## 3 Strategy of Cold-Sky Calibration for Synthetic Aperture Radiometers  
It is necessary that the location of the inverted position of the synthetic aperture radiometer satellite for cold-sky viewing be well chosen to obtain an accurate calibration. The effective selection of an optimized cold-sky calibration location, a calibration area based on the maximum brightness temperature stability for each antenna, and consideration of the thermal environmental variation around the orbit are critical. Therefore, the strategy of cold-sky calibration for synthetic aperture radiometer satellites is depicted as follows:  
1. The location should be as far away from land or ice as possible, while the attitude errors of the satellite are considered. The FOV of the synthetic aperture radiometer is far wider than the real aperture radiometer, and the brightness temperature of the land is larger than the brightness temperature of the ocean. Therefore, the contribution from the Earth's surface can cause brightness temperature readings that are several Kelvins higher from the back lobes of the antenna. The brightness temperature of the ocean is generally considered to be about 100 K in the model. The brightness temperature of the land is about 250 K, the brightness temperature of the celestial sky is approximated by 2.7 K\(\sim\)10 K, and the brightness temperature of the atmosphere is generally 2.5 K [10; 11]. The land contribution via the antenna back lobes should be minimized; that is, the land fraction should be as little as possible. 2. The location should be far from the plane of the galaxy, moon, and sun. Due to Gibbs ringing in the synthetic aperture radiometer, it will cause some changes in the signal observed if foreign sources radiate into the field of view of the antennas, which can lead to a large error in antenna brightness temperature. When flat target transformation (FTT) is performed, this deviation in the cold-sky observation will be considered the antenna error. In addition, the impact of the antenna pattern model biases can be introduced and wrongly re-calibrated. Therefore, calibration should be performed where the brightness temperature of the antenna is the most stable. The sun and other external sources should not enter the main lobes of the antenna, avoiding strong fluctuations in the brightness temperature. 3. The antenna's thermal stability should also be considered in the strategy. According to the emulated relationship between antenna thermal deformation and antenna pattern changes at the pre-launch phase, the appropriate \(\beta\) value for cold-sky observation is determined by minimizing the antenna pattern variation. If the \(\beta\) angle meets the requirements, the corresponding time is suitable for cold-sky calibration. Once the satellite orbit is determined, the antenna temperature field distribution can be calculated from the orbital beta angle (\(\beta\) angle) and the antenna thermal parameters [17]. The antenna's thermal parameters are known by the material properties, so the temperature field distribution is only determined by the beta angle, that is, FA(x,y) = f(\(\beta\)). The antenna thermal deformation can also be determined by f(\(\beta\)). Then, according to the acceptable range of antenna pattern error, the acceptable \(\beta\) range of external calibration can be determined. A look-up table can be obtained before the satellite is launched by simulation. The red dot area in Figure 6 should be avoided. Based on all the above principles, the time and location for cold-sky calibration can be selected by the following process, as shown in Figure 7.  
Finally, the optimized region and time for cold-sky calibration can be found according to the above conditions. The real-time geometrical relationships of the direct/reflected sun vector, the cold-sky region, and the satellite radiometer antenna can be determined by the method mentioned in Section 2.