## 2 Characteristics of SNR  
The SNR is an index indicating signal strength, and it is high for a direct signal received at the receiver antenna without any interference and low for a multipath signal bounced from nearby obstructions. If the measured SNR is high, it can generally be considered a direct and multipath-free signal, whereas low SNR signals can be regarded as multipath-impacted signals [15; 16; 17]. In addition, as the elevation angle decreases, the signal path length increases, and its SNR value decreases. This is because the signal must pass through a longer path through the ionosphere and, in particular, the troposphere before it reaches the receiver antenna, and the signal strength diminishes during the process. These two characteristics hold regardless of the receiver type and user environment. Nevertheless, the specific patterns and magnitudes of the SNR values depend on the receiver type and environment. To characterize the SNR according to the receiver type, we used temporary GPS equipment at Inha University, located in the city of Incheon, South Korea. One set of equipment consisted of a NovAtel OEMStar receiver and a NovAtel GPS-701 GG antenna (NovAtel Inc., Calgary, AB, Canada), while the other set consisted of a u-blox EVK-5T receiver and a u-blox ANN-MS-0-005 patch antenna (u-blox AG, Zurcherstrasse, Switzerland). The data collection was conducted for four hours on DOY 296 (23 October 2013), and, during this period, the total number of satellites observed down to the horizon was 19. As we aimed to use the developed algorithm on mobile platforms, expensive geodetic-quality receivers and antennas were avoided. Figure 1a,c show the GPS L1 SNR values against the elevation angle, and Figure 1b,d show the averages and standard deviations at 1-degree intervals. It should be noted that the u-blox receivers output SNR values only in integers; thus, their plot contains vertical gaps, as shown in Figure 1c. As shown in Figure 1, the magnitudes and changing patterns of the SNR were slightly different between the two receiver antenna types. However, the general pattern of \"high SNR for high elevation\" holds in both cases. It is also notable that the variance was low at high elevation angles, and most of the signals observed below an elevation angle of 10\({}^{\circ}\) had SNR values lower than 40. To investigate how the characteristics of the SNR values recorded at a GPS receiver change according to the signal reception environment, we collected data on a building roof, typical city streets, and urban canyons. Hereafter, we will denote a location without any signal obstruction above the elevation angle of 15\({}^{\circ}\) as OS, short for open sky. The worst hard-to-obtain GNSS reception location, such as metropolitan city streets with skyscrapers, is referred to as urban canyons (UC). Receivers located on typical city streets will be called CS, short for city streets. In our analysis, the OS case was chosen for the permanent IHU4 site located on the roof of a five-story building with clear satellite visibility in all directions. For the CS, a campaign-type station, SOND, was installed on the sidewalk of a four-lane street with five-to seven-story commercial buildings on both sides of the street. As a UC case, a campaign-type site named TEHE was placed in a parking lot on the southern side of Teheran-ro in Seoul. Teheran-ro is the street with the highest density of skyscrapers in South Korea, where one can obtain visibility from more than four GPS satellites for only 2-3 h during a day. The data was collected over 24 h at IHU4 and TEHE, and over three hours at SOND. The GPS equipment at IHU4 consisted of a Trimble NetRS receiver and Trimble Zephyr Geodetic II antenna, whereas a NovAtel OEMStar receiver and NovAtel GPS-701 GG antenna were used at SOND and TEHE.