Rotation state estimation of slow-rotating multi-reflector defunct spacecraft through laser ranging measurements from a single short arc

The satellite laser ranging (SLR) echo signals of the multi-reflector defunct spacecraft contain multiple distance information corresponding to the corner cube reflectors (CCRs) in different installation positions. The relative distances between different CCRs and their variations depend on the rotation state of the object. However, the rotation of many defunct spacecraft is relatively slow over a short observation time span. In this case, estimating the effective rotation state is still difficult due to the limited amount of information. In this paper, a slow-rotating multi-reflector defunct spacecraft CZ-2C R/B (NORAD ID 31114) is taken as an example to develop a new method to estimate the rotation state through laser ranging measurements from a single short arc. The reference vector method is used in new attitude representation. The reduced expressions between the relative distances, their first derivative and rotation state are derived. Through the state estimation method combining grid search and differential corrections, the reduced parameters are estimated efficiently and accurately. In addition, the consistent orientation of maximum principal axis of inertia of CZ-2C R/B are obtained, which provides effective information for the subsequent research.