# Utilization of Quasi-Zenith Satellite System for Navigation of a Robot Combine Harvester
## 3 Results
### Static Experiment
The blue points represent the mean of the position points. The CLAS position points are scattered over an area about 0.25 m by 0.50 m and they are uniformly grouped inside this area shown in Figure 6a. The sudden oscillations or instabilities are not too big as shown by the mean position which is centered in the cloud of position points. From Figure 6b, the MADOCA position points are scattered over an area of about 0.70 m by 0.70 m and display a loop inside this area, which accounts for the instability of this positioning augmentation system. However, the mean position is inside the area where the position points are dense, although it is not as good as the CLAS mean position. The 2 DRMS and the CEP circles in Figure 6 are smaller for the CLAS in comparison with the MADOCA, which is an expected result caused by the size of the area of the position points measured. Table 3 list the 2 DRMS, the CEP and the average number of satellites Tracked during the test for each one of the receivers. It can be observed that the CLAS positioning augmentation system has a reasonably small 2 DRMS and CEP; although they are around four times bigger than the RTK results, they are still less than 0.05 m. In the other hand, the MADOCA positioning augmentation system displays 2 DRMS and CEP about 10 times bigger than the RTK. Although Figure 6 provides an overview of the static positioning experiment, it is not possible to see how the measurements behave over time. The data summarized in Table 3 gives a good accuracy analysis for the total length of the static positioning experiments but provides no information for a specific time. Therefore, Figure 7 shows the position data logged by the CLAS and MADOCA from the static positioning experiments plotted against time in easting and northing coordinates. For the CLAS, there is a small oscillation of around 0.20 m in the northing coordinate during the first hour, the position data becomes stable since the second hour until the end of the experiment. However, the position data in the easting coordinate converges to an approximately constant value within a 0.10 m range and it is stable from the beginning to the end of the experiment. In contrast, the MADOCA has a big oscillation of almost 0.70 m in both the easting and northing coordinates during the first hour. The bias with respect to the reference measured by the RTK is around 0.40 m and it is not as constant as the CLAS bias during the six hours of the static positioning experiment. However, the oscillation gets smaller in the second hour, then the position data become stable since the third hour and it starts to converge to a range of 0.20 m for both the easting and northing coordinates. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Positioning** & **2 DRMS** & **CEP** & **No. of** & **N-S Offset** & **E-W Offset** & **RMS Error** \\
**System** & **(m)** & **(m)** & **Satellites** & **(m)** & **(m)** & **(m)** \\ \hline RTK & 0.010 & 0.008 & 14.6 & Ref. & Ref. & Ref. \\ MADOCA & 0.107 & 0.089 & 12.7 & \(-\)0.427 & 0.326 & 0.54 \\ CLAS & 0.041 & 0.034 & 11.0 & \(-\)0.447 & 0.352 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy analysis.