On the identifiability of noise statistics and adaptive KF design for robust GNSS carrier tracking

Carrier synchronization is of paramount importance in any communications or positioning system. Mass-market Global Navigation Satellite System (GNSS) receivers typically implement traditional carrier tracking techniques based on well-established phase-locked loop architectures, which are only reliable in quite benign propagation conditions. Under nonnominal harsh propagation conditions, the signal may be affected by shadowing, strong fading, multipath or severe ionospheric scintillation, and thus, traditional architectures are not valid anymore and there exists an actual need for robust tracking solutions. Several approaches to overcome the conventional PLL limitations have appeared during the last decade, being the Kalman filter (KF) based architectures the most promising research line. The main drawback of standard KFs is the assumption of perfectly known process and measurement noise statistics, a knowledge that is always constrained by the system model accuracy. Beyond heuristic solutions, a general framework for the design of adaptive KFs correctly dealing with both process and measurement noises, that would be of capital importance for the practitioner, has not been established. The main goal of this contribution is to provide a clear answer to this fundamental question. It is shown that the main driver on the KF performance is not the adjustment of the measurement noise but the adequate tuning of the process noise statistics. Within this framework, a comprehensive discussion is given for the correct design of adaptive KF architectures for robust carrier tracking applications, where the key idea is to use two independent noise statistics estimation strategies to sequentially adapt both parameters. The design choice is supported by a discussion on the identifiability of the noise statistics' parameters. Simulation results are provided showing the need of fully adaptive solutions, and the achieved performance gain of KF-based architectures when compared to traditional tracking loops.