# Reduction of Satellite Signature Effect in High-Accuracy Satellite Laser Ranging to Etalon
## 5 Conclusions  
Etalon is one of the most important geodetic satellites, which is responsible for a wide range of scientific research and observation activities. Due to its spherical shape and optical properties of retroreflectors, Etalon is susceptible to the effects of satellite signatures on laser ranging. A numerical simulation of the satellite signature effect on Etalon signals is carried out by using an uneven distribution model for retroreflectors. It has been demonstrated by the data collected from the kHz SLR system in Changchun that the average residual distribution of simulated returns is consistent. By processing the simulated signals via the standard algorithm, the center of mass corrections for Etalon are found to be shifted from 558.8 to 586.8 mm at various incident angles. Based on this evidence, it seems that the standard procedures for SLR data cannot minimize the effect of range bias caused by deviations in the center of mass corrections..  
For further reduction of satellite signature effects on ranging data, a center of mass correction filter is applied as part of the standard post-processing of Etalon observations. The range measurements with the lowest RMS of center of mass corrections are selected  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Etalon-1**} & \multicolumn{3}{c}{**Etalon-2**} \\ \cline{2-7}  & **RMS (ps)** & **Kurtosis** & **Skewness** & **RMS (ps)** & **Kurtosis** & **Skewness** \\ \hline Normal point & \(163.7\pm 41.8\) & \(-0.91\pm 0.1\) & \(0.16\pm 0.1\) & \(145.4\pm 34.3\) & \(1.96\pm 0.2\) & \(0.15\pm 0.14\) \\ algorithm New proposed algorithm & \(118.2\pm 8.94\) & \(2.02\pm 0.18\) & \(0.01\pm 0.1\) & \(120\pm 7.47\) & \(-0.95\pm 0.12\) & \(-0.04\pm 0.1\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: SLR observation characteristics of Etalon satellites.  
Figure 10: Residual distribution of Etalon-1/2 processed by different SLR algorithms: (**a**) Etalon-1; (**b**) Etalon-2.  
for the formation of normal points. Statistical analysis of the results demonstrates that a reduction in the average RMS of normal points per pass is from 163.7 \(\pm\) 41.8 ps to 118.2 \(\pm\) 8.94 ps, while the stability of normal points is improved by 79%. It is evident from the distribution of returned signals that are processed via the new algorithm that the distribution is more concentric and stable with smaller kurtosis and skewness per NP. Additionally, we applied the new algorithm into the post-processing for Etalon-2, which improved the ranging accuracy and stability of the normal points. A theoretical reference is provided in this study, which identifies previously unrecognized errors in the observation and provides a practical approach to further enhance its quality.  
It is admitted that the present study cannot be used for all satellites, but only for sphere satellites with significant satellite signature effects on echo signals. In contrast to satellites with a flat-plate structure, satellites with a flat-plate structure do not have any problems related to variations in satellite signature effects caused by varying incident angles.  
Conceptualization, N.A. and B.G.; methodology, J.G.; formal analysis, N.E.N.; investigation, R.C.P.; writing--original draft preparation, N.A.; writing--review and editing, X.D.; software, H.Z. and B.G.; funding acquisition, N.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 12073052 and 11973064, Jilin Province Science and technology development program, grant number 20230101006 JC, Chinese Academy of Sciences International Talent Program, grant number 2024 VIMA0009.  
The data presented in this study are openly available.  
The authors declare no conflict of interest.