Theoretical analysis and tuning criteria of the Kalman filter-based tracking loop

In recent years, Kalman filter (KF)-based tracking loop architectures have gained much attention in the Global Navigation Satellite System field and have been widely investigated due to its robust and better performance compared with traditional architectures. However, less attention has been paid to the in-depth theoretical analysis of the tracking structure and to the effects of Kalman tuning. A new approach is proposed to analyze the KF-based tracking loop. A control system model is derived according to the mathematical expression of the Kalman system. Based on this model, the influence of the choice of the setting parameters on the temporal evolution of the system response is discussed from the perspective of a control system. As a result, a reasoned and complete suite of criteria to tune the initial error covariance as well as the process and measurements noise covariances is demonstrated. Furthermore, a strategy is presented to make the system more robust in higher order dynamics without degrading the accuracy of carrier phase and Doppler frequency estimates.