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Session F2: Advanced Software and Hardware Technologies for GNSS Receivers

Hypercomplex Representation and Processing of GNSS Signals
Daniele Borio, European Commission Joint Research Centre (JRC)
Date/Time: Wednesday, Sep. 21, 1:50 p.m.

Peer Reviewed Best Presentation

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.



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