This paper proposes moving set-point state feedback for a LQG control system. In contrast to the independent code and carrier tracking loop of a conventional receiver algorithm, the code and carrier tracking variables are correlated in the LQG system. Not only are the multiple states correlated with each other, but also the control inputs are formulated from a combination of the states and the optimal LQG controller gain. In addition, this paper develops a moving set point to estimate the GNSS signal more accurately. To analyze the advantage of the proposed method, a signal tracking simulation using hardware GNSS simulator is performed and the simulation results show that the tracking performance of the moving set-point LQG system is better than that of a conventional loop filter, especially in terms of the code tracking performance.