## 4 Measurement Quality Analysis
### MQA3: Error Source Analysis  
This section estimates the tropospheric delay, ionospheric delay, and receiver clock bias. First, the ionospheric error is generated by the GPS signal being refracted by free electrons in the ionosphere. The ionospheric delay was calculated from dual-frequency pseudorange measurements. This research utilizes the Hatch filter with a slightly modified ionospheric delay algorithm [31]. This ionospheric Hatch filter is used to estimate the smoothed ionospheric delay using the dual-frequency code and carrier measurements. In order to analyze the relationship between the error source and the local effect, the time axis was changed into the local time to analyze the ionospheric error. Figures 17 and 18 show the ionospheric delay values for all GPS and BDS satellites, respectively. The colors represent the ionospheric delay value for each satellite. In Figure 17, the GPS ionospheric error varies with time. The maximum ionospheric delay occurs at 14:00 local time, and the minimum occurs at 04:00 local time. This result shows that ionospheric delay is related to solar activity. Figure 18 shows that the ionospheric error for BDS has the same tendency as that for GPS. However, at night (local time), the ionospheric delays of the GPS satellites converge to almost the same value no matter the satellite elevation angle. The BDS satellites have a larger variation range of the ionospheric delay during the night. The two systems have almost the same variation in ionospheric error. The maximum and minimum values during a day for GPS and BDS are similar. However, during night time, BDS has a dispersed ionospheric delay value. The distribution of BDS ionospheric error is larger than that of GPS for the whole day. It should be noted that the satellite differential code biases are not considered in the ionospheric delay computation shown in this paper, and the differences of the ionosphere delays in Figures 17 and 18 could be due to satellite differential code biases. The tropospheric error was also analyzed. Tropospheric error is caused by the GPS signal passing through the troposphere. Variations in temperature, pressure, and humidity all contribute to variation in the speed of light of radio waves. In comparison to the vacuum speed of light, the delay value is the tropospheric error. Although some new mapping functions are available for estimating tropospheric delay [34; 35], this research selected the Saastamoinen model [36] and the Black and Eisner troposphere formula [37] as the tropospheric delay model and mapping function, respectively, because they are the most commonly used in GNSS augmentation systems [31]. The input parameters for the Saastamoinen model was obtained from [38]. The tropospheric delays of all satellite pseudoranges were calculated. As shown in Figures 19 and 20 the tropospheric delay value is inversely proportional to the satellite elevation angle. The maximum and minimum tropospheric delay values of GPS and BDS are almost the same. The horizontal line in Figure 20 represents the BDS GEO tropospheric delay. The tropospheric delay changed only slightly because GEO satellite elevation angles do not change much. As a result, by comparing different GNSS, the tropospheric corrections provided by the Saastamoinen model are almost the same. Figure 19: GPS tropospheric error during a day. Figure 20: BDS tropospheric error during a day. The user clock bias was analyzed next. Even if a user uses the same receiver to receive both GPS and BDS signals at the same time, the receiver clock offset is different for the two systems. Because the measurement generation of GPS and BDS is different, the user clock bias needs to be estimated separately. By using the modeled ionosphere and troposphere delays, the ionosphere- and troposphere-free pseudorange measurements are used to estimate the user clock bias. Figure 21 shows the user clock biases calculated for the two systems (blue points for GPS and red points BDS). The variation trends of these two clock biases are similar.