# Precise Orbit Determination of BDS-2 and BDS-3 Using SLR
## 2 Methodology  
### Orbit Determination Strategy  
The methodology of SLR-only orbit determination is consistent with that of [PERSON], [PERSON] and [PERSON] (1998), while the strategy of configuration of some parameters is changed and applied to BDS GEO, as well as for BDS-3 satellites, in this contribution. As shown in Table 1, the microwave-based precise orbits and the corresponding Earth Rotation Parameter (ERP) derived from WUM (ftp: //cddis.gsfc.nasa.gov/gnss/products/mgex/) are used to estimate the a priori orbital parameters, as well as the 9-parameter Empirical CODE Orbit Model (ECOM) SRP model ([PERSON] et al., 2016). As for the other dynamic model parameters, the N-body perturbation of the Sun, the Moon, and the major planets (Jupiter, Venus, and Mars) are considered using JPL DE405 ([PERSON] et al., 2017) while the Earth gravity field terms are limited to the degree and order of 12 of the EGM2008 model. In addition, the SLR site displacement models are consistent with the Earth Rotation and Reference System Service (IERS) conventions 2010 ([PERSON] et al., 2016), including the solid Earth tide, the related pole tides, the ocean tidal loading, and the general relativistic effect. The SLR site coordinates are fixed to the a priori reference frame SLRF2014 ([[ftp://cddis.nasa.gov/slr/products/resource/](ftp://cddis.nasa.gov/slr/products/resource/)]([ftp://cddis.nasa.gov/slr/products/resource/](ftp://cddis.nasa.gov/slr/products/resource/))), with the corresponding corrections of the site coordinate eccentricity, as presented in [[ftp://cddis.gsfc.nasa.gov/slr/slrocc/ecc_une.snx](ftp://cddis.gsfc.nasa.gov/slr/slrocc/ecc_une.snx)]([ftp://cddis.gsfc.nasa.gov/slr/slrocc/ecc_une.snx](ftp://cddis.gsfc.nasa.gov/slr/slrocc/ecc_une.snx)). Besides, the troposphere delay is corrected via the Mendes-Pavlis model ([PERSON], 2019). For the estimated parameters, the station coordinates are strongly constrained to \(10^{-5}\) metres in each direction, while the ERP are fixed to the corresponding a priori value provided by WUM. A range bias is estimated simultaneously with other parameters in each multi-day arc solution for all available SLR sites and each BDS satellite. The SLR range bias parameters are constrained to a priori sigma of 0.1 m with no constraints to the Keplerian and empirical orbit parameters. The 'ALL' for range biases in Table 1 means that a range bias is estimated for all available SLR site and each BDS satellite. Moreover, the offset of the Centre-of-Mass of LRAs for BDS-2 satellites is fixed the same as in [PERSON] et al. (2019). The China Academy of Space Technology (CAST) and the Shanghai Engineering Center for Microsatellites (SECM), as the two manufacturers of BDS-3, calibrated the Centre-of-Mass offset of LRAs related to the centre of mass of the satellite body for BDS-3 satellites respectively, as shown in Table 2.  
Figure 1 shows the multi-day arcs solution strategy in this contribution. The whole procedure is implemented in the batch processing mode by moving time window. The procedure is realized through our modification of the Bernese GNSS Software 5.2 [21]. At first, the SLR Normal Points (NPs) data is preprocessed by comparing the station-satellite distance between SLR and the microwave-based priori orbit from WUM. For BDS IGSO and MEO, when the residuals of the SLR observations exceed 300 mm, the observations are eliminated in our preprocessing stage, while for BDS GEO satellites, the corresponding threshold is 1,000 mm. Then, the 1-day parameters are estimated and the corresponding normal equations (NEQs) are generated synchronously, based on the clean SLR observations. The multiple 1-day NEQs are combined into the multi-day NEQs in accordance with to the moving time window sequence. Subsequently, each set of stacked multi-day NEQs estimates a set of corresponding orbital parameters. This classic methodology was initially implemented by [PERSON] et al.