## 1 Introduction
Additionally, the cost of the GNSS-R satellite platform and payload are relatively low, thus a \(\sim\)6-8 satellites constellation can be formed to increase the amount and frequency of observation by several times combined with a parameter optimized design of the dedicated nadir-pointing antenna, orbit, and constellation [24; 25]. Therefore, GNSS-R satellite network observation is an effective means to obtain global high-spatial-resolution SSH. On the other hand, the retrieval of high-accuracy ocean gravity field requires sea surface altimetry to achieve centimeter level accuracy [26]. The GNSS-R sea surface altimetry has strict requirements for path delay error control of signal transmission. The main error sources include the errors of transmission in atmospheric, sea surface scattering and receiving, and processing of the electromagnetic wave signals emitted by GNSS satellites, as well as the errors of positioning the specular reflection point and the receiver nadir point on the complex and changing sea surface [27; 28]. The specular reflection point is the point on the reflection surface that minimizes the distance that the GNSS satellite signal reaches the receiver through reflection [1]. The GNSS-R Delay Doppler Map (DDM) which contains the information of the Doppler shift and code phase delay takes the specular reflection point position as standard reference. The position information of the specular reflection point is also used to accurately model the rising edge of the delayed wave [29]. Calculating the SSH according to the Leading Edge Derivative (LED) algorithm requires calculating the time delay of the reflected signal relative to the direct signal based on the positions of the transmitter, the receiver, and the specular reflection point [15; 30]. In the case where the error caused by the orbital uncertainty of the GNSS satellite and the receiver is known, the error of the time delay and the length of the reflected signal path are mainly determined by the specular reflection point positioning error at the sea surface and the atmospheric transmission error of the signal [27; 28]. In addition, the output signal-to-noise ratio of the dual-base radar system is related to the signal propagation path, which is directly related to the position of the specular reflection point [31]. In sea surface remote sensing applications, the precise position information of the specular reflection points can also be used to determine whether the reflected signal is from the surface of the sea, the land or the ice. The specular reflection point is taken as the reference point of the GNSS-R signal reflection geometry and the relevant parameters, its positioning error affects the accuracy of GNSS-R remote sensing products and the estimation of observation capabilities parameters such as spatiotemporal resolution on the reference datum [32], especially the SSH accuracy which is directly related to the path error. The specular reflection point positioning methods can be divided into physical methods and geometric methods. The physical methods are based on the processing of the received signals [30], the geometric methods, on which this study carries out research, are based on the geometric conditions that the specular reflection points should satisfy [27; 28; 29; 33; 34; 2]. At present, the geometric positioning methods of the specular reflection point are mainly the Sien-Chong (S-C) Wu method, the dichotomy, the Wagner method, and the Gleason method. The S-C Wu method has two steps: the first step is to use the spherical surface as the reflection surface to search the rough position of the specular reflection point, and the second step corrects the specular reflection point from the spherical surface to the reference ellipsoid [28]. The dichotomy iteratively searches the position of the specular reflection point on the spherical surface based on solving the zero-crossing solution of the equation by the dichotomy [33].