State estimation of double-pyramid tethered satellite formations using only two GPS sensors

Recently, space tethered satellite system has attracted widespread attention due to its attractive potential in space applications. Significant research on the tethered satellite formations has been undertaken to study the dynamics and control, vibration modes, tether models, and tether applications and it is generally assumed that the state information of the tethered satellite system is completely known or can be easily measured. However, few studies have been presented on the state estimates of the tethered formations. In this study, a state estimation scheme, with a minimal sensor fusion design, is presented for double-pyramid tethered satellite formations. The objective is achieved by fusing only the measurements of the two GPS sensors and the tether constraints. Furthermore, the observability of the proposed fusion design is proved through the analyses of Lie derivatives. Simulation results are presented that validate the proposed scheme. The proposed scheme provides a general hint of state estimation for a class of satellite formations with the tethered constraints.