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 performed through two factors, frequency thermal noise and frequency dynamic stress error, which determine total frequency tracking error. We derive the thermal noise and dynamic stress error formula in LQG-VTL. From frequency tracking error analysis, we can determine control gain matrix in LQG controller and show that the frequency tracking error of LQG-VTL is lower than that of EKF-VTL in all C/N0 ranges. We also confirm that the maximum trackable CN/0 value is at last 5 dB-Hz lower in LQG-VTL compared to EKF-VTL under the same EKF tuning and pre-integration time. This results show that LQG-VTL is more robust for weak signals in high dynamics environments.

Keywords: vector tracking loop, LQG, frequency tracking error, thermal noise, dynamic stress error