Are PLLs dead? A tutorial on kalman filter-based techniques for digital carrier synchronization

Abstract

Carrier synchronization is a fundamental stage in the receiver side of any communication or positioning system. Traditional carrier phase tracking techniques are based on well-known phase-locked loop (PLL) closed-loop architectures, which are still the methods of choice in modern receivers. Those techniques are well understood, easy to tune and perform well under benign propagation conditions, but their applicability is seriously compromised in harsh propagation environments where the signal may be affected by high dynamics, shadowing, strong fadings, multipath effects or ionospheric scintillation.From an optimal filtering standpoint, the Kalman filter (KF) is clearly a powerful alternative, but the synchronization community seems still reluctant to exploit all the potential it has to offer. The purpose of this paper is twofold: i) to review the basics and state-of-the-art on both PLL and KF-based tracking techniques, and ii) to present and justify the reasoning behind the systematic use of KF-based tracking approaches instead of the well-established PLL-based architectures from both theoretical and practical points of view. To support the discussion, two specific scenarios of interest to the aerospace community are numerically evaluated: robust carrier tracking of Global Navigation Satellite Systems' signals and synchronization in a deep space communications system.

Multi-frequency GNSS robust carrier tracking for ionospheric scintillation mitigation

“…Notice that the Kalman gain, K k , is computed from the possibly time-varying system noise matrices, Q k and R k , which implies that the filter is adapting its behavior to the actual working conditions and has an implicit adaptive bandwidth, in contrast to the traditional PLL with constant coefficients (i.e., fixed bandwidth) (Vilà-Valls et al 2017b). …”

“…Specifically, the performance obtained with the AEKF-AR and MAR-EKF is improved with respect to the othermethods. This is due to the Gaussianity assumption,which is does not hold when working with a discriminator under fading conditions (Vilà-Valls et al 2017b). …”

“…Most of state-of-the-art (SoTA) techniques propose methods to robustify DLL/PLL schemes via fine tuning and augmentation (Yu et al, 2006;López-Salcedo et al, 2014), either by using adaptive bandwidth schemes (Skone et al, 2005) or combined architectures (Chiou, 2010;Won, 2014). It has already been shown that Kalman filter (KF)-based solutions provide better performances and robustness in these situations (Humphreys et al, 2005;Macabiau et al, 2012), being nowadays the performance benchmark for the development of new methodologies (Vilà-Valls et al, 2017b). The natural extension is to use adaptive KF-based solutions (Zhang et al, 2010;Won et al, 2012), which aim at sequentially adapt the filter parameters.…”

Centralized dynamics multi‐frequency GNSS carrier synchronization

“…For this reason, an adaptive scheme is needed to effectively change the equivalent noise bandwidth with respect to the signal C / N 0 value and signal dynamics estimated using the signal carrier phase error measurements. There are many approaches to realize an adaptive tracking loop with respect to changing signal environment as discussed in Vilà‐Valls et al…”

On the Mitigation of Ionospheric Scintillation in Advanced GNSS Receivers

“…It is well known that, under certain conditions, both PLL and KF architectures are equivalent [59], [60], [61]. The standard prediction/update KF equations [62] can be easily interpreted as a gain PLL [61], where the KF innovations' sequence can be seen as the output of a discriminator. The standard KF formulation, as implicitly done by the PLL, considers that θ k = θ d,k .…”