## 1 Introduction to the Tracking and Imaging Radar TIRA
### Current Configuration of the Tracking Radar  
The tracking radar operates in the L band in a frequency band around 1.3 GHz. Radar pulses are sent to space objects and received after reflection of the electromagnetic waves by the large radar antenna. Range, range rate, azimuth angle, elevation angle, and time are calculated from the radar echoes by using a monopulse system in order to estimate the orbits of the space objects with high precision. The tracking of space objects starts when they cross the horizon and stops just before they disappear below the horizon. For this, the tracking radar uses a monopulse system which consists of four horns for transmit and receive. The ratio of the sum channel to the respective difference channels is a measure of the deviation of the object direction from the antenna axis. This allows the antenna position to be continuously corrected so that space objects are always close to the center of the main lobe and can be precisely tracked. TIRA's mechanical alignment accuracy corresponds to 3 m at a distance of 1000 km. Since the true object positions differ from the measured positions due to the refraction of the radar waves in the Earth's atmosphere, the data are corrected after the measurement using recorded environmental parameters (e.g., temperature, atmospheric pressure, and humidity) with a suitable atmospheric model. The main lobe has a width of almost half a degree (about the diameter of the full moon), which corresponds to a lobe diameter of 8.6 km at a distance of 1000 km. Thanks to the high transmission power in combination with the large antenna area to achieve high sensitivity, even objects with a diameter of just a few centimeters can be detected, tracked, and measured at a distance of 1000 km.  
For a standard RSO observation, the TIRA system uses a two-line-element (TLE) dataset to initially acquire and track a selected space object. The knowledge of the space object position can be more or less accurate, depending on different factors. As the orbit of a space object is affected by diverse forces, e.g., solar radiation pressure (SRP), atmospheric drag, and third-body attraction forces from the Moon and the Sun, the age of the TLE dataset plays a fundamental role. The largest deviation between the actual orbit and the propagated one using the TLE dataset is in the along-track direction. It can already be about 1 s (i.e., about 7 km to 8 km along-track distance in low Earth orbit (LEO)) for a one/two-day old TLE. The tracking method, which is currently implemented in the L-band radar, estimates the time offset (along-track) between the actual orbit of the space object and the one derived from the TLE dataset in real time. This time offset is then compensated continuously for each pulse to ensure that the object remains in the main lobe of the antenna  
Figure 2: Block diagram illustrating the current system architecture of TIRA. Components of the tracking radar are shown in dark blue, the imaging radar is show in turquoise, and common system components have a light blue background.  
beam. Without this correction, the object could be missed as the antenna lobe of the L-band radar at a range of 1000 km is 8.6 km.