Broadcast ephemerides for LEO augmentation satellites based on nonsingular elements

Position, Navigation, and Timing (PNT) Through Low Earth Orbit (LEO) Satellites: A Survey on Current Status, Challenges, and Opportunities

“…The legacy broadcast ephemeris models are therefore not capable of describing these complex orbital dynamics. Meng et al [110], for instance, developed a broadcast model that takes into account the Keplerian elements being singular in some cases due to small eccentricities of the LEO orbits. The best results with this method were obtained using 22 Keplerian parameters in contrast to 16 in the legacy messages.…”

“…In addition, the legacy messages of MEO orbit are described by arcs of two hours length. However, the authors in [110]- [112] have found reasonable accuracy only when describing LEO orbits with 20 to 30 min arc lengths.…”

Simulations of Dedicated LEO-PNT Systems for Precise Point Positioning: Methodology, Parameter Analysis, and Accuracy Evaluation

“…The six orbital elements, described in Table II, specify the orbit eccentricity, inclination, altitude, and the starting point of the orbit at a particular time. Details on how to use them in orbit determination are shown by [47], [14]. The Keplerian orbital parameters allow us to initialize the satellite orbits.…”

“…In this regard, most of the current simulations have focused on fragmented topics of the fullchain LEO-PNT solution [9]. They have focused on how to define new orbit models embedded to the broadcast messages [13], [14], [15], orbit determination [16], [17], [18], signal structure designs [19], [20], [21], atmospheric models [22], [23], [24], constellation optimization strategies to improve the GNSS convergence time [6], [25], satellite clocks [26], [27], user performance estimation [28], [29], [30], [31], [32], [33], [34], and integration with distinct sensors [35]. To expand the simulations, there is still a gap in the process of implementing an end-to-end LEO-PNT system, binding all segments in a unified model.…”

A Flexible Ephemeris Representation for Global Navigation Satellite Systems and Alternative Positioning, Navigation, and Timing Signal Sources Using B-Splines

“…It is more challenging to represent satellite positions in LEO because of increased secular and harmonic gravitational perturbations. To adapt the global positioning system (GPS) ephemerides representation for LEO, Meng et al (2021) proposed six additional parameters to tackle singularities and account for perturbations that resulted in a fit accuracy of 0.08 m for 20-minute intervals. More recently, Guo et al (2022) proposed a similar parameter set for LEO augmentation systems that is slightly more compact (i.e., contained one less parameter) than the one proposed by Meng et al (2021) that achieved an improved accuracy of 0.01 m for 20-minute intervals.…”