China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing (bw) model based on the estimated optical properties is introduced. Various physical effects, such as yaw bias, self-shadowing, radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model, 5 parameters), ECOM+along-track and ECOM2 (both 7 and 9 parameters) models are employed on top of the a priori box-wing model in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. The STD (standard deviation) of daily LOD estimates with respect to IERS-C04-14 series increases from 40 s (ECOM) to 85 s (ECOM+along-track). After the consideration of the a priori box-wing model, satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons; dependencies of SLR (satellite laser ranging) residuals on the sun elongation angle almost vanish for BDS-3 satellites. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters. In particular, the total amplitude of the 1, 3, 5, 7 cpy signals for the geocenter Z component has been reduced by a factor of 4.5 for the ECOM model. In general, the combination of the introduced physical a priori box-wing model and the ECOM model is preferred for BDS satellites.

The Russian Global Navigation Satellite System (GLONASS) satellites have a stretched body shape and take a specific attitude mode inside the eclipse. Based on previous studies, the new Empirical CODE orbit model (ECOM2) performs better than the classical ECOM model if a satellite has elongated shape or does not maintain yaw-steering mode, and the use of an a priori box-wing (BW) model improves the orbits significantly when employing the ECOM model. However, we find that the ECOM model performs better than the ECOM2 model for GLONASS satellites outside eclipse seasons, while it performs two times worse in eclipse seasons. The use of the conventional box-wing model results in very little improvement. By assessing the ECOM $$Y _{0}$$Y 0 estimates, we conclude that there are potential radiators on the $$-x$$- x surface of GLONASS satellites causing orbit perturbations also inside the eclipse. The higher-order Fourier terms of the ECOM2 model can compensate for such effects better than the ECOM model. Based on this finding, we first confirm that GLONASS-K satellites take a similar attitude mode as GLONASS-M satellites inside the eclipse. Then, we adjust optical parameters of GLONASS satellites as part of precise orbit determination (POD) considering the potential radiator and thermal radiation effects. Finally, the adjusted parameters are introduced into a new box-wing model and jointly used with the ECOM and ECOM2 model, respectively. Results show that the amplitude and the dependency of the empirical parameters on the $$\beta $$β angle are greatly reduced for both ECOM and ECOM2 models. Rather than the conventional box-wing model, the new box-wing model reduces the orbit misclosure between two consecutive arcs for both GLONASS-M and GLONASS-K satellites. In particular, the improvement in GLONASS-M satellites is more than 30% for the ECOM model during eclipse seasons. Further evaluation from 24-h predicted orbits demonstrates that the improvement during eclipse seasons is mainly in along- and cross-track directions. Finally, we validate GLONASS satellite orbits using Satellite Laser Ranging (SLR) observations. The use of the new box-wing model reduces the spurious pattern of the SLR residuals as a function of $$\beta $$β and $$\Delta u$$Δ u significantly, and the linear dependency of the SLR residuals on the elongation drops from as large as $$-0.760$$- 0.760 mm/deg to almost zero for both ECOM and ECOM2 models. In general, GLONASS-M satellites benefit more from the new a priori box-wing model and the BW+ECOM model results in the best SLR residuals, with an improvement of about 50% and 20%, respectively, for the mean and standard deviation (STD) values with respect to the orbit products without a priori model.

Solar radiation pressure (SRP) is the dominant non-gravitational perturbation for GPS satellites. In the IGS (International GNSS Service), this perturbation is modeled differently by individual analysis centers (ACs). The two most widely used methods are the Empirical CODE orbit Model (ECOM, ECOM2) and the JPL GSPM model. When using ECOM models, a box-wing model or other a priori models, as well as stochastic pulses at noon or midnight, are optionally adopted by some ACs to compensate for the deficiencies of the ECOM or ECOM2 model. However, both box-wing and GSPM parameters were published many years ago. There could be an aging effect going with time. Also, optical properties and GSPM parameters of GPS Block IIF satellites are currently not yet published. In this contribution, we first determine Block-specific optical parameters of GPS satellites using GPS code and phase measurements of 6 years. Various physical effects, such as yaw bias, radiator emission in the satellite body-fixed − X and Y directions and the thermal radiation of solar panels, are considered as additional constant parameters in the optical parameter adjustment. With all the adjusted parameters, we form an enhanced box-wing model adding all the modeled physical effects. In addition, we determine Block-specific GSPM parameters by using the same GPS measurements. The enhanced box-wing model and the GSPM model are then taken as a priori model and are jointly used with ECOM and ECOM2 model, respectively. We find that the enhanced box-wing model performs similarly to the GSPM model outside eclipse seasons. RMSs of all the ECOM and ECOM2 parameters are reduced by 30% compared to results without the a priori model. Orbit misclosures and orbit predictions are improved by combining the enhanced box-wing model with ECOM and ECOM2 models. In particular, the improvement in orbit misclosures for the eclipsing Block IIR and IIF satellites, as well as the non-eclipsing IIA satellites, is about 25%, 10% and 10%, respectively, for the ECOM model. Therefore, the enhanced box-wing model is recommended as an a priori model in GPS satellite orbit determination.

To resolve undifferenced GNSS phase ambiguities, dedicated satellite products are needed, such as satellite orbits, clock offsets and biases. The International GNSS Service CNES/CLS analysis center provides satellite (HMW) Hatch-Melbourne-Wübbena bias and dedicated satellite clock products (including satellite phase bias), while the CODE analysis center provides satellite OSB (observable-specific-bias) and integer clock products. The CNES/CLS GPS satellite HMW bias products are determined by the Hatch-Melbourne-Wübbena (HMW) linear combination and aggregate both code (C1W, C2W) and phase (L1W, L2W) biases. By forming the HMW linear combination of CODE OSB corrections on the same signals, we compare CODE satellite HMW biases to those from CNES/CLS. The fractional part of GPS satellite HMW biases from both analysis centers are very close to each other, with a mean Root-Mean-Square (RMS) of differences of 0.01 wide-lane cycles. A direct comparison of satellite narrow-lane biases is not easily possible since satellite narrow-lane biases are correlated with satellite orbit and clock products, as well as with integer wide-lane ambiguities. Moreover, CNES/CLS provides no satellite narrow-lane biases but incorporates them into satellite clock offsets. Therefore, we compute differences of GPS satellite orbits, clock offsets, integer wide-lane ambiguities and narrow-lane biases (only for CODE products) between CODE and CNES/CLS products. The total difference of these terms for each satellite represents the difference of the narrow-lane bias by subtracting certain integer narrow-lane cycles. We call this total difference “narrow-lane” bias difference. We find that 3% of the narrow-lane biases from these two analysis centers during the experimental time period have differences larger than 0.05 narrow-lane cycles. In fact, this is mainly caused by one Block IIA satellite since satellite clock offsets of the IIA satellite cannot be well determined during eclipsing seasons. To show the application of both types of GPS products, we apply them for Sentinel-3 satellite orbit determination. The wide-lane fixing rates using both products are more than 98%, while the narrow-lane fixing rates are more than 95%. Ambiguity-fixed Sentinel-3 satellite orbits show clear improvement over float solutions. RMS of 6-h orbit overlaps improves by about a factor of two. Also, we observe similar improvements by comparing our Sentinel-3 orbit solutions to the external combined products. Standard deviation value of Satellite Laser Ranging residuals is reduced by more than 10% for Sentinel-3A and more than 15% for Sentinel-3B satellite by fixing ambiguities to integer values.