## 9 Performance Validation and Analysis
### High Dynamic Moving Scenario  
The most critical requirement for every GNSS receiver is the performance under high dynamics when moving in the severe surroundings. Examples of harsh surroundings are moving under trees, under elevated roads and in urban canyons with partial visible sky. High dynamic characterizes the condition when the Doppler shift may vary in the range of \(\pm 60\) kHz. Although this is difficult to  
Figure 8: Carrier-to-noise ratio of visible satellites (**a**) BeiDou (**b**) GPS.  
Figure 9: HRE of proposed estimator against LSE and WLSE.  
achieve in normal urban canyons, still at carrier-to-noise ratio of the order of 30-40 dB-Hz and sudden loss of tracking satellites make it challenging to maintain the navigation accuracy. The following scenario is designed to evaluate the dynamic performance of the proposed estimation procedure against classic LSE and WLSE algorithms. GNSS signal data is recorded in remote rural area near shanghai during driving on the road with antenna fixed on the roof of van. Ephemeris information and other navigation data is produced by offline processing of signal data.  
Experiment trajectory of vehicle is shown in Figure 10. The experiment route is designed so that there must be multiple full and partial sky visibility regions. Figure 11 illustrates the \(CNo\) of GPS satellites. As the \(CNo\) of satellites represent the signal characteristics, observations from the satellites, with unstable \(CNo\), can lead the estimator to wrong approximation.  
Figure 11: CNo of visible GPS satellites.  
Figure 10: Vehicle route for data logging (courtesy of Google Earth).  
Figure 12a shows the errors in the estimated position from LSE, WLSE and our proposed algorithms. As described before, there are several open sky and partial visible sky regions, mentioned with arrows. In Figure 12b, position errors for open sky are zoomed. Estimated positions errors, for the duration of driving under trees, are showed in Figure 13. From Figure 11b, it is found that the performance of three algorithms is similar under (LoS) line-of-sight signal propagation conditions such as open sky. In LoS conditions, signals are biased with Gaussian-only white noise, hence LSE showed high positioning accuracy.  
However, the circumstances are quite different for NLoS (non-line of sight) conditions i.e., driving under trees. During NLoS conditions, other than Gaussian errors are dominant such as multipath, signal diffraction or reflection etc. We cannot say that the standalone positioning accuracy of the proposed scheme is very high (Figure 13b), however there is a significant improvement in positioning accuracy in comparison to LSE and WLSE.  
Positioning error for moving scenario from three algorithms are analyzed in Table 5. Maximum and RMS (root mean square) position errors from the proposed estimation algorithm are significantly lower than LSE and WLSE. The maximum error are resulted when vehicle was moving under dense trees and majority of the received observations were corrupted.  
Figure 12: (**a**) Estimated position error from three algorithms; (**b**) estimated position error during open sky region (zoomed in).  
Figure 13: Estimated position errors when during driving under trees (zoomed in).