. The main difference of static position errors among different cases lies in the first six hours, and then the four single-system cases can almost achieve the same positioning accuracy as GRECJ-PPP. Table 9 provides the statistical positioning accuracy and convergence time of post-processed PPP with WHU products for different system combinations in the static mode, while Tables 10 and 11 show the corresponding statistics using GFZ and ESA products, respectively. It should be noted that all the following statistics are only valid for the long-term performance of PPP. The positioning accuracy does not exhibit significant difference for different system combination cases, and the difference of positioning accuracy among different combination cases is smaller than 0.4, 0.2 and 0.5 cm in the east, north and up directions, respectively. The positioning accuracy of post-processed GRECJ-PPP with WHU, GFZ and ESA precise products in the east/north/up directions is 0.3/0.2/1.1, 0.3/0.3/1.1 and 0.2/0.2/1.0 cm, respectively. Different from the positioning accuracy, there is obvious difference in the convergence time for different combination cases. Due to the increased satellite number and improved satellite geometry, multi-system integration can shorten the convergence time. Compared with R-PPP, E-PPP and C-PPP, the improvement on the convergence time is 53%/57%/53%, 22%/47%/47% and 41%/58%/38% for the cases using WHU products, 48%/49%/47%, 28%/34%/42% and 44%/53%/39% for the cases using GFZ products, and 59%/64%/52%, 39%/37%/46% and 55%/62%/44% for the cases using ESA products, after an integration with GPS in the east/north/up directions, respectively. \begin{table}
\begin{tabular}{l l} \hline
**Items** & **Strategies** \\ \hline Observations & Code and carrier phase observations \\ Signal selection & GPS: L1/L2, QZSS: L1/L2, GLONAS: G1/G2, Galileo: E1/E5a, BDS: B1/B3 \\ Cut-off elevations & 10 \\ Sampling rate & 30 s \\ Estimator & Kalman filter \\ Weighting scheme & Elevation-dependent weight \\ Phase wind-up effect & IERS conventions 2010 \\ Earth rotation parameters & Fixed to a priori values (with the products from multi-system analysis centers) \\ Relativistic effect & IERS conventions 2010 \\ Station displacement & Solid Earth tide, Ocean tide, Pole tide, IERS conventions 2010 \\ Satellite orbits and clocks & Fixed with precise products from multi-system analysis centers \\ Satellite: corrected with IGS14 atx file (using suggested values by ESA for BDS for PPP \\  & processing with ESA products)Receiver: corrected with IGS14 atx file (using GPS values for other systems if not available) \\  & corrected using Saastamoin model \\  & Estimated as random walk process (epoch-by-epoch) \\ Ionospheric delay & First-order effect eliminated by IF linear combination \\ Phase ambiguity & Estimated as float constants \\ Receiver position & Estimated as constants in static mode, and as white noise process in kinematic mode \\ Receiver clock & Estimated as white noise process \\ Inter-system bias & Estimated as random walk process \\ \hline \end{tabular}
\end{table} 
Table 8: Processing strategies for PPP.