## 4 Experimental Analysis
### Analysis of the Spaceborne Measurement Noise
Images were obtained with various ocean and land color sensing instruments, sea and land surface temperature radiometers, and synthetic aperture radar altimeter, microwave radiometer, and POD instruments. Its ocean and land revisit cycles are less than 3.8 days and 1.4 days, respectively. Unlike Swarm and GRACE, the orbit determination for an individual Sentinel-3 satellite can be performed via GPS, Doppler orbit determination and radio-positioning integrated by satellite, or satellite laser ranging. In this study, only GPS data were used; the observations were obtained from [[https://scihub.copernicus.eu/grss](https://scihub.copernicus.eu/grss)]([https://scihub.copernicus.eu/grss](https://scihub.copernicus.eu/grss)), accessed on 5 June 2021. In this study, we calculated the measurement noise for the Swarm-A, GRACE-A pseudo-range, and carrier-phase spaceborne GPS observations with a cut-off elevation of 1\({}^{\circ}\), and 10\({}^{\circ}\) for the Sentinel-3A observations as the receiver onboard this satellite is actually set at collecting data with a cut-off elevation of 10\({}^{\circ}\). The three types of LEO-constellation spaceborne data can provide a better understanding of the actual spaceborne observation noise level, as well as a clear reference for our data simulation. The zero-baseline method is usually applied to assess the ground observation noise using the difference between two very closely located stations. However, this approach is not applicable to spaceborne receivers because two LEO satellites in an LEO formation are hundreds or thousands of kilometers apart. The orbit and high-order satellite clock offset errors can result in a discrepancy in the observational residuals by causing an inter-satellite single or double-difference between two spaceborne receivers. Therefore, a more \begin{table}
\begin{tabular}{c c c c} \hline
**LEO Constellation** & **Swarm** & **GRACE** & **Sentinel-3** \\ \hline Satellite & Swarm-A/B/C & GRACE-A/B & Sentinel-3A/B \\ \hline Spaceborne & GPS & GPS & GPS \\ \hline Altitude & A/C: \(\sim\)460 km, B: \(\sim\)510 km & \(\sim\)500 km & \(\sim\)814.5 km \\ \hline Inclination & A/C: 87.35\({}^{\circ}\), B: 87.75\({}^{\circ}\) & 89.5\({}^{\circ}\) & 98.65\({}^{\circ}\) \\ \hline Orbit type & Circular near-polar orbits & Circular near-polar orbits & Repeating frozen sun-synchronous orbit [33] \\ \hline Repeat cycle & 7–10 months & A sparse repeat track of 61 revolutions every four days [34] & 27-day repeat cycle, 14 + 7/27 orbits per day [34] \\ \hline Goal & Geomagnetic observation & Detection of the Earth’s gravity variations & Earth monitoring and operational oceanography \\ \hline \end{tabular}
\end{table} 
Table 4: Detailed information of Swarm, GRACE, and Sentinel-3 constellations. appropriate method, namely the geometry-free (GF) method, was applied. This method directly finds the differences between the pseudo-range and carrier-phase measurements at the two frequencies. The drawback of the GF approach lies in the amplified pseudo-range and carrier-phase measurement noises, which can fortunately be resolved using the covariance propagation theory, allowing the true-measurement noise to be obtained. The calculated GF pseudo-range noises of the Swarm-A, GRACE-A, and Sentinel-3A GPS data are 1.88 m, 1.97 m, and 1.46 m, respectively, and the carrier-phase measurement noises are 0.0098 m, 0.0041 m, and 0.0022 m, respectively. Figure 5 indicates that the measurement noises of GRACE-A and Sentinel-3A tend to be much smaller than those of Swarm-A. This is due to the stronger signal-to-noise ratio (SNR) of GRACE-A. The pseudorange noise is closely related to the SNR or the carrier-to-noise ratio (C/N0). Signals with weaker signal strengths have larger tracking noise. In addition, the Sentinel-3A spaceborne observations were sampled at a cut-off elevation of 10\({}^{\circ}\), resulting in a much lower noise level.