LEO GPS Attitude Determination Algorithm Designed for Real-time On-board Execution

Paul Cross and Marek Ziebart

Abstract:	This paper describes a Low Earth Orbiter (LEO) micro- satellite attitude determination algorithm, developed at University College London, to run in real-time, at a rate of 10 Hz, on-board the spacecraft. The spacecraft design includes four GPS antennas deployed on boom arms to mitigate multipath affects and to improve the antenna separations. The boom arms feature smart sensors, from which time-varying deformation data is used to calculate changes in the body-fixed system (BFS) co-ordinates of the attitude antennas. This data is used as input to the attitude algorithm to improve the accuracy of the output. The project aims were to deliver 0.05° (two sigma) precision in the spacecraft attitude parameters. The conventional double-difference phase observation equations have been re-arranged so that the only unknown parameters in the functions are the spacecraft Euler angles. This greatly increases the redundancy in the mathematical model, and is exploited to enhance the algorithm's ability to trap observations contaminated by unmodelled multipath. A de-weighting strategy is then used to reduce the influence of the lower quality observations on the output attitude parameters. This approach has been shown to be successful in identifying phase outliers at the 5-10mm level, whilst still meeting the project quality specifications. Speed of execution of the program is improved by utilising numerical differentiation of the model equations in the linearisation process. Furthermore, as the number of solve-for parameters is reduced to three by the chosen mathematical model, matrix inversion requirements are minimised. A novel approach to ambiguity resolution and determination of initial estimates of the attitude parameters has been developed utilising a heuristic technique and the known, and time varying, BFS co-ordinates of the antenna array. Algorithm testing is based on a simulation of the micro- satellite trajectory combined with variations in attitude derived from spin-stabilisation and periodic roll and pitch parameters. The trajectory of the spacecraft centre of mass was calculated by numerical integration of a force model using Earth gravity field parameters, third body effects due to the Sun and the Moon, dynamic Earth tide effects (solar and lunar), and a solar radiation pressure model. Frame transformations between J2000 and WGS84 utilised Lagrangian interpolation of IERS bulletin B parameters, as well as tidal model corrections to UT1- UTC. A similar approach was used to calculate the trajectories of all available GPS satellites during the same period, using initial conditions of position and velocity from IGS precise orbits. RMS differences between the published precise orbit and the integrated satellite positions were at the 5mm level. Phase observables are derived from these trajectories, biased by simulation of receiver and satellite clock errors, cycle slips, random or systematic noise and initial integer ambiguities. In the actual simulation of the attitude determination process in orbit, GPS satellite positions are calculated using broadcast ephemerides. The results show that the aims can be met provided that the phase multipath can be reduced to the level of a mixture of observations in the range 1-8mm. Attitude precision was found to vary strongly with constellation geometry, which can change quite rapidly depending on the variations in spacecraft attitude. The redundancy in the mathematical model was found to be very effective in trapping and isolating cycle slips to the double difference observable that is contaminated. This allows for the possibility of correcting the integer ambiguity without full recourse to the ambiguity resolution algorithm. The design of the algorithm enables rapid execution within both the time frame required and the allocation of chip resources, without sacrificing accuracy or robustness.
Published in:	Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) September 24 - 27, 2002 Oregon Convention Center Portland, OR
Pages:	1051 - 1063
Cite this article:	Cross, Paul, Ziebart, Marek, "LEO GPS Attitude Determination Algorithm Designed for Real-time On-board Execution," Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 1051-1063.
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