GPS satellite differential code bias estimation with current eleven low earth orbit satellites

Many low earth orbit (LEO) missions have been launched recently for different geoscience studying purposes such as ionosphere detecting and gravity recovering. The onboard observations from LEO satellites provide us a great opportunity to estimate the differential code bias (DCB) which is vital for precise applications of global navigation satellites system. This paper mainly focuses on the contribution of multi-LEO combination to the DCB estimation using onboard data collected by current eleven LEO satellites from day of year (DOY) 061, 2018 to DOY 120, 2018. The single-LEO solutions with different LEO and multi-LEO solutions with different LEO subsets are compared and analyzed in detail to fully exploit the potential of LEO onboard observations in the DCB estimation. We also evaluate and discuss the vertical total electron content (VTEC) results and posterior residuals to validate the estimation accuracy. Our results show that the average DCB standard deviation (STD) values are within 0.140 ns for all eleven single-LEO solutions with the best stability of 0.082 ns for Swarm-B solution. The evaluation of multi-LEO solutions indicates that with the increase in LEO satellites, the GPS DCB stability gets improved gradually. The 9-LEO solution can achieve the stability with STD value of 0.051 ns, better than that of DCB products from the German Aerospace Center (DLR) (0.055 ns) but slightly worse than that of DCB products from the Chinese Academy of Sciences (CAS) (0.048 ns). The results suggest that the GPS DCB stability based on the onboard observations of nine LEO satellites can be comparable to the ground-based solution derived from a global ground network with hundreds of stations. The LEO space-borne receiver DCB results illustrate that the inclusion of more LEO satellites can contribute to the stability improvement of receiver DCB. In addition, the VTEC estimation can benefit from the joint processing of multiple LEO observations and achieves a noticeable reduction in the percentage of negative VTEC values. Our results also reveal that the spherical symmetry ionosphere assumption might cause accuracy degradation in the DCB estimation at low latitudes.