# Utilization of Quasi-Zenith Satellite System for Navigation of a Robot Combine Harvester
## 2 Materials and Methods
### Static Experiment  
In this study, the Trimble SPS855 receiver used the RTK positioning technique. Both the CLAS and MADOCA positioning augmentation systems were provided with the Magellan MJ-30008-GM4-QZS receiver. Each receiver was connected to the PC through serial port in order to log the positioning data obtained from the NMEA messages. The position data of each one of the GNSS receivers were logged at the same exact location and were stored in the PC at a rate of 10 Hz. A simple activation test was performed on each of the receivers at the experimental location before the experiments under static conditions. The test consisted of powering on each receiver and recording the convergency time; this means, the time each receiver takes to achieve its RTK fixed status. Please note that the Magellan MJ-3008-GM4-QZS receiver can only achieve RTK float status when using the MADOCA positioning augmentation system. An additional reactivation time test was also performed. This test consisted of disconnecting the receiver antenna, waiting for the positioning signal to drop and then reconnecting the antenna. The time it took each receiver to achieve its enhanced positioning status after this antenna disconnection and reconnection was also recorded. This test is relevant because sometimes in field conditions the GNSS signal might drop due to external factors, so it is necessary to know an estimation of how much time does the receiver needs to recover from a sudden signal loss. The time of the activation tests and the reconnection tests was recorded using the timestamp from the PC and it was estimated from the average of ten different measurements. The standard deviation, and the minimum and maximum values were calculated and helped to verify that measuring more times would not evidence any different behavior. Please note that the receiver using the CLAS positioning augmentation system cannot achieve RTK fixed status automatically after disconnecting the antenna or after powering on the receiver, it needs to be set up manually again. Therefore, the reactivation time is omitted because it would be the same as the activation time. The experiments under static conditions were conducted at the experimental farm of Hokkaido University, Hokkaido, Japan, between June of 2019 and January of 2020. The experimental location was an open sky environment, meaning there were no sight-blocking buildings or trees. Each one of the receivers was tested individually using their own antenna, these receiver antennas were mounted on a tripod stand at a height of 1.2 m above the ground surface. One post hole of the experimental location was selected as a ground landmark. For each experiment, a brass plumb bob was used to set the tripod in the exact same central position of the landmark. This simple procedure guarantees that the two different receivers are measuring the very same spot. The experiment took six hours, starting at 10:00 and finishing at 16:00 (UTC+9 Time). There are different methods for determining the accuracy the accuracy of a GNSS under static conditions [19]. The most used are the twice distance root mean square (2 DRMS) and the circular error probability (CEP). The 2 DRMS accuracy indicates that the measured position will be within the stated distance from the true position 95% of the time. It is given by Equation (1):  
\[2 DRMS=\sqrt{\left(\sigma_{E}^{2}+\sigma_{N}^{2}\right)} \tag{1}\]  
where \(\sigma_{E}\) is the Standard deviation of the easting values and \(\sigma_{E}\) is the standard deviation of the northing values. The \(CEP\) is the radius of a circle containing 50% of the horizontal position measurements reported by the GNSS receiver. It is given by Equation (2):  
\[CEP=0.59(\sigma_{E}+\sigma_{N}) \tag{2}\]  
However, the \(2 DRMS\) and the \(CEP\) are good accuracy estimators under some conditions; namely if the measured position points have a normal distribution towards a central point [20].