# Evaluation of the GPS Precise Orbit and Clock Corrections from MADOCA Real-Time Products
## 4 Orbit and Clock Evaluation
### Orbit/clock Statistic Accuracy Results  
Based on the concepts and algorithms described above, the short-term orbit difference between the MADOCA recorded real-time and IGS final products before and after Helmert transformation was determined from 11 November 2018 to 17 November 2018. The corresponding comparison results are collated in Figure 3. It shows the orbit comparison of all available GPS satellites between the MADOCA and IGS final products in radial and along/cross-track components before and after Helmert transformation. The different color points represent different GPS satellites. To quantify the orbit accuracy of each satellite in three directions, the seven-day RMS for each direction and three-dimensional (3D) RMS values are represented in Figure 4.  
As shown in Figure 3, the orbit errors in radial direction for all GPS satellites show better performance compared to the other two directions; the accuracy differences among the three components, however, are not significant. It can be seen from Figure 4 that the orbit errors of all available satellites in 3D component are within 5 cm, which basically meets the accuracy goals of MADOCA real-time products.  
In addition, special attention needs to be paid to the fact that all satellite orbit errors are improved after conducting the 7-parameters Helmert transformation, particularly in the radial direction, and which can be further verified from subsequent SISRE (orb) value plots. After the coordinate reference is unified, the average-RMS values of the MADOCA real-time orbits are roughly less than 2 cm in the three components and below 4 cm in the 3D direction.  
Figure 3: Time series of the MADOCA real-time GPS satellite orbit errors in radial and along/cross-track directions from 11 November 2018 to 17 November 2018.  
Afterwards, the IGS final clock products are utilized as reference to assess the quality of the GPS real-time clocks provided by MADOCA products. The STD values, rather than RMS, are taken as the evaluation indexes because the mean biases of GPS clock offsets can be absorbed by ambiguity parameters and will not affect the positioning results [23; 24]. Figure 5 shows the clock errors of all available GPS with respect to IGS products, and the average-STD of clock differences are given in Figure 6.  
As show in Figures 5 and 6, the various generations of GPS satellites exhibit the better consistency in clock accuracy, which will ultimately be reflected in the respective SISRE budgets. Again, one-day periodical variations are visible for almost all GPS satellites. For each GPS satellite, the averaged-STD value is typically better than 0.16 ns and most of them are at the 0.1 ns level, which confirms that the satellite clocks show a good short-term stability and are capable of achieving the accuracy at cm level in real-time applications.  
Figure 4: Seven-day average-RMS errors of all available GPS satellites in radial, along/cross-track, and three-dimensional (3D) directions.  
Figure 5: Time series of the MADOCA GPS satellite clock errors from 11 November 2018 to 17 November 2018.