The tracking precision of fine tracking system is the premise of high-precision positioning in the quantum positioning system. Considering the influence of satellite platform jitter and working environment noise on the tracking accuracy of quantum positioning system, a fine tracking system model with a satellite platform vibration signal model and colored noise signal is established. An adaptive strong tracking Kalman filter （ASTKF）algorithm is designed to estimate the state disturbance and output noise online. The proportionintegrationdifferentiation (PID) controller with ASTKF is designed to perform closed-loop tracking control on the fine tracking system. In the system simulation design, experiments are carried out on the parameters selection of ASTKF. The performance comparison of the fine tracking system with filter and PID controller is compared with the method with PID control or active disturbance rejection control (ADRC). The experimental results show that when adopting PID control with the proposed ASTKF, the tracking accuracy is significantly improved compared with PID or ADRC and can reach the quantum positioning requirement within ±2 μrad.