# A GNSS-Cellular Network Hybridization Strategy for Robust Positioning
## 3 Results  
### Position-Level Hybridization Method results  
The positioning performance of the GNSS-only, 4G-only, and hybrid solutions is presented in Tables 4-9 for the outdoor, urban canyon, and indoor scenarios. Tables 4-6 report the estimated coordinates along with their associated standard deviations. Tables 6-8 summarize the corresponding positioning accuracies relative to the reference coordinates. In both cases, an additional RSS column was included to present the root sum square of the east, north, and up components, providing a compact and interpretable metric of the overall precision (Tables 4-6) and accuracy (Tables 7-9). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Collected** & **GNSS RMS (m)** & **4G RMS (m)** \\ \hline Indoor & 27.81 & 20.87 \\ Urban canyon & 18.80 & 43.03 \\ Outdoor & 12.62 & 53.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Root mean square (RMS) positioning errors computed from the raw field data corresponding to Figures 5–7. The values quantify the positioning performance of GNSS and 4G across the three experimental scenarios: indoor, urban canyon, and outdoor. These are a priori errors as directly reported by the UE, prior to applying any hybridization methods or outlier suppression techniques. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Obs** & **E (m)** & **N (m)** & **U (m)** & \(\sigma_{\text{E }}\)**(m)** & \(\sigma_{\text{N }}\)**(m)** & \(\sigma_{\text{U }}\)**(m)** & **RSS** \\ \hline Hybrid & 729,037.88 & 4,373,589.12 & 64.99 & 1.19 & 1.22 & 1.17 & 2.07 \\
4G & 729,031.99 & 4,373,574.26 & 60.20 & 1.78 & 1.01 & 0.73 & 2.17 \\ GNSS & 729,042.29 & 4,373,598.98 & 72.29 & 1.22 & 1.98 & 2.16 & 3.17 \\ \hline \end{tabular}
\end{table} 
Table 6: Estimated coordinates and standard deviations for the indoor scenario using the hybrid, GNSS-only, and 4G-only solutions. The RSS column reflects the total standard deviation across the east, north, and up components. \begin{table}
\begin{tabular}{c c c c c} \hline
**Obs** & **dE (m)** & **dN (m)** & **dU (m)** & **RSS** \\ \hline Hybrid & 1.64 & 0.62 & \(-\)0.96 & 2.00 \\
4G & 28.93 & \(-\)13.80 & \(-\)1.20 & 32.08 \\ GNSS & \(-\)2.25 & 1.73 & \(-\)1.63 & 3.27 \\ \hline \end{tabular}
\end{table} 
Table 8: Accuracy comparison of the hybrid, GNSS-only, and 4G-only solutions in the urban canyon environment. The RSS column provides the total 3D positioning error using the root sum square of the individual component errors. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Obs** & **E (m)** & **N (m)** & **U (m)** & \(\sigma_{\text{E }}\)**(m)** & \(\sigma_{\text{N }}\)**(m)** & \(\sigma_{\text{U }}\)**(m)** & **RSS** \\ \hline Hybrid & 729,009.80 & 4,373,590.02 & 73.22 & 0.34 & 0.49 & 0.11 & 0.61 \\
4G & 729,006.45 & 4,373,576.40 & 72.39 & 2.24 & 1.97 & 0.35 & 3.00 \\ GNSS & 729,009.63 & 4,373,590.20 & 72.54 & 0.04 & 0.17 & 0.21 & 0.27 \\ \hline \end{tabular}
\end{table} 
Table 4: Estimated coordinates and standard deviations for the outdoor scenario using the hybrid, GNSS-only, and 4G-only solutions. The RSS column reports the root sum square of the standard deviations for the east, north, and up components, providing a compact measure of internal precision. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Obs** & **dE (m)** & **dN (m)** & **dU (m)** & **RSS** \\ \hline Hybrid & 1.64 & 0.62 & \(-\)0.96 & 2.00 \\
4G & 28.93 & \(-\)13.80 & \(-\)1.20 & 32.08 \\ GNSS & \(-\)2.25 & 1.73 & \(-\)1.63 & 3.27 \\ \hline \end{tabular}
\end{table} 
Table 9: Accuracy comparison of the hybrid, GNSS-only, and 4G-only solutions in the indoor environment. The RSS column indicates the combined positioning error in three dimensions based on the root sum square calculation.