Analytical and simulation-based comparison between traditional and Kalman filter-based phase-locked loops

Abstract

We investigate and quantitatively analyze the similarities and differences between traditional phase-locked loops (PLLs) and Kalman filter (KF)-based PLLs. We focus on three aspects. First, the transient response of traditional and KF-based PLLs versus the steady-state bandwidth is investigated, where the transient time is used as a criterion to compare their tracking performance in the transient state. Second, the noise performance and the dynamic response of the PLL are investigated and compared, in the cases that the Doppler shift is extracted from either the velocity accumulator or the filter output. Moreover, the steady-state frequency error due to the high signal dynamics is derived. Third, a method that feeds back the frequency rate to numerically controlled oscillator (NCO) is proposed, where a detailed derivation of the quantitative mathematical relationship between the phase mismatch, the coherent integration interval and the signal dynamics is performed. The proposed method provides an effective approach to reducing the significant phase mismatch and obtaining more accurate carrier phase measurements in applications where high dynamics or long integration intervals may influence the tracking performance of the GNSS receivers.