Abstract: A constrained state estimation scheme based on the pseudo measurement method is proposed for the linear N-body space tethered system (STS), which takes the tether length as prior information and uses only two GPS (global positioning system) sensors. Firstly, a novel general dynamic model of linear N-body STS is established based on UdwadiaKalaba method. Then, an improved square root unscented Kalman filter (IUKF) is developed considering the low update frequency of GPS sensors and the high complexity of Jacobian matrix calculation in the linearization of the nonlinear system model. Furthermore, the rank criterion based on the local weak observability of Lie derivatives is utilized to prove that the proposed estimation scheme is observable. Finally, extensive simulation results are presented to verify the effectiveness of the proposed scheme. The simulation results show that the proposed scheme can guarantee the precise state estimation and real-time tracking.