M-estimation-based robust and precise baseline determination for formation-flying satellites

Abstract

Precise baseline determination (PBD) is usually required for formation-flying satellite missions. For that purpose, the classical least squares (LS) estimation has been widely used for parameter estimation. It is known, however, that the LS estimation is highly sensitive to outliers in observations. Due to this fundamental defect, the LS estimation may fail to fulfill sub-millimeter or even millimeter precision PBD. We propose to use the M-estimation, which is resistant to outliers, on the basis of the LS estimation to achieve robust and precise baseline estimates. To demonstrate the added value of the M-estimation, we used one year of GPS data collected by the Gravity Recovery and Climate Experiment (GRACE) mission and two sets of precise baselines are produced using both the LS and M-estimation. The obtained baselines are validated by independent K-Band ranging (KBR) measurements. The validation shows that the dynamic and kinematic baselines are improved significantly by 25 and 39%, respectively, when the M-estimation is used. Specifically, the standard deviations of KBR residuals are reduced from 0.51 to 0.38 mm for the dynamic baselines and from 2.30 to 1.40 mm for the kinematic ones. Furthermore, the improvements are more significant when GRACE suffered from a degraded data quality in the first half of 2010, since the baselines produced with the M-estimation are less affected by the degraded quality than those with the LS estimation. These results, therefore, demonstrate that the M-estimation, together with the LS estimation, can offer more robust and precise baselines for formation-flying satellites.