## 4 Simulation Experiments and Discussion
### Experiment 1: Validation of the MO-Based ABP Determination Model  
In order to verify the correctness of the MO-based ABP determination model (which we refer to hereafter as the MO-based model) presented in this study, it was necessary to choose an evaluation benchmark. The software GRASP developed by TICRA ([[http://www.ticra.com/](http://www.ticra.com/)]([http://www.ticra.com/](http://www.ticra.com/)) accessed on 6 July 2021) uses the PO approximation to calculate the 3-D far field antenna patterns at different frequency bands, which is considered the most reliable tool for the analysis of reflector antennas. Therefore, we set the simulation results of GRASP as the reference and employed the angular distance between the ABP from the MO-based model and the reference ABP to evaluate the ABP determination accuracy of the model. Due to the limitation of the response time performance of the GRASP software, we took the 54 GHz frequency band (the lowest frequency band to be used) as an example to implement the comparative experiment for ABP determination. To ensure statistical reliability, we used the GRASP software (steps required to execute the GRASP software (e.g., defining the geometrical and electrical objects, selecting the PO method of calculation, and setting the commands for running the analysis of the antenna) can be found in the manual of GRASP [31]) and the MO-based model to calculate the ABP at intervals of 1\({}^{\circ}\) within one complete 360\({}^{\circ}\) scan cycle of the ECF. Figure 5 shows the calculation errors of the MO-based model for ABP determination. Table 1 gives a statistical summary of the ABP calculation errors presented in Figure 5.  
It can be seen from the above experimental results that the MO-based model and the GRASP software generated almost the same results for ABP determination. The ABP calculation errors of the MO-based model showed an irregular fluctuating pattern within the 360\({}^{\circ}\) scan cycle of the ECF, which could reach a maximum of 5.16 \(\times\) 10\({}^{-2}\) \(\upmu\)rad at the ECF scan azimuth of 280\({}^{\circ}\). According to the current system design, the scan azimuth of the ECF ranged from 305\({}^{\circ}\) to 55\({}^{\circ}\) during scanning of the Earth. Thus, this maximum ABP calculation error would have no direct impact on the geolocation accuracy of the radiometric data. When the ECF scan azimuth was in the range of 305\({}^{\circ}\)-55\({}^{\circ}\), the maximum ABP calculation error of the MO-based model was 3.94 \(\times\) 10\({}^{-2}\) \(\upmu\)rad, which was equivalent to a positioning deviation of 1.4 m at the GEO SSP. Compared with the currently achievable SSP spatial resolution at 54 GHz (\(\sim\)60 km), this error could be totally ignored with respect to the NWP operational requirements. As for time consumption, the MO-based model only took about 0.011 ms on average to complete a single ABP determination. On the contrary, the GRASP software took approximately 50 s to realize one ABP determination (which was about 4,730,000 times that of the MO-based model). This was mainly because the GRASP software consumed extra time in calculating the 3-D far field antenna pattern. In particular, the time for calculating the 3-D antenna pattern by GRASP would increase dramatically with the increase in the beam operating frequency, and it was even impossible for GRASP to achieve one ABP determination within an acceptable time (as the beam operating frequency was increased to 425 GHz (the highest frequency band to be used), the GRASP software still could not complete one ABP determination after 2 h). However, the time consumption of the MO-based model was frequency-independent, which means that the MO-based model would exhibit a more significant advantage in computational efficiency as the beam operating frequency increased.