To mitigate the loss of satellite navigation signals in urban canyons and indoor environments, we propose an active simultaneous transmitting and reflecting reconfigurable intelligent surface (ASTARS) empowered satellite positioning approach. Deployed on building structures, ASTARS reflects navigation signals to outdoor receivers in urban canyons and transmits signals indoors to bypass obstructions, providing high-precision positioning services to receivers in non-line-of-sight (NLoS) areas. The path between ASTARS and the receiver is defined as the extended line-of-sight (ELoS) path and an improved carrier phase observation equation is derived to accommodate that. The receiver compensates for its clock bias through network time synchronization, corrects the actual signal path distance to the satellite-to-receiver distance through a distance correction algorithm, and determines its position by using the least squares (LS) method. Mathematical modeling of the errors introduced by the proposed method is conducted, followed by simulation analysis to assess their impact. Simulation results show that: 1) in areas where GNSS signals are blocked, with time synchronization accuracy within a 10 ns error range, the proposed method provides positioning services with errors not exceeding 4 m for both indoor and outdoor receivers, outperforming conventional NLoS methods with positioning errors of more than 7 m; 2) the additional errors introduced by the proposed method do not exceed 3 m for time synchronization errors within 10 ns, which includes the phase shift, beamwidth error, time synchronization errors, and satellite distribution errors, outperforming traditional NLoS methods, which typically produce positioning errors greater than 5 m.