# Telescopic Network of Zhulong for Orbit Determination and Prediction of Space Objects
## 2 Data and Methods
### CPF Data  
Various sources of errors in telescopes, such as optical distortion, instrumental noise, and atmospheric turbulence, can affect the accuracy of angular data. This section will aggregate observation files spanning multiple days for three celestial bodies. It will utilize precise CPF orbits as reference orbits. These orbits will be compared with angular data to quantify differences. Subsequently, an analysis of angular data accuracy will be conducted. Three space objects have been chosen, and their NORAD (North American Aerospace Defense Command) numbers, orbital information, and names are provided in Table 1. The table presents the calculated orbital period, inclination, perigee height, and apogee height based on the data from October 2023. Please note that the orbital period is measured in minutes, the inclination is measured in degrees, and the perigee height and apogee height are measured in kilometers, with all data dates falling within 2023. To evaluate the accuracy of the angular measurements for the three chosen space objects, 38 sets of angular arc files from mid-June to early October 2023 were collected. The reference orbit used is ephemeris files in CPF. CPF serves as a predictive format offered by the International Laser Ranging Service (ILRS), facilitating the dissemination of precise orbit prediction data concerning more than 100 SLR satellites. Its purpose extends to furnishing guidance for satellite laser ranging operations [21]. Each CPF file contains the satellite's position information at regular time intervals over several days, usually in the form of x, y, and z coordinates in a geocentric coordinate system. Currently, more than 30 institutions provide CPF for various satellites [22]. CPF files are usually created using satellite laser ranging data, and their accuracy is affected by factors such as the distribution and precision of the data, the satellite orbit altitude, the geometric characteristics of the satellite, and the precise orbit determination strategy used for the laser ranging data [28; 29; 30]. Typically, the accuracy of the CPF is considered to be within several meters [31; 32; 33]. The format of CPF varies for different satellites but generally includes three parts: a header, data records, and end-of-file identification. The orbits of the three selected space objects have a precision of approximately 2 m, which is adequate for evaluating the accuracy of angular data with an objected precision of 3 arc seconds. The method for analyzing the accuracy of angular data is as follows:  
1. Data collection and preprocessing. Register on the website [[https://spacemapper.cn/](https://spacemapper.cn/)]([https://spacemapper.cn/](https://spacemapper.cn/)) (accessed on 1 June 2024). and download the angular data for selected objects. Download the CPF files for the objects from the ILRS website at the time of the angular data. Perform outlier detection and remove any outliers. 2. Reference angular data generation. According to the telescopic position and time provided in the angular data file, the method for calculating the reference angular data using the reference orbit is as follows: First, the three-dimensional coordinates obtained from the CPF file are denoted as \(\overset{\rightarrow}{\boldsymbol{r}}_{t}= \begin{bmatrix}x_{t}\\ y_{t}\\ z_{t}\end{bmatrix} \). Second, based on the telescopic \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**NORAD** & **Name** & **Size/m** & **Period** & **Inclination/deg** & **Apo-gee/km** & **Peri-gee/km** & **File Count** & **Start Date** & **End Date** \\ \hline
41240 & JASON 3 & \(1\times 1\times 3.7\) & 112.42 & 66.04 & 1344 & 1332 & 16 & June 27 th & October 5 th \\
46984 & S6 MICHAEL & \(5.13\times 4.17\) & 112.42 & 66.04 & 1344 & 1332 & 14 & June 17 th & October 7 th \\  & FREILICH & \(\times\) 2.34 & & & & & & & \\
1328 & EXPLORER 27 & \(\sim\)2.3 \(\times\) 2.3 & 107.56 & 41.18 & 1303 & 924 & 8 & July 23 rd & September 30 th \\ \hline \end{tabular}
\end{table} 
Table 1: Selected space object information.