## 3 Satellite Signal Measurements in Various Weather Conditions
### Measurements, Data Conversion Techniques

Table 1: x, y coordinates with assigned time. Figure 3: Geographical coordinates conversion. They allowed determination of the assumed positions, and calculation of coordinates x2 and y2, by substituting x with specified time (see Table 2). Ad 4. The next step was to compare the obtained results with the measurement points read from the receiver. The arithmetic mean and the standard deviation were calculated to allow the comparison. Arithmetic mean was calculated based on Equation (7) [60]:  
\[S_{a}=\overline{x}=\frac{\sum_{k=1}^{n}x_{k}}{n} \tag{7}\]  
Standard deviation was calculated based on Equation (8) [60]:  
\[S=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}{n-1}} \tag{8}\]  
where  
\(x_{i}\)--individual measurements;  
\(\overline{x}\)--average value of measurements;  
\(n\)--number of measurements. Calculation of standard deviations, both of the measured points and the results obtained from the trend line, made the comparison of those values and estimation of the measurement error possible (see Table 3). \begin{table}
\begin{tabular}{c c c c} \hline
**Time [s]** & **y [km]** & **x [km]** & **y2 [km]** & **x2 [km]** \\ \hline
0 & \(-2579\),463661 & 4104,031343 & \(-2579\),5000 & 4091,687906 \\
17 & \(-2579\),510050 & 4104,031565 & \(-2579\),5374 & 4091,687905 \\
47 & \(-2579\),576051 & 4104,028103 & \(-2579\),6034 & 4091,687916 \\
77 & \(-2579\),640251 & 4104,025706 & \(-2579\),6694 & 4091,687923 \\
107 & \(-2579\),706555 & 4104,021771 & \(-2579\),7354 & 4091,687935 \\
137 & \(-2579\),772036 & 4104,019176 & \(-2579\),8014 & 4091,687942 \\
155 & \(-2579\),808401 & 4104,013526 & \(-2579\),8410 & 4091,687959 \\ \hline \end{tabular}
\end{table} 
Table 2: x2, y2 coordinates with assigned time. Figure 5: Geographical coordinates conversion, x axis. Ad 5. The difference in the average deviations shows the average error in position determination by the GNSS receiver. In the above example: the error along Y axis is very small = 0.000074336 km \(\approx\) 7.4 cm; the error along the X axis is equal to 0.00470937 km \(\approx\) 4.7 m. The last measurement cannot be considered satisfactory. The entire procedure was repeated for subsequent measurements on the following measurement days. The results obtained are shown in Table 4.  
The values for measurement numbers six, eight, and fourteen are missing. It was impossible to read the data from the receiver. It is likely that no satellites were visible at the right moment or the measurement input was set incorrectly. Generally, to sum this part up, it can be stated that position determination error varies. The lowest deviation value for Y axis is for measurement no 5: 0.00006751 km = 6.751 cm, and for X axis, measurement no 16: 0.00008695 km = 8.7 cm, which are perfect even for autonomous machines movements. On the other hand, the highest deviation for the Y axis is obtained for measurement no 18: 0.02027631 km = 20.28 m, and for X axis, measurement no 4: 0.03411303 km = 34.1 m, which is far from satisfactory! Did it depend on the weather conditions? Which component influenced the result the most? \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement Number** & **Deviation Difference along** & **Deviation Difference along** \\  & **Y axis [km]** & **X axis [km]** \\ \hline
1 & **0.000074336** & **0.00470937** \\
2 & 0.00373305 & 0.01089750 \\
3 & 0.00550258 & 0.01107862 \\
4 & 0.00330949 & 0.03411303 \\
5 & 0.00006751 & 0.00022016 \\
6 & - & - \\
7 & 0.01865231 & 0.000090735 \\
8 & - & - \\
9 & 0.00963509 & 0.00039513 \\
10 & 0.00526347 & 0.00680266 \\
11 & 0.00311555 & 0.00065142 \\
12 & 0.01557693 & 0.01631348 \\
13 & 0.01220545 & 0.00423828 \\
14 & - & - \\
15 & 0.00034146 & 0.00012886 \\
16 & 0.00041352 & 0.00008695 \\
17 & 0.00022089 & 0.00190523 \\
18 & 0.02027631 & 0.00084854 \\
19 & 0.00306734 & 0.00095147 \\
20 & 0.00499201 & 0.00350703 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Differences in the standard deviations for all measurements.