Frequency Tracking Error Analysis of LQG Based Vector Tracking Loop for Robust Signal Tracking

In this paper, we implement linear-quadratic-Gaussian based vector tracking loop (LQG-VTL) instead of conventional extended Kalman filter based vector tracking loop (EKF-VTL). The LQG-VTL can improve the performance compared to the EKF-VTL by generating optimal control input at a specific performance index. Performance analysis is conducted through two factors, frequency thermal noise and frequency dynamic stress error, which determine total frequency tracking error. We derive the thermal noise and the dynamic stress error formula in the LQG-VTL. From frequency tracking error analysis, we can determine control gain matrix in the LQG controller and show that the frequency tracking error of the LQG-VTL is lower than that of the EKF-VTL in all C/N0 ranges. The simulation results show that the LQG-VTL improves performance by 30% in Doppler tracking, so the LQG-VTL can extend pre-integration time longer and track weaker signals than the EKF-VTL. Therefore, the LQG-VTL algorithm is more robust than the EKF-VTL in weak signal environments.