Hypercomplex Representation and Processing of GNSS Signals

Daniele Borio

Peer Reviewed

Abstract:	Generalized binary offset carrier (BOC) modulations and global navigation satellite system (GNSS) meta-signals require advanced processing algorithms to overcome the problems associated to their complex multi-peaked correlation functions. In this paper, hypercomplex numbers are introduced for GNSS signal representation and for algorithm development. The term “hypercomplex” is generally used to denote sets generalizing complex numbers and having more than one imaginary unit. They have the potential to represent multi-component signals, such as GNSS meta-signals, leading to a compact notation allowing effective derivations and algorithm development. The set of bicomplex numbers is considered and it is shown that they can be used to effectively represent a meta-signal made of components from two different frequencies. Using bicomplex numbers, it is possible to express a meta-signal as the product of a code, a carrier and a subcarrier component: this representation and the properties of bicomplex numbers lead to acquisition and tracking algorithms able to effectively process GNSS meta-signals solving the code ambiguity problem. Theoretical developments are demonstrated using real data collected using a software defined radio (SDR) front-end for the Galileo alternative binary offset carrier (AltBOC) signal.
Published in:	Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022) September 19 - 23, 2022 Hyatt Regency Denver Denver, Colorado
Pages:	3160 - 3179
Cite this article:	Borio, Daniele, "Hypercomplex Representation and Processing of GNSS Signals," Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022), Denver, Colorado, September 2022, pp. 3160-3179. https://doi.org/10.33012/2022.18392
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