## 6 Imaging Radar
### Challenges of Tracking for the New Imaging Radar  
The new imaging radar, like its predecessor, requires guidance from the tracking radar. To ensure high-quality imaging, the object must be within the 3 dB beam width of the antenna for a sufficient observation interval. This requirement concerns the angle \(\alpha\) between the antenna direction and the line of sight to the satellite, illustrated in Figure 23. Instead, the angle \(\vartheta\) is the antenna 3 dB beam width, which, for the new imaging radar, is  
Figure 22: Modeled specific attenuation for precipitation, liquid water, and atmospheric gases with different relative humidity and temperature values along the ITU-assigned IEEE radar bands. smaller than the current imaging radar due to the higher frequency band. The condition \(\alpha\leq\theta/2\) must be satisfied to guarantee the object is within the antenna beam. Figure 24 displays the beam's pointing accuracy for a standard observation of TIRA. Two thresholds for angle \(\alpha\) are depicted: the green one for the current imaging radar and the red one for the new imaging radar. Compared to the current imaging radar, the new system, due to its narrower beam width, requires improved tracking capabilities. Therefore, a new tracking filter has to be developed and implemented in the TIRA system. As previously mentioned, TIRA measures the range, range rate, azimuth, and elevation of a space object in real time. A sensitivity analysis was performed to understand the impact of the accuracy of each radar observable on the tracking performance. Another investigation was conducted by including an additional parameter, the range-rate rate, as input to the tracking filter. This parameter can be estimated from the phase independently of the other observables [6]. An extended Kalman filter (EKF) was used for the simulations. Results showed that the tracking performance could be strongly improved by increasing the angular accuracy of the radar measurements. Instead, the other parameters (range, range rate, range-rate rate) only increased slightly the tracking performance [31]. A possibility to obtain angular measurements independent of the L-band radar is to take advantage of the imaging radar of the TIRA system directly during tracking. To achieve this, the imaging radar needs to be equipped with a monopulse system. The benefit of this is to provide more accurate angular data than those of the tracking radar, thanks to  
Figure 23: Geometry of the angles \(\theta\) and \(\alpha\). \(\theta\) is the 3 dB beam width of the antenna. \(\alpha\) is the angle between the antenna pointing direction and the line of sight to the satellite with the origin at the radar. Figure 24: Beam’s pointing accuracy of the TIRA system during a standard tracking observation. the higher frequency band. Therefore, it is possible to enhance the tracking performance by combining the information of the two radars of TIRA. A common technique is the multi-sensor data fusion that consists in combining the output of several sensors to describe a single probabilistic state [32]. A first investigation of the multi-sensor data fusion between the tracking and the imaging radar of the TIRA system was performed in [31]. Again, an EKF was used for the simulations. Results confirmed that the multi-sensor data fusion could be a solution to achieve a more accurate tracking system by ensuring the target object within the 3 dB beam width of the antenna of the future imaging radar. Currently, different scenarios are being investigated based on the idea of a two-step tracking filter. It consists of two tracking filters running in parallel: an EKF and a batch least-squares filter. While the EKF tracks the object in real-time, the batch least-squares filter works in near real time by collecting data over a certain period of time. Every time the batch filter provides an output, it is injected in the EKF with the purpose of improving the tracking performance. Some first results are shown in [33].