# A GNSS-Cellular Network Hybridization Strategy for Robust Positioning
## 4 Discussion
As a result, the system of equations cannot be reliably solved and the variance estimators may become unstable. Consequently, in many real-life scenarios, only 2D positioning is feasible. Altitude information must therefore be obtained through additional technologies, such as barometric sensors, as previously discussed. By summarizing the results in Table 16 and focusing on the performance of the proposed hybrid algorithms across the outdoor, urban canyon, and indoor scenarios, it can be observed that the position-level hybridization method consistently yielded a better precision and accuracy than the measurement-level hybridization method. The root sum square (RSS) metrics presented in Figures 8-11 complement the tabular results by providing a visual comparison of both the precision and accuracy across methods and environments. Figures 8 and 10 show the RSS of the standard deviations, highlighting the internal consistency of each solution, while Figures 9 and 11 illustrate the total positioning error relative to the reference coordinates. These plots clearly confirm the superior performance of the position-level hybridization method, particularly in indoor and urban canyon scenarios, where GNSS-only methods degrade significantly. The visual summaries also reinforce the advantages of hybridization over standalone 4G or GNSS solutions, both in terms of robustness and reliability. This difference is mainly attributable to the underlying math ematical models. Measurement-level hybridization requires the linearization of GNSS pseudoranges, making it a linear approximation model [16]. Additionally, the observation equation includes a multipath error term, which increases depending on the complexity of the environment, further degrading the performance. In contrast, the position-level hybridization method relies on pre-corrected coordinates provided by the mobile network. Its mathematical model is also linear, but it does not require a first-order Taylor series expansion, thereby minimizing linearization errors. Furthermore, the design matrix's condition number is always 1, meaning the system is well conditioned and robust--perturbations in the input data have minimal impact on the final solution. Overall, the position-level hybridization method outperformed the measurement-level method in terms of both precision and accuracy across most scenarios. In particular, the 4G-only and hybrid methods consistently demonstrated a superior performance in the vertical component in all environments. Finally, it is important to emphasize once again that, in environments where GNSS signals are weak or unavailable--such as indoors or in urban canyons--both the hybrid and 4G-only methods present robust and competitive alternatives, offering a reliable positioning performance even under challenging conditions. While the proposed GNSS-cellular hybridization strategies were evaluated using commercially available smartphone sensors in controlled static environments, future research may expand toward incorporating additional sensor modalities. Advanced fusion frameworks such as GNSS/INS, GNSS/UWB, or multi-sensor integrations (e.g., IMU, ultrasonic, and UWB) have demonstrated promising results in environments with degraded GNSS signals. For instance, [PERSON] et al. [37] reported a sub-meter accuracy using a semi-tightly coupled GNSS/UWB/INS system, while [PERSON] et al. [38] achieved a 12.3 cm RMSE by integrating IMU, ultrasonic, and UWB data through factor graph optimization. Similarly, [PERSON] et al. [39] demonstrated that hybrid systems combining 3D map-aided GNSS and terrestrial signals, including UWB, maintain a robust sub-meter accuracy under dynamic conditions. These works underscore the value of extending hybridization research to include alternative sensors. Therefore, future studies will explore the integration of GNSS, 4G/5G, and complementary technologies such as IMU and UWB within a unified framework.