A Flexible Ephemeris Representation for GNSS and Alternative PNT Signal Sources Using B-Splines

Mikaela Dobbin, Penina Axelrad

Abstract:	Most Global Navigation Satellite System ephemeris representations rely on the user equipment implementing a straightforward, but specialized, algorithm in order to extract the correct transmitter position. As potential PNT signal sources expand beyond medium Earth orbit (MEO) to geostationary (GEO), inclined geosynchronous (IGSO), and low Earth orbit (LEO), modifications to these specialized representations are required, to properly capture the different dynamics of these regimes and operational characteristics of the host satellites. Researchers have already introduced several new modifications for these specific cases. Our work explores the use of B-splines as a highly flexible framework for creating transmitter ephemerides, applicable to any orbital or airborne regime and host platform. A B-spline curve is made of sections of connected piecewise polynomials and are fully defined by curve order, a sequence of knots and coefficients. The user implementation requires a very simple algorithm to compute satellite positions from the B-spline ephemeris representation. A key advantage of the B-spline approach is that it requires no knowledge or orbital mechanics or platform dynamics to compute satellite positions. This work presents the proposed B-spline ephemeris and compares the accuracy achieved and message length required for this representation, to examples of the current GPS broadcast messages and precise LEO orbits. The results show that the B-spline requires a moderate increase in message length as compared to the GPS broadcast. Additionally, the work shows that the B-spline representation can achieve varying levels of fit accuracy, ranging from 1 m to 5 cm.
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:	799 - 807
Cite this article:	Updated citation: Published in NAVIGATION: Journal of the Institute of Navigation
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