## 4 Experimental Analysis
### Analysis of the Spaceborne Measurement Noise  
The a priori measurement noise of the ground observations is usually set as the default for positioning or orbit determinations, i.e., the pseudo-range and carrier-phase noises are usually set to 1 m and 5 mm, respectively, regardless the type of receiver [7,8]. However, receivers mounted on a spaceborne instrument, such as an LEO satellite, do not always have the same performance as geodetic receivers. The measurement noise reflects the inner properties of a receiver and is usually regarded as a factory calibration value; in addition, it does not change unless the hardware of the spaceborne receiver is damaged in an extreme space event, such as a strong solar storm. To identify the actual measurement noise for our observation simulation, the different magnitudes of the measurement noise levels of the simulated BDS/LEO combined POD are first calculated and compared; then, the measurement noises of the three types of real LEO constellations are analyzed. The Walker 24/4/2 LEO constellation was used to calculate the effects of different levels of measurement noise on the BDS POD. According to our knowledge of the observation quality of the GNSS receivers, carrier-phase measurement noises of 0.001 m, 0.005 m, 0.01 m, and 0.05 m were calculated. The results are shown in Figure 4.  
We can see there is an evident difference in the BDS orbit accuracies calculated from different levels of measurement noise: the average GEO, IGSO, and MEO 3D RMS values are 0.24 m, 0.17 m, and 0.14 m, respectively, for the 0.001-m noise level. When the noise level increases to 0.005 m and 0.01 m, the orbit accuracy decreases by 14.3%, 26.1%, and 30.0%, and by 36.8%, 41.4%, and 39.1% on average for the GEO, IGSO, and MEO satellites, respectively. For a noise level of 0.05 m, the orbit accuracy degrades considerably to approximately 0.73 m, 0.54 m, and 0.47 m on average. Therefore, it is necessary to identify and calibrate the actual spaceborne measurement noise. Table 4 lists detailed information concerning the Swarm, GRACE, and Sentinel-3 constellations. The Swarm constellation consists of three identical satellites: Swarm-A, Swarm-B, and Swarm-C. Swarm-A and Swarm-C are flying in a synchronous formation at an altitude of approximately 460 km and an inclusion of 87.35\({}^{\circ}\), while Swarm-B is cruising at a higher altitude of approximately 510 km. The Swarm constellation is dedicated to exploring the Earth's magnetic field, atmosphere, and gravitational field. The satellites  
Figure 4: BDS orbit solutions calculated with different levels of spaceborne measurement noise. From left to right: 0.001 m, 0.005 m, 0.01 m, and 0.05 m.  
are equipped with several instruments including an absolute scalar magnetometer, an electric field instrument, and a GPS receiver (GPSR) [32]. The dual-frequency 1-s sampling interval spaceborne GPS data are used in this study; these data are freely available at [[ftp://swarm-diss.eo.esa.int/Levellb/](ftp://swarm-diss.eo.esa.int/Levellb/)]([ftp://swarm-diss.eo.esa.int/Levellb/](ftp://swarm-diss.eo.esa.int/Levellb/)) accessed on 5 June 2021. The GRACE constellation consists of two identical satellites that are 220 km apart in orbit at an altitude of 300-500 km. The precise scientific instruments mounted on the satellite can accurately measure the distance between the two satellites, allowing variations in the gravity field to be detected. The spaceborne GPS receiver can track the GPS signal for the POD of the satellites; the spaceborne GPS data and corresponding data conversion tool can be downloaded from [[https://isdc.gfz-potsdam.de/grace-isdc/](https://isdc.gfz-potsdam.de/grace-isdc/)]([https://isdc.gfz-potsdam.de/grace-isdc/](https://isdc.gfz-potsdam.de/grace-isdc/)), accessed on 5 June 2021. Sentinel-3 is a multi-sensor system used to measure the sea-surface topography, land and sea-surface temperature, and color of the land and sea with high precision and reliability to support marine prediction systems and environmental and climate monitoring.