Enhanced orbit determination for formation-flying satellites based on M-estimation

Abstract

The classical least-squares estimation (LS) has been widely used for parameter estimation in satellite precise orbit determination (POD). However, the classical LS estimation with uniform weighting is very sensitive to outliers in the observations. To overcome this issue, we use the M-estimation on the basis of the LS estimation to improve the POD solutions. To demonstrate the added value of the M-estimation, we use one year of GPS data collected by the GRACE Follow-On mission, and two sets of orbits are produced using both the LS and M-estimation. The obtained orbits are assessed through orbit formal error analysis, orbit comparison, residual analysis of satellite laser ranging (SLR), and K-band ranging (KBR) measurements. Formal error analysis shows that the precision can be improved with the M-estimation notably by 25 and 40% for the dynamic and kinematic orbit, respectively. Orbit comparison reveals that the M-estimation can offer better solution consistency between the dynamic and kinematic orbit, with the differences being reduced by 23% when compared to the LS estimation. KBR validation reports that the relative precision can be improved with the M-estimation significantly by 23 and 40% for the dynamic and kinematic orbit, respectively. Specifically, the KBR residuals are reduced from 0.65 to 0.50 mm for dynamic orbit, and from 3.24 to 1.96 mm for kinematic orbit. These results demonstrate that the M-estimation can improve the orbit precision in both absolute and relative senses. Finally, we find that the current orbit accuracy is likely dominated by systematic errors, which can obscure the contribution of the M-estimation. The SLR measurements, with precision at 5–10 mm level, also seem to be not precise enough to validate the potential contribution. As a result, the improvements as indicated by the SLR validation are shown to be insignificant.