## 4 Results and Analyses
### Pedestrian Data in Urban Canyon  
As discussed in Section 3, GNSS data in harsh environments such as urban and natural canyons are significantly affected by multipath. A rough idea about these measurement discrepancies would be very helpful on analyzing the results. In this regard, the approximate range errors of all the GNSS measurements were computed using the procedure described in Appendix B. The range errors thus obtained for the OEM6 receiver in the urban canyon is depicted in Figure 8 as a function of time. It can be observed that the range errors are quite significant at many epochs, exceeding well over 100 m. The presence of NLOS multipath signals and signal fading can cause the receiver to generate such erroneous measurements through shift of the NCO and distortion of the correlation function. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & & **No Errors Added** & **Errors Added on \(\mathbf{\rho}\)** & **Errors Added on \(\mathbf{\rho}\) and \(\hat{\mathbf{\phi}}\)** \\ \hline \multirow{4}{*}{**RMSE (m)**} & \multirow{2}{*}{**N**} & **Hor** & 3.6 & 9.0 & 9.2 \\  & & **Vert** & 2.3 & 7.9 & 7.5 \\  & & **Hor** & 3.8 & 7.0 & 8.5 \\  & & **Vert** & 2.3 & 6.9 & 6.3 \\ \hline \multirow{4}{*}{**Reliability (\%)**} & \multirow{4}{*}{**N**} & **East** & 93.4 & 73.0 & 68.4 \\  & & **North** & 81.0 & 56.2 & 46.0 \\ \cline{1-1}  & & **Up** & 97.0 & 66.5 & 61.6 \\ \cline{1-1}  & & **East** & 72.3 & 71.9 & 70.0 \\ \cline{1-1}  & & **North** & 80.0 & 60.3 & 73.4 \\ \cline{1-1}  & & **Up** & 69.0 & 55.7 & 62.1 \\ \hline \end{tabular}
\end{table} 
Table 2: RMSE and reliability for open sky data. Figure 8: Range errors in urban canyon (OEM6). Additionally, the carrier to noise ratios (C/N\({}_{\rm o}\)) of available GNSS measurements are plotted in Figure 9 and show low values for many measurements in the middle section of the test duration. Such low values will result in higher measurement noise. This further shows the limitations of signal conditions in the test environment. To assess the performance of the proposed scheme in such environment, a standard tightly coupled GNSS/INS filter with residual based FDE was first implemented whereby the GNSS range and Doppler measurement errors were assumed to follow a normal distribution. The GNSS measurement distribution was then replaced by the \(t\) distribution thus transitioning the navigation filter to a VB filter. Finally, the variance adaptive scheme discussed in Section 2.2 was also implemented along with the VB filter. These three cases are termed as: (i) _Standard_; (ii) _VB_ and (iii) _VB Adaptive_, respectively. Since C/N\({}_{\rm o}\) based weighting has been found to be more robust in harsh GNSS signal conditions, the Sigma-e variance model discussed by [13] was used to scale the GNSS range and Doppler measurements in all three cases. The performances of these three filters were first inter-compared by computing absolute values of horizontal and vertical errors. These horizontal and vertical errors are plotted only for the portion of the data in which the GNSS conditions were very harsh and the errors were more severe as depicted in Figure 10a,b. However, it is noted that the error values can grow very large corresponding to the times for which the satellite geometry was very poor as indicated by the dilution of precision. Thus, to segregate the effect of biased and diffused measurements from that of poor satellite geometry, the errors statistics were computed only for the times in which the position dilution of precision (PDOP) values were less than or equal to 10. The effect of masking in the urban environment is clearly depicted by the high PDOP values plotted alongside the errors in Figure 10a,b. Moreover, the portion of the data in which the user was static in a relatively open sky condition with many line of sight (LOS) GNSS measurements was also discarded in order to confine the analysis to degraded environments. Figure 9: C/N\({}_{\rm o}\) values of measurements in urban canyon (OEM6).