Bicomplex Kalman Filter Tracking for GNSS Meta-Signals

Daniele Borio, Melania Susi

Peer Reviewed

Abstract: Modern global navigation satellite systems (GNSSs) broadcast several signals on different frequencies, potentially providing enhanced positioning performance and opening several opportunities such as the study of ionospheric conditions. Signals from different frequencies can be effectively treated as a single entity, characterized by common delays and carrier phases, leading to the so-called GNSS meta-signals. A convenient approach for deriving meta-signal acquisition and tracking algorithms has been recently introduced and is based on bicomplex numbers, which are a four-dimensional extension of complex numbers. Bicomplex numbers allow one to represent two signals from different frequencies as a single quantity, providing a compact notation for algorithm development. In this paper, we develop an error state (ES) Kalman filter (KF) where two signals from different frequencies are tracked simultaneously using the bicomplex number paradigm. A triple loop architecture, where loop filters are replaced by a single KF, is developed, implemented and tested using real Galileo alternative binary offset carrier (AltBOC) and Beidou B1I/B1C meta-signals. The analysis clearly shows the advantages of KF tracking for processing GNSS meta-signals with components from different frequencies.
Published in: Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023)
September 11 - 15, 2023
Hyatt Regency Denver
Denver, Colorado
Pages: 3353 - 3373
Cite this article: Borio, Daniele, Susi, Melania, "Bicomplex Kalman Filter Tracking for GNSS Meta-Signals," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 3353-3373. https://doi.org/10.33012/2023.19233
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