Dave Conkey, a.i. solutions; Mitchell Zielinski, a.i. solutions
Keywords: SGP4, SGP4-XP, Analytic Propagation, Mean Element Fits
Abstract:
In 2020 the United States Space Force (USSF) released the SGP4-XP propagator, an advanced version of the existing SGP4 propagation algorithm featuring Extended Perturbations. The existing SGP4 (Simplified General Perturbations No. 4) algorithm has been widely used for over thirty years to generate and propagate two-line mean element sets (TLEs) describing the orbital state of objects in space. Compared to the existing SGP4 algorithm, SGP4-XP offers improved lunar perturbation modeling, new solar radiation pressure modeling, and updated static atmosphere and geopotential models. The USSF states that SGP4-XP offers significant accuracy improvements for all orbit regimes and delivers accuracy that is statistically equivalent to that of the USSF Special Perturbations (SPEPH) propagator with propagation runtimes only 50% to 100% longer than SGP4. In this paper we analyze different performance characteristics of this new algorithm and consider new and existing practical applications where it can be used more effectively than the existing SGP4.
We discuss our findings regarding the advantages and limitations of the SGP4-XP propagator as compared to SGP4. We describe specific, practical use cases that would take advantage of SGP4-XPs improved accuracy compared to SGP4 or faster run times compared to SPEPH. These use cases include station contact planning, coarse conjunction assessment screening, high-accuracy pointing angles for high-frequency (laser) ground to space communications, and TLE generation for objects with poor observability. Performance characteristics are analyzed for different orbital regimes to determine what limitations exist with the SGP4-XP algorithm where the extended execution time provides little benefit.
For this analysis we use FreeFlyer astrodynamics software to generate SGP4-XP TLEs derived from high-precision reference ephemerides. Orbit states are sampled at a given interval from the reference ephemeris and a batch least squares fit is then performed to determine an optimized mean state to best fit the ephemeris. This approach is taken since SGP4-XP-derived TLEs, known as Type 4 TLEs, generated by the USSF are not yet available to the public. For consistency, the same approach is used to generate traditional SGP4 TLEs. The performance characteristics of these TLE fits are then evaluated for accuracy against the reference ephemeris as well as for runtime and accuracy against SP propagation using FreeFlyer. For this study, the FreeFlyer implementation of the RungeKutta 8(9) numerical integrator configured with a force model equivalent to that of the USSF SPEPH propagator is used. This approach avoids the need to obtain access to the USSF SPEPH propagation library and vector covariance messages (VCMs) from the high-accuracy catalog.
Accuracy and runtime performance of the TLE fits are assessed for different orbit regimes, including low Earth orbit (LEO), GPS-like medium Earth orbits (MEO), and geosynchronous orbit (GEO). Accuracy performance metrics include positional fits over the fit-span, velocity fits over the fit-span, and positional accuracy for propagation beyond the fit-span. We explore whether the improved accuracy of SGP4-XP provides the opportunity to use TLE-based propagation to satisfy mission requirements that would typically require Special Perturbations integration. Runtime is considered in both the context of the amount of time to propagate a single trajectory from an estimated state as well as the amount of time required for the fit process to converge. This scenario may be particularly applicable when an object is poorly tracked.
Results to date indicate that the various performance claims of the USSF hold up well. SGP4-XP fits performed in MEO and GEO seem to provide significantly better positional fits over the fit span. SGP4-XP propagation error remains low for longer periods after the TLE fit span, indicating a better velocity fit over the fit span. These results hold true across all orbit regimes. However, position fits for objects in LEO have shown little improvement compared to the existing SGP4. Indications are that runtime performance for the overall fit process, including the batch least squares fit and data processing, is slightly slower, but runtimes are closer to those of SGP4 than to those of SPEPH.
Date of Conference: September 27-20, 2022
Track: Astrodynamics