# A Staring Tracking Measurement Method of Resident Space Objects Based on the Star Tacker
## 3 Results
### Physical Experiment  
To verify the effectiveness of the STM method, the ground physical experiment was carried out in this section. As shown in Figure 12a, the smallest observable region is a circular area wherein the optical axis of the star tracker is perpendicular to the orbital plane. Thus, the ground physical experiment was carried out under this vertical condition. Figure 12b shows the schematic of the ground experiment system. The LED panel, used as an RSO generation device, displays the actual and estimated RSO locations. The CMOS (complementary metal oxide semiconductor) camera was used for taking pictures of the LED panel, which plays the role of the star tracker.  
Figure 11: Errors of the RSO locations: (**a**) ascension direction; and (**b**) declination direction.  
Figure 12: Experimental schematic diagram of the observable region search range: (**a**) observable region; and (**b**) schematic of the ground experiment system.  
The principle of the physical experiment system for the STM method validation is geometric scaling. This means that the parameters on the ground experiment system and the on-orbit parameters are scaled at 1:10\({}^{7}\). The parameters of the experimental system are listed in Table 4. The object distance between the camera and the LED panel is 60 cm, which means that the actual distance between the star tracker and the RSO is 6000 km according to the scale bar. Additionally, the ground experiment system is shown in Figure 13. To achieve sub-pixel centroid algorithm accuracy, the 3 \(\times\) 3 pixel-matrix is used to complete the display of the RSO, as shown in Figure 13. The two centroids of the pixel-matrix represent the actual and estimated RSO positions.  
To simplify the experimental process, the estimated RSO locations are set to the center of the LED panel. When a specific real RSO is in the scope of the camera, the location can be measured through the proposed observation method. The estimated and the real RSO locations in each image are generated by the orbital elements listed in Table 2. To improve the reliability of the experiment, Gaussian noise with a mean of 3 pixels is added to the actual and estimated RSO locations. When the image frequency is set to 5 Hz in ground experiment, 9000 images containing the actual and estimated RSO locations are shown on the LED panel within 30 min, and the CMOS camera is used to take pictures. Due to the limited distance on the ground and the pixel size of CMOS, it is impossible to obtain the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Serial Number** & **Ground Experiment Parameters** & **Value** \\ \hline
1 & Focal length of the camera & 7 mm \\
2 & Pixel size of CMOS & 7 μm \\
3 & Pixel size of LED & 2 mm \\
4 & Size of the LED panel & 1.94 m \(\times\) 1.44 m \\
5 & Imaging frequency & 5 Hz \\
6 & Object distance & 60 cm \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ground experiment parameters.  
Figure 13: Ground physics simulation experiment system.  
same measurement accuracy of the RSO as that in numerical simulation. However, the length of the observable arc can be verified in the ground experiment. The observable arc in the experiment is a set of all observable positions, which is shown as Figure 14. The acquisition time of the measurable arc in the experiment is approximately 5.8 min. According to the results in Section 3.2.1, the theoretical acquisition time is approximately 6 min, which is like the acquisition time obtained in the experiment.