Reduced-Dynamic Orbit Determination

Reduced-Dynamic Orbit Determination for LEO satellites that carry a dual-frequency GPS receiver

This package implements reduced-dynamic orbit determination (RDOD) for low Earth orbit (LEO) satellites that carry a dual-frequency GPS receiver. The estimator combines ionosphere-free carrier-phase observations with a high-fidelity force model within an extended Kalman filter (EKF), augmented with empirical accelerations in the along-track/cross-track/radial (ACR) frame and estimated Cd and Cr states. An optional body-Y PCO state exists in the filter but is off in the Swarm-A demo: the lever arm is the published L1b r_CoG_ARP, not an SP3-fitted offset. A Rauch-Tung-Striebel (RTS) backward smoother is applied over the processed arc. Carrier-phase modeling uses the LEO antenna phase centre (APC) for light-time, range, wind-up, and satellite PCV; GPS 2(r·v)/c and Shapiro stay on the centre of mass. Frame rotations are IAU 2006/2000A CIO-based (GCRS2ITRS and the bundled SOFA iau*.m routines). Gravity is GGM03C 120×120 with IERS 2010 / EGM2008 low-degree rates from epoch 2005.0. Other refinements include Earth-rotation SP3 interpolation, Hatch warm-up smoothing, LLI/GF cycle-slip detection, ANTEX az×nadir satellite PCV when DAZI > 0, OBX attitude at transmit time rotated into receive-time ECEF, and IF receiver PCV formed as α1·PCV_L1 + α2·PCV_L2 when L1/L2 maps exist.

The bundled example is Swarm-A on 10 May 2023 (DOY 130). The same script runs any other UTC day when a consistent product set is placed in the folder: FindInputFiles matches CODE (YYYYDDD) and Swarm (YYYYMMDDTHHMMSS windows) names to the GPSA RINEX day and ignores leftover files from another date. It prefers GPSA L1b headers over MODA, extracts a companion GPSA .HDR from a .ZIP when needed, and unpacks SW_OPER_STRAATT*.CDF.ZIP to MDR_SAT_AT.cdf. CODE final GPS products provide the GNSS satellite orbits, clocks, and observable-specific biases. ESA Swarm Level-1b GPS RINEX, GPSA header, and star-tracker attitude are the LEO inputs. The official Swarm SP3 precise orbit is used only for final comparison and is never ingested by the filter.

References:

• Montenbruck, O., Gill, E., Satellite Orbits: Models, Methods, and Applications. Springer, 2005.
• Montenbruck, O., et al. (2018) — Swarm GPS receiver performance and precise orbit determination (GHOST; ~0.5–1 cm 1D SLR for official Swarm RD POD).
• IERS Conventions (2010); IERS 2018 secular pole (Ch. 7.1.4); FES2004 ocean-tide Stokes coefficients (Chapter 6).
• Teunissen, P.J.G. — LAMBDA.
• Siemes, C. (2019) — Swarm satellite thermo-optical properties and 15-plate macromodel.
• ESA Swarm Level 1b Product Definition / Processor Algorithms.
• CODE MGEX final products — SP3, CLK, OSB, OBX.
• ITSG GROOPS — LEO receiver antenna PCV products.
• RTKLIB (pephpos / preceph) — Earth-rotation Neville precise-ephemeris interpolation.
• Hatch, R. — The synergism of GPS code and carrier measurements (IF Hatch only in this package).
• Wu, J.T., et al. (1993) — GPS phase wind-up.
• Park, R.S., et al. — JPL DE440 planetary ephemeris (c, AU, GM_Sun/GM_Moon).
• Colombo, C., McInnes, C.R. (2012) — orbital dynamics of LEO solar sails / drag sails; Cd ≈ 2.1 (sphere) and 2.2 (flat plate) used as the generic drag prior.
• Hackel, S. (2019) — Refinement of Reduced-Dynamic Orbit Determination for Low Earth Satellites (TUM): Swarm macromodel, cannonball SRP area 5.0 m², empirical a priori at nm/s² scale.
• IAU 2015 Resolution B3 — nominal total solar irradiance 1361 W/m² at 1 AU.
• IAU SOFA (Standards of Fundamental Astronomy) — IAU 2006/2000A CIO transformations used by GCRS2ITRS.