## 4 Results
### Signal Degradation Due to Reflective Environment  
Data collected from the GNSS receiver on the excavator was post processed using GipsyX software version 2.3 to generate pseudorange residuals of the code signal using the Ionosphere-free combination of dual frequency GNSS during the stationary period.  
Figure 9 shows the post processed code residuals for GPS using the traditional and the modern GPS signals. One can easily notice the improvement in the performance using the modern L2C GPS signal.  
Due to reflective environments, GNSS signals become degraded due to multi-path. But signal degradation is also possible over sharp metallic edges such as that of the roof of the house to the left of the excavator shown in Figure 1c. In such cases, the GNSS signal diffracts or bends over the edge, thus traversing a longer path length than the direct line-of-sight path length and degrading the position computation of the receiver. Thus, the GNSS signal becomes available even in shadowed and non-line-of-sight regions. In order to demonstrate such an effect of signal bending due to reflective environments in the near vicinity of the antenna, controlled experiments were carried out both using the Leica AS10 and high-grade geodetic antenna, as shown in Figure 10a,b.  
Figure 8: Skyplots for different code signals of Galileo satellites during the stationary period: (**a**) C1C and (**b**) C7Q.  
Figure 7: Skyplots for different code signals of all affected GPS satellites (G04, G07, G09, G10, G14, G18, G23 and G29) during the stationary period: (**a**) C2W and (**b**) C2L.  
Figure 10: _Cont._  
Figure 9: GipsyX code residuals using the Ionosphere-free combination of dual frequency GPS. (**a**) Using C1C and C2W; (**b**) using C1C and C2L.  
Figure 10c shows a plot of the pseudororange residuals using dual frequency GNSS measurements. The colour bars in Figure 10c-e indicate values of these residuals in mm. The enhanced values of residuals noted at low elevations and an azimuth of 225\({}^{\circ}\) to 360\({}^{\circ}\) is the effect of signal degradation due to bending over a steel edge, marked with the green dashed line in Figure 10b. The signal diffraction model of Figure 10f is used to estimate the residuals. From Figure 10f, the vertical height of the obstruction is dv and the horizontal distance to the obstruction from the receiver antenna is dh. Thus, for any elevation angle \(\varepsilon\), at a given azimuth angle, the path length difference (\(R\)-\(R_{0}\)) can be estimated using the following equations.  
\[b=dv-dh\cdot\tan(\varepsilon) \tag{1}\]  
\[R=\sqrt{\left(dv^{2}+dh^{2}\right)} \tag{2}\]  
\[R_{0}=\sqrt{\left(\left(dh\cdot\tan(\varepsilon)\right)^{2}+dh^{2}\right)}+c \quad where\quad c=b\cdot\sin(\varepsilon) \tag{3}\]  
Variations in dh for varying azimuth angle \(\alpha\) can be computed as shown in Figure 10a. A plot of the modelled residuals based on these estimations is shown in Figure 10d. Figure 10e is the plot of the corrected residuals. GNSS signals can also be degraded due to metallic surfaces causing reflections. Such effects are expected to degrade the GNSS signal received on the antenna over the excavator, resulting in erroneous positioning performance.  
Figure 10: Demonstration of signal degradation due to reflective environments. (**a**) Antenna environment. (**b**) Signal diffraction over metallic edges. (**c**) GPS/GLONASS/Galileo L1/E1 and L2/E5a range residual plots. (**d**) Estimations using a diffraction model. (**e**) Corrected measurements using the model. (**f**) Signal diffraction model (plot dynamics \(\pm\) 20 mm).  
The signal bending effect as well as signal degradation due to reflective environments will be studied as future work to this paper.