Ephemeris and Almanac Design for Lunar Navigation Satellites

TL;DR

The paper tackles the challenge of creating compact, high-fidelity ephemeris and almanac messages for lunar navigation under LunaNet constraints. It propos es a hybrid ephemeris using osculating elements plus Chebyshev polynomials and Fourier series, and a compact almanac with a polynomial–Fourier per-element model, validated across 30-, 24-, 12-hour ELFOs and a 6-hour polar orbit. Results show sub-meter position and sub-mm/s velocity accuracy for short arcs within a 900-bit budget, and 15-day almanac performance that supports reliable warm-start satellite visibility discrimination. The approach offers a scalable, interoperable foundation for LANS data products, with future work extending to clock models, orbit determination, and receiver simulations for end-to-end navigation assessments.

Abstract

This paper presents almanac and ephemeris message representation for lunar navigation satellites supporting the Lunar Augmented Navigation System (LANS). The proposed method combines osculating orbital elements, Chebyshev polynomials, and Fourier series to efficiently represent lunar satellite trajectories subject to complex perturbations from lunar gravity and third-body effects. For the ephemeris, a hybrid Chebyshev--Fourier formulation improves fitting accuracy over long arcs while maintaining message compactness under the data-size constraint of the LunaNet Interoperability Specification. For the almanac, a compact low-order polynomial and Fourier model is introduced to capture mid-term orbital variations over a 15-day fitting arc. The approach is validated for multiple orbit regimes, including 30-hour, 24-hour, and 12-hour elliptical lunar frozen orbits (ELFOs) and a 6-hour polar orbit. Results show that the proposed framework achieves sub-meter position and sub-millimeter-per-second velocity fitting errors within the 900-bit limit for 6-hour ephemeris arcs, and almanac fitting accuracy sufficient for reliable satellite-visibility identification in warm-start operations.

Figures (13)

• Figure 1: Time histories of osculating orbital elements for the 30-hour ELFO (LCRNS) over 365 days.
• Figure 2: Fourier spectra of the osculating orbital elements for the 30-hour ELFO (LCRNS) over 365 days.
• Figure 3: Time histories of osculating orbital elements for the 6-hour polar orbit over 365 days.
• Figure 4: Fourier spectra of the osculating orbital elements for the 6-hour polar orbit over 365 days.
• Figure 5: Data size versus 95th-percentile position and velocity errors for the 30-hour ELFO (LCRNS) across fitting lengths and parameterizations. Blue: Chebyshev only; green: Chebyshev + osculating elements; red: Chebyshev + osculating elements + Fourier. Each point corresponds to a Chebyshev order (darker = higher order). Points with black outlines satisfy both error targets (3 m, 0.25 mm/s, horizontal dashed line) within 900-bits (vertical dashed line)