# ATLAS: Latest Advancements and First Observations
## 2 Materials and Methods
### Space Object Tracking in LEO: Error Sources and Observation Strategy  
Observing space objects in low Earth orbit (LEO) with a monostatic tracking radar is no trivial task due to the dynamics between the radar and the space objects and because of the multiple sources of error that arise. Tracking radars feature narrow beamwidths to increase the resolution and signal-to-noise ratio (SNR). On the other hand, objects in LEO have very high velocities [13]. These two facts make the window of opportunity for observation very short. Errors in both the pointing system and the orbit prediction can easily lead to missing objects. The most complete source of orbital information is the US Two-Line Element (TLE) catalog. Given the sheer number of objects present in this catalog and the speed at which the orbital information is updated, the majority of SST stations, including ours, use it to perform predictions of the objects to observe. The correct method for propagating TLE orbital data is by using an SGP propagator, with the most popular one being the SGP4 [14]. Although using TLE+SGP4 is a fast, convenient, and sufficient approach for other use cases, our experience suggests that it is less than ideal for uncooperative tracking in LEO given the errors associated with the usage of mean elements and simplified propagation models. Accuracy depends on sensor quality, data quantity, and space conditions, none of which are disclosed by the US Space Surveillance Network. ESA published a notable article, where it was estimated that TLE orbit errors in LEO were around 0.102 km (radial), 0.471 km (along-track), and 0.126 km (out-of-plane) [14]. These errors increase as we propagate further from the epoch, but it is difficult to quantify how much. TLE data do not include any information related to maneuvers, making it very difficult to predict a satellite's position after one. The history of the TLE sets of a given object can be used to understand whether it has undergone maneuvers, which can be useful information when dealing with uncooperative satellites [15]. Inaccurate geo-referencing of the antenna homing system may lead to biases in the azimuth and elevation measurements. Once the homing system is correctly geo-referenced, a finer calibration can be performed using celestial sources like the Sun/Moon to further decrease the offset errors [16]. Periodic calibration routines involving celestial sources should be performed to ensure the pointing system remains accurate. The selection of resident space objects (RSOs) to track during the calibration phase can also play an essential role in mitigating these sources of error. The International Space Station (ISS) serves as an ideal candidate for initial measurements due to its significantly large Radar Cross-Section (RCS), approximately 400 m\({}^{2}\), and its ability to orbit within the lower LEO region (below 500 kilometers in altitude), resulting in the reception of higher-energy echoes compared to other RSOs. Position and velocity state vectors for the ISS are provided by NASA and are publicly available [17; 18]. These vectors are listed at four-minute intervals over the last 15 days, and during maneuvers, the vectors are reported at two-second intervals [18]. The ephemeris files also contain other important information, such as the mass of the ISS, drag area, drag coefficient, solar radiation area, and solar radiation coefficient, allowing orbit propagation with special perturbation techniques [19]. Other LEO operational satellites such as CRYOSAT-2 and Jason-3 are equipped with telemetry and retroreflectors, which provide precise ephemeris information [20]. This information can be used for highly accurate predictions of their passages, offering valuable data for both calibration procedures and evaluating the performance of ground-based  
Figure 3: Functional diagram of the receiver subsystem. sensors [21].