Study of Low-Cost Orbit Determination System for Tethered Satellites

Abstract

The statistics of estimated errors when conducting the orbit determination of a tethered satellite system (TSS) by only using Doppler frequencies is shown. TSS consists of two satellites connected each other by a tether. The center of mass (CM) moves like a single satellite, so this system can be utilized in case of a single satellite as well as TSS. This is considered as a low-cost orbit determination system because it can be realized with simple instruments. This kind of low-cost ground station will charm institutions that are developing a micro satellite in a small budget. The result will provide a useful reference in constructing a ground station for the orbit determination by only Doppler frequencies. The TSS motion model is explained at first. The transformation from covariance matrix of TSS state into the easy-to-image coordinates is explained. Following simulations are examined by supposing 800-km altitude circle LEO with high inclination: Case of measurement from two satellites in 7-day span, Influence by different values of tether length or epoch swing amplitude, and Comparison with patterns of measurement or the number of ground stations. From the results, estimated standard deviations of TSS are quantified when using measurement data of two satellites. If either satellite’s data is only available, it is difficult to determine the tether length and the mass ratio. However, state of CM can be determined in accuracy of some extent.