Abstract: Geometry computation is crucial for global navigation satellite systems reflectometry (GNSS-R), serving as a fundamental aspect for processing the reflected signals onboard and determining the measurement locations. However, the existing geometry computation methods can not meet the requirements of various scenarios, including land, ocean, and cryosphere applications, as this technique expands into new domains. This paper proposes a geometry computation strategy that achieves high accuracy and incorporates considerations for the Earth's curvature and ellipsoidal height. It integrates a initialization model for specular point calculation, and the accuracy of the initial estimation error can be reduced to within 5 km for different orbital altitudes (300~900 km) and geometric conditions. This method allows for high-precision geometry computation based on the WGS-84 ellipsoid, and takes into account the ellipsoidal height of the reflective surface, with an accuracy of less than 1 mm. The computational efficiency is significantly improved compared to existing methods, which can be beneficial for future demands of efficient computation considering surface height. Furthermore, the method can calculate the geometric path of the reflection signal by modifying the iterative equation, and achieves the integrated solution from the observed delay to the specular point and ellipsoidal height. Compared with the previous methods, it considers the Earth's curvature and the spatial offset of the reflection point varying with the ellipsoidal height, which can avoid the problem of inaccurate positioning of measurements in altimetric applications.

Key words: GNSS reflectometry, geometry computation, initial specular point estimation, Earth's curvature, ellipsoidal height