# A GNSS-Cellular Network Hybridization Strategy for Robust Positioning
## 4 Discussion  
The position-level hybridization method was evaluated in three environments--outdoor, urban canyon, and indoor--and compared with the GNSS-only and 4G-only positioning configurations. The following results were obtained:  
Figure 11: Root sum square (RSS) of positioning errors with respect to the reference coordinates for the measurement-level hybridization method. This graph summarizes the total positioning accuracy for each solution in the three test environments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Obs** & **dE (m)** & **dN (m)** & **dU (m)** & **RSS** \\ \hline Hybrid & \(-6.89\) & \(-8.29\) & \(-13.39\) & \(17.19\) \\
4G & \(-4.51\) & \(4.98\) & \(1.20\) & \(6.82\) \\ GNSS & \(-12.30\) & \(-31.57\) & \(-25.64\) & \(42.49\) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Accuracy comparison of the hybrid, GNSS-only, and 4G-only solutions in the indoor environment. The RSS column contains the root sum square of the positional error components, offering a single accuracy metric. Figure 10: Root sum square (RSS) of standard deviations for the measurement-level hybridization method across the outdoor, urban canyon, and indoor scenarios. This metric quantifies the internal precision of each method tested. Outdoor scenario: GNSS-only delivered the highest precision in the horizontal components, with standard deviations of \(\sigma_{\rm E}=0.04\) m and \(\sigma_{\rm N}=0.17\) m. In contrast, the 4G-only and hybrid methods showed a superior performance in the vertical component, achieving \(\sigma_{\rm U}=0.11\) m and \(\sigma_{\rm U}=0.35\) m, respectively (Table 4). * Urban canyon scenario: GNSS also yielded the best horizontal precision in this more complex environment, with \(\sigma_{\rm E}=0.58\) m and \(\sigma_{\rm N}=0.90\) m. However, for the vertical component, the 4G-only solution provided the most accurate result, with \(\sigma_{\rm U}=0.12\) m (Table 5). * Indoor scenario: The hybrid method provided the most precise horizontal positioning, with \(\sigma_{\rm E}=1.19\) m and \(\sigma_{\rm N}=1.22\) m, while the 4G-only configuration again delivered the best vertical precision (\(\sigma_{\rm U}=0.73\) m) (Table 6). These findings underscore the effectiveness of the 4G-only and hybrid methods in improving the vertical positioning accuracy across all environments. This improvement may be attributed to the integration of barometric data from the UE, which enhances the elevation estimates [36]. According to the 3 GPP standard, the network can leverage information from UE sensors, including the barometric pressure, to refine the vertical positioning. It is also noteworthy that real positioning errors (i.e., accuracy, Tables 7-9) were generally higher than the estimated uncertainties (i.e., standard deviations, Tables 4-6). A notable exception was the 4G-only vertical component, where the measured accuracy \(dU\) (Tables 7-9) closely matched its standard deviation \(\sigma_{\rm U}\) (Tables 4-6), suggesting a consistent and reliable performance in that dimension. Importantly, in environments where GNSS signals are weak or unavailable--such as indoors or in urban anyons--both the hybrid and 4G-only methods offer robust alternatives with a competitive performance. In contrast, the measurement-level hybridization method fuses GNSS and computed 4G BS pseudoranges into a unified positioning solution. It was also assessed against GNSS-only and 4G-only configurations, with the following results:  
* Outdoor and urban canyon scenarios: GNSS-only provided the most precise results, with values such as \(\sigma_{\rm E}=1.27\) m, \(\sigma_{\rm N}=3.70\) m, and \(\sigma_{\rm U}=4.44\) m (Tables 10 and 11). * Indoor scenario: The 4G-only solution yielded the best performance, with \(\sigma_{\rm E}=4.81\) m, \(\sigma_{\rm N}=0.51\) m, and \(\sigma_{\rm U}=22.80\) m (Table 12). However, the vertical component showed significant inaccuracies. This was primarily because all BSs are at similar altitudes, which may lead to a nearly singular design matrix [11] (p. 234).