GPS Block IIR Non-Conservative Force Modeling: Computation and Implications

M. Ziebart, S. Adhya, A. Sibthorpe, P. Cross

Abstract:	This paper discusses the development of a high precision non-conservative force model for the GPS Block IIR spacecraft, carried out at University College London. The model computation uses a suite of newly developed techniques that can incorporate a high level of complexity in the spacecraft structural description. The modelling approach caters for thermal effects due to the behaviour of the spacecraft multi-layered insulation, and the thermal imbalance force induced by the solar panels during solar full-phase and eclipse seasons. The foundation of the modelling precision derives from simulating the incident photon flux using a pixel array. This is projected onto a computer simulation of the spacecraft structure, and ray-tracing algorithms are used to accurately compute both the insolated and shadowed parts of the spacecraft. The ray tracing is extended to compute the effects of reflected radiation striking other parts of the spacecraft, causing further acceleration. The pixel array can be rotated anywhere around the spacecraft's circumscribing sphere, and the solar panels within the simulation are automatically adjusted mimicking the attitude control's on orbit behaviour. The mathematical and physical modelling of the non-conservative force field is seen as a limiting factor in many applications involving GPS, ranging from the orbit determination of low Earth orbiting spacecraft, through to issues of real-time realisation of the global reference frame, which are limited by the accuracy of the medium Earth orbit navigation satellite trajectories. Specific characteristics of the Block IIR spacecraft are presented that impact upon non-conservative force modelling, and, hence, orbit determination and prediction. These include the spacecraft attitude behaviour during eclipse seasons and high yaw rate maneuvers, as well as potential problems related to the power draw of the solar panels. The characteristic effects of these design facets on the spacecraft trajectory are assessed by numerical integration of the spacecraft dynamic model. This employs an 8th order embedded Runge-Kutta integrator with adaptive step-size control. High order gravity field coefficients are used, generating the associated Legendre polynomials with a numerically stable recursive formulation. International Earth Rotation Service conventions are used to compute frame transformations. Comparisons are made with the older Block IIA constellation in terms of how well the dynamics could be modelled a priori, and the impact this has on orbit prediction and determination. The force modelling technique allows for high precision assessment of Y-bias effects due to uncertainties in the spacecraft attitude control. This is a specific strength of the technique in that forms of assessment can be used that were previously impossible. The study results are presented, along with a discussion of the implications for orbit prediction and attitude control design. Mean orbit prediction errors over a 12 hour arc using the models were 0.266m in height, 0.046m across track and 1.171m along track.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	2671 - 2678
Cite this article:	Ziebart, M., Adhya, S., Sibthorpe, A., Cross, P., "GPS Block IIR Non-Conservative Force Modeling: Computation and Implications," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 2671-2678.
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