# Evaluation of the GPS Precise Orbit and Clock Corrections from MADOCA Real-Time Products
## 6 PPP Validation  
To further verify the quality of current MADOCA real-time products from a practical perspective, PPP experiment was performed using the RTKLIB software developed by Dr. [PERSON] [29]. GPS observation data of 20 globally distributed IGS stations on 11 November 2018 (DOY 315) were collected for testing with a sampling rate of 30 s. The geographical location of the selected stations for this PPP experiment is shown in Figure 9. In the data processing, the kinematic PPP algorithm provided in the RTKLIB software was applied to process GPS dual-frequency ionospheric-free combination data. To simulate real-time kinematic processing, the forward Kalman filter method was used for PPP validation. The station coordinates provided by the IGS weekly SINEX file (i.e., igs18 Pweek.snx) were used as the reference in the positioning error calculations except for the PGEN and MAYG stations. Since there were no precise coordinate messages for these two stations in the IGS SINEX file for the testing periods, the reference coordinates of PGEN and MAYG stations were derived from post-processing of static PPP using IGS final products.  
Five of the 20 stations were selected to present the accuracy of positioning errors. Their geographical locations have been marked by orange dots in Figure 9. Figure 10 shows the positioning error of the five stations in which the east, north, and up components are denoted by blue, red, and yellow lines,  
Figure 8: Daily RMS of orbit-error-only SISRE and SISRE of MADOCA real-time products for all available GPS satellites relative to IGS final products from 1 January 2018 to 31 December 2018.  
Figure 9: The distribution of 20 IGS stations for PPP validation.  
respectively. As seen from Figure 10, the positioning errors of the five stations vary within \(\pm\)10 cm in the horizontal components and are stable after the convergence/initialization period. For the up component, the positioning errors exhibit more remarkable fluctuation compared to the horizontal components that can even reach up to 15 cm for some epochs, especially a few jumps at the PGEN station. This phenomenon may be explained by the lower accuracy of the clock products in the corresponding epochs.  
Moreover, the statistics of convergence time for all 20 stations are summarized in Figure 11. We consider the positioning results to be convergent when both horizontal and vertical positioning errors are less than 15 cm over consecutive 20 epochs. From Figure 11, the convergence time of all stations is within 80 min, and the average convergence time is 40 min.  
Figure 11: The convergence time for the 20 global distributed IGS stations.  
Figure 10: An example of time series of PPP positioning errors on 11 November 2018 for the five IGS stations using the MADOCA real-time product.  
Subsequently, the daily RMS values of positioning errors in the east, north, up, and 3D directions for the 20 stations are calculated and depicted in Figure 12. It should be noted that the positioning results after 360 epochs (with a sampling rate of 30 s) were used for the daily RMS calculation to avoid the influence of convergence/initialization time on the positioning accuracy evaluation. After filter convergence, it is shown in Figure 12 that the real-time kinematic positioning accuracy using MADOCA real-time products is at centimeter level for horizontal direction and 1 decimeter for up direction, which may be attributed to MADOCA real-time 30-s high sampling rate orbit and clock products. The daily RMS values of all selected stations can reach 4.9, 4.2, 11.7, and 12.1 cm in the east, north, up, and 3D directions, respectively. This means that the current MADOCA real-time products can meet the accuracy requirements of the PPP solution and also demonstrate the validity and authenticity of the above-mentioned orbit and clock products evaluation work.