## 1 Introduction  
The microwave radiometer is a passive remote sensing instrument which receives electromagnetic radiation from atmospheric, land, and oceanic environments through a reflector antenna to obtain the radiative properties of the viewed scene. Ever since the Microwave Sounding Unit (MSU) [1] on TIROS-N (1978) was first applied to the operational sounding of the Earth's atmosphere, the space-borne microwave radiometer has been widely used for its advantages in weather forecasting, disaster early warning, and environmental monitoring [2; 3; 4]. However, constrained by the current state of the art in instruments and satellite platforms, all in-orbit microwave radiometers to date have been deployed in low-Earth orbit (LEO) with an altitude below 1000 km. To meet the requirement of a higher frequency of Earth observation for meteorological applications (e.g., operational weather nowcasting, short-term forecasting, and continuous monitoring of highly dynamic phenomena such as severe convective storms and tropical cyclones), the deployment of microwave radiometers in geostationary orbit (GEO) has gradually attracted worldwide attention. Technically, a GEO microwave radiometer can be realized using either a real- or a synthetic-aperture system. GeoSTAR [5; 6] from the U.S., GAS [7] from the E.U., and GIMS [8; 9; 10], GIMS-II [11; 12], as well as CSMIR [13] from China are representative of synthetic-aperture schemes. Because the synthetic-aperture system is inferior to the real-aperture system in terms of system complexity and calibration, scan flexibility, and real-time sounding of dynamic time-varying targets (e.g., clouds, rain, and atmosphere), none of the above projects have entered the space-borne stage. The real-aperture schemes are represented by GEM [14] from the U.S., GOMAS [15; 16; 17] from the E.U., and GeoMWR [18] from China. However, due to technical difficulties in the large-aperture antenna, such as processing and manufacturing, assembly and unfolding, mechanical scanning, radiometric calibration, and on-board thermal distortion compensation, the above projects also remain in the scheme design stage. Owing to the limited instantaneous field of view (IFOV) of the antenna beam, the GEO microwave radiometer requires the commanded two-dimensional (2-D) attitude maneuvers of an agile satellite to help implement beam coverage in the particular scene. Ideally, if the satellite could maneuver properly in an ideal geostationary orbit in accordance with the pre-planned scan instructions, and the antenna of the microwave radiometer was free of thermal distortions, the radiometer would provide the end user with near-real-time radiometric data that were perfectly preregistered with respect to a nominal fixed grid valid for the GEO satellite [19; 20]. In this case, the sampled radiometric observations could be directly transmitted to the follow-on GEO meteorological applications (without the time-consuming and laborious postprocessing of re-geolocation) to ensure timeliness. However, in practice, influenced by many disturbing factors (e.g., platform vibration, orbital motion, attitude deviation, solar and lunar gravity, and orbital heat flux), the mounting positions and mounting angles of antenna elements will inevitably change, thus making the actual antenna beam pointing (ABP) deviate from the ideal settings. This would cause the acquired samples to drift away from their corresponding nominal grid cells and consequently affect the accuracy of their subsequent applications. The development of modern numerical weather prediction (NWP) technology proposes higher requirements for the direct geolocation accuracy of satellite radiometer data. For GEO microwave radiometers in particular, a slight deviation in the ABP will have a significant impact on the absolute positioning accuracy of the radiometric data. When the absolute positioning accuracy at the GEO sub-satellite point (SSP) is in the magnitude of 1 \(\times\) 10\({}^{3}\) m, the ABP accuracy should be better than 28 \(\upmu\)rad (about 6\({}^{\prime\prime}\)).