## 2 Materials and Methods
### RSSI Localization
#### 2.4.3 Field Test of the Intelligent Off-Road Vehicle  
The three criteria used for choosing the test plot were the following: (1) the plot was nearly flat; (2) the plot was sufficiently large for five 20 m rows; and (3) the plot was within range of the base station used in the experiment.  
A static test was performed on top of an approximately 20 m-long building with an open sky. As a dynamic test, the correction signal was measured for 30 min at different times of days on three days within the same week. According to the manufacturer [12], this testing procedure would provide exposure to a sufficient range of satellite constellation to estimate the GNSS system accuracy.  
Each dynamic test consisted of five 20 m passes following straight-line paths (Figure 5). The geospatial location of two points (A and B) at both ends of each straight line was determined with an RTK-GNSS receiver using a handheld surveying system interfaced to an RTK-GNSS rover (Trimble model Bx982). The GNSS coordinates for points A and B were obtained by placing the bottom of a 2 m survey pole with a GPS antenna attached at the top on the soil surface and holding the pole vertically using the aid of a bubble level. A WGS 84 Datum was used during all the RTK-GNSS measurements. The position of points A and B were obtained for two purposes: (1) to establish the straight line paths for the autonomous tractor and (2) to mark straight lines on the ground. All passes were traversed at a speed of 2.5 km h\({}^{-1}\). In this experiment, the RTK-GNSS signal was provided by the base station.  
The following raw GNSS data were recorded for all the dynamic tests performed with the autonomous tractor: the UTC time, longitude, latitude, height, velocity, quality of GNSS, PDOP, heading and number of satellites. Only the time, longitude, latitude and heading were used in the accuracy analysis. A program implemented in LabVIEW (National Instruments, Austin, TX, USA) was used to convert the geographic data into UTM coordinates. To determine the accuracy of the intelligent off-road vehicle path with respect to the prescribed path, the single-point cross-track error (XTE) was used, which is defined as the perpendicular distance along the ground from the straight line AB to each error measurement. Measurements were taken every 0.2 m within the ideal straight line path. The total XTE was calculated using the root mean squared (RMS) error of all the single-point XTEs along the length of the straight line [13]. The cross-track error is a useful value that measures the potential skip or overlap between passes of an agricultural vehicle through a field.  
For each pass, the RMS error was calculated using the following equations:  
\[\epsilon\ {}_{\mathrm{RMS}_{i}}=\sqrt{\frac{1}{N_{{}_{t}}}\sum_{i=1}^{N_{{}_{t}}} e_{{}_{i}}^{2}} \tag{1}\]  
\[e_{{}_{i}}^{2}=\left(x_{i}-x_{{}_{t}}\right)^{2}+\left(y_{i}-y_{{}_{t}}\right) ^{2} \tag{2}\]where \(RMS_{i}\) is the RMS error for the \(t\) th pass, \(N_{t}\) is the total number of measurement points for the \(t\) th pass, and \(e_{it}\) is the distance from the point \(i\) th point to the \(t\) th straight line path. For the statistical analysis, the errors were calculated for each measurement. The SAS general linear models procedure [14] was used to test for significant differences in the treatment (based on the RTK data) using an ANOVA. Statistics for the GNSS receiver position accuracy values in static tests were calculated using JMP [13].