Performance analysis of a Kalman filter carrier phase tracking loop

The equivalent bandwidth of a Kalman filter (KF) tracking loop for a Global Navigation Satellite System receiver is widely used to compare the performance of the KF with that of the traditional phase lock loop (PLL), but the existing literature does not adequately describe why they are comparable in terms of the equivalent bandwidth. The literature does neither address how the factors, including the line-of-sight (LOS) jerk, the local oscillator error, and the measurement noise, impact on the performance of the KF. Furthermore, there is no the rule-of-thumb threshold for the KF up to now. We prove that the steady KF is equivalent to a 3rd-order PLL in the sense of the minimum covariance in the continuous KF form, which makes it possible to compare the KF and the PLL loops in terms of the equivalent bandwidth. The factors that impact the performance of the KF are further investigated by error budgeting and suboptimal analysis. The analysis results show that the oscillator error, the LOS jerk, and the measurement error affect the steady KF error significantly while the initial state covariance has little effect on the convergence of the KF. A rule-of-thumb threshold for the KF, which is determined by the root mean squares of the loop thermal noise and the dynamic stress noise, is presented by analyzing the counterpart for the PLL. Four KF tracking loops are designed upon the proposed rule-of-thumb analysis, which are further validated by the Monte Carlo simulations.