## 4 A New Weight Model Based on SNR  
In Section 2, we confirmed that the magnitude and variability of the SNR change significantly depending on the signal-reception environment, even when using the same type of receiver and antenna. Especially on city streets and inside urban canyons, where GPS signals are severely affected by multipath errors, the standard deviations of SNR observables show relatively high values. Thus, the traditional weight models introduced in Section 3 are not effective in situations with multiple signal paths. This is because multipath errors can corrupt high-elevation angle measurements, and large SNR values can be observed for multipath-contaminated signals. It is necessary to separate the direct signals from the multipath signals and assign appropriate weights accordingly. We refer to the direct signal from a visible satellite as LOS, and the indirect or multipath signal as NLOS (Non-LOS). To enhance positioning capabilities in CS and UC environments, a new criterion should be established to distinguish between LOS and NLOS and then allocate optimal weights based on these decisions. To analyze the SNR characteristics of LOS and NLOS signals, we first determined whether the received signal was LOS or NLOS. This can be accomplished by conducting a satellite visibility analysis with 3D building models. If an observable is recorded on a receiver, we can compute the satellite position at that moment and derive an LOS vector that connects the user's location to the satellite. If 3D geospatial information is available for nearby buildings, the signal blockage can be determined based on a visibility collision analysis. The LOS collision analysis utilizes a straight-line-polygon collision detection algorithm, which is widely used in fields such as 3D physics engines and graphics programming. In this context, the straight line refers to the LOS vector connecting an observation point and a satellite, and the polygon represents a building surface situated between the user and the satellite. The straight-line-polygon collision detection process is performed in three steps: (1) checking whether the two points that define the straight line lie on opposite sides of the polygon; (2) calculating the intersection point of the straight line and the plane that defines the polygon; and (3) checking whether the intersection point of the line and the plane lies within the area of the polygon. A detailed mathematical explanation can be found in [22]. Figure 4 shows the SNR measurements for all the GPS satellites observed for 24 h at TEHE, whose location corresponds to the UC case. In Figure 4, blue dots denote \"predicted-and-observed\" LOS signals, while red dots denote \"not-predicted-but-observed\" NLOS signals. The term \"predicted\" refers to the case in which GPS signals should be recorded because no signal blockage is anticipated. From the figure, it can be observed that the SNR values are significantly larger for the LOS signals. Figure 5 shows the time series of the SNR observables, with their standard deviations of PRN 16 at TEHE. Ten immediately preceding consecutive values have been used to compute the standard deviation of SNR at the final tenth epoch. PRN 16 was chosen because this satellite provides a representative mix of both LOS and NLOS signals. To compare the SNR values with their variability owing to surrounding buildings, Figure 6 shows the SNR observables of PRN 16 in a skylpot overlaid with an aerial photograph. In Figure 5, the blue and red dots depict the LOS and NLOS, respectively. While the SNR changes smoothly in an open-sky environment as the elevation angle increases or decreases, rapid fluctuations are observed at TEHE because of signal blockage by buildings existing in the  
line of sight of the satellite trajectory. It should be noted that NLOS measurements generally have a lower magnitude and higher variability than LOS signals. These unpredictable behaviors necessitate a new approach for separating LOS and NLOS signals and assigning appropriate weights accordingly.