# Utilization of Quasi-Zenith Satellite System for Navigation of a Robot Combine Harvester
## 3 Results  
### Static Experiment  
Table 2 shows the results of the ten measurements of the activation time and the reactivation time as well as the different test dates for each one of the receivers. The minimum and maximum time values are also included in the Table 2, as well as the standard deviation. It can be observed that for each one of the receivers the ten different time measurements were almost the same, the minimum and maximum values show a difference of around one second. A low standard deviation close to 0.5 indicates that the values tend to be close to the mean (also called the expected value) of the set. Therefore, it is safe to consider the average time for comparison purposes. Concerning the activation time, the RTK positioning augmentation system achieved RTK fixed status on average in 14.2 s.  
The MADOCA positioning augmentation system can achieve RTK float status in 30 s on average. From the activation point of view, this is also a short time considering that by using the MADOCA mode this receiver does not require an NTRIP service provider. In contrast, the CLAS positioning augmentation system performs a little slower; it can achieve RTK fixed status in 128 s on average. Concerning the reactivation time in Table 2, the RTK and MADOCA show similar times compared to the activation time. The CLAS cannot achieve RTK fixed status automatically  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RTK (Real-Time Kinematic)**} & \multicolumn{2}{c}{**MADOCA**} & \multicolumn{2}{c}{**CLAS**} \\  & \multicolumn{2}{c}{**(2019/06/25)**} & \multicolumn{2}{c}{**(2019/07/08)**} & \multicolumn{2}{c}{**(2020/01/16)**} \\ \cline{2-7}
**Test Number** & \multicolumn{2}{c}{**Act. **} & \multicolumn{2}{c}{**React. **} & \multicolumn{2}{c}{**Act. **} & \multicolumn{2}{c}{**React. **} & \multicolumn{2}{c}{**Act. **} & \multicolumn{2}{c}{**React. **} \\  & **Time (s)** & **Time (s)** & **Time (s)** & **Time (s)** & **Time (s)** & **Time (s)** \\ \hline
1 & 13.9 & 13.4 & 31.5 & 43.7 & 127.1 & - \\
2 & 15.1 & 12.5 & 30.2 & 42.8 & 128.4 & - \\
3 & 13.7 & 12.3 & 29.5  
after disconnecting the antenna, it needs to be set up manually again. Therefore, the reactivation time is omitted because it would be the same as the activation time. Please remember that the RTK positioning system is used as the reference for comparison. However, even the RTK positioning system might show small variations in position over time [21]. Therefore, it is necessary to analyze the RTK variations to clarify whether variations during the comparison are caused by variations in the RTK reference or due to variations in the MADOCA or CLAS. Figure 5 shows the result from the static position experiment of the RTK positioning augmentation system. The plots are shown in UTM coordinates instead of latitude and longitude coordinates because it is easier to visualize the distance in meters than in degrees. Figure 5a shows that the position points logged by the RTK are scattered over a small area about 0.05 m by 0.06 m. Figure 5b confirms the shows that the RTK position data has small variations over time. Moreover, since the time series plots display an overall stability, it is possible to use the RTK mean position as an origin point for reference for comparison with either MADOCA or CLAS. In other words, the purpose of the mean position is to neglect small variations in position over time. The 2 DRMS calculated using Equation (1), and the CEP calculated using Equation (2) can be plotted as shown in Figures 5 and 6; the 2 DRMS is measured withing the circle in black while the CEP is the radius of the circle in green. Figure 6 provides an overview of the static positioning experiment. The plots are shown in UTM coordinates. The origin point (0,0) of both plots in Figure 6 is the mean point of the position data logged by the RTK. The purpose of using only the mean position data logged by the RTK is to neglect small variations in position over time. The red points represent the position points measured by the CLAS and MADOCA.