# Advancing the Solar Radiation Pressure Model for BeiDou-3 IGSO Satellites
## 4 Discussion  
Daily clock fitting residual RMS for BeiDou-3 IGSOs based on the ECOM1 model show prominent \(\beta\) -dependent effects. This originates from not taking into account the contribution of BeiDou-3 IGSO stretched body, especially at a low \(\beta\) -angle, which results in systematic once-per-revolution radial orbit errors. Therefore, a box-wing model is developed for BeiDou-3 IGSOs by estimating the surface optical parameters, which are not yet published or not precisely known. This systematic error is effectively removed overall by augmenting the ECOM1 model with the developed a priori box-wing model. Moreover, the orbit quality improvement during non-eclipse seasons is very significant. Compared to the ECOM1 and ECOM2 solutions, the clock residual RMS decreases by 3.2 cm (47.1%) and 1.4 cm (28.0%), respectively, and the radial and 3D orbit consistency outside eclipse seasons improves by about 2.2 (32.7%) and 5.1 cm (29.5%), 1.2 (21.1%) and 2.6 cm (17.6%), respectively. However, the orbit performance over the eclipse seasons is much worse than during the non-eclipse periods for the ECOM1, ECOM2 and ECOM1 + BW solutions according to the deteriorated estimates of satellite clocks and elevated orbit DBDs. Attitude analyses show that the yaw behaviors of BeiDou-3 IGSOs have been well reproduced in the study. This rules out the possibility that attitude errors are the reason for the orbit deterioration. Therefore, the orbit degradations are caused by unaccounted non-conservative forces, such as thermal radiation during Earth's shadow transitions. Considering the signal presented in the BeiDou-3 IGSO clock residuals can be also seen in the Galileo FOC satellites, the method proposed by [22] for servicing eclipsing Galileo FOC satellites, i.e., introducing the \(D_{\rm s}\) term and keeping it active during the Earth's shadow transitions, are used for eclipsing BeiDou-3 IGSO orbit determination. The resulted solution has almost the same performance inside and outside the eclipse reasons measured by the orbit DBDs and the estimated clocks. Therefore, the SRP model which contains the ECOM1 model and \(D_{\rm s}\) term active during eclipse seasons and the developed box-wing model as initial value is recommended for BeiDou-3 IGSO orbit determination. For BeiDou-3 IGSOs with poor observation geometry, the addition of empirical parameters will potentially increase correlations between the parameters, leading to a weakening of the parameters in the estimation process. Therefore, developing a high-fidelity force model to interpret the unaccounted orbit effects causing the solution deterioration is preferred over the activation of the empirical parameter \(D_{\rm s}\). This requires the BeiDou-3 IGSO manufacturers to disclose the more detailed spacecraft metadata package. Conceptualization, F.X. ; methodology, F.X. ; software, M.G. and F.X. ; writing--original draft preparation, F.X. ; writing--review and editing, M.G. and F.N. ; formal analysis, D.C.,  
Figure 12: Orbit 3D DBDs of BeiDou-3 IGSOs for the ECOM1 + BW (**left**) and ECOM1D + BW (**right**) solutions against \(\beta\) -angle. The area shaded in gray indicates eclipse seasons. L.T. and C.W. ; project administration, S.Y. and F.X. All authors have read and agreed to the published version of the manuscript. This work of [PERSON] and [PERSON] was funded by the National Key Research and Development Program of China (Grant No. 2019 YFC1509603) and the National Science Foundation of China (Grant No. 41974031, 41974038). The work of [PERSON] was supported by Natural Science Basic Research Program of Shaanxi (Grant No. 2022 JQ-283). [PERSON] is financially supported by the China Scholarship Council (CSC) for his study at the Institute of Geodesy and Geoinformation Science, Technische Universitat Berlin. Not applicable. The raw GNSS data from MGEX stations are publicly available at [[ftp://cddis.gsfc.nasa.gov](ftp://cddis.gsfc.nasa.gov)]([ftp://cddis.gsfc.nasa.gov](ftp://cddis.gsfc.nasa.gov)) (accessed on 15 May 2021).