A key limitation for precise orbit determination of BeiDou satellites, particularly for satellites in geostationary orbit (GEO), is the relative weak geometry of ground stations. Fortunately, data from a low earth orbiting satellite with an onboard GNSS receiver can improve the geometry of GNSS orbit determination compared to using only ground data. The Chinese FengYun-3C (FY3C) satellite carries the GNSS Occultation Sounder equipment with both dual-frequency GPS (L1 and L2) and BeiDou (B1 and B2) tracking capacity. The satellite-induced variations in pseudoranges have been estimated from multipath observables using an elevation-dependent piece-wise linear model, in which the constant biases, i.e., ambiguities and hardware delays, have been removed. For IGSO and MEO satellites, these variations can be seen in onboard B1 and B2 code measurements with elevation above 40°. For GEO satellites, a different behavior has been observed for these signals. The GEO B2 pseudoranges variations are similar to those of IGSO satellites, but no elevation-dependent variations have been identified for GEO B1. A possible cause is contamination of the larger noise in GEO B1 signals. Two sets of precise orbits were determined for FY3C in March 2015 using onboard GPS-only data and onboard BeiDou-only data, respectively. The 3D RMS (Root Mean Square) of overlapping orbit differences (OODs) is 2.3 cm for GPS-only solution. The 3D RMS of orbit differences between BeiDou-only and GPS-only solutions is 15.8 cm. Also, precise orbits and clocks for BeiDou satellites were determined based on 97 global (termed GN) or 15 regional (termed RN) ground stations. Furthermore, also using FY3C onboard BeiDou data, two additional sets of BeiDou orbit and clock products are determined with the data from global (termed GW) or regional (termed RW) stations. In general, the OODs decrease for BeiDou satellites, particularly for GEO satellites, when the FY3C onboard BeiDou data are added. The 3D OODs reductions are 10.0 and 291.2 cm for GW and RW GEO solution with respect to GN and RN solution, respectively. Since the OODs in the along-track direction dominate the OODs reduction, no improvement has been observed by satellite laser ranging, which mainly validates the accuracy of the radial orbital component. With the GW BeiDou orbit and clock products, the FY3C orbits determined with onboard BeiDou-only data also show improvement in comparison with those determined with BeiDou GN products.