Efficient Numerical Integration Method of GLONASS Satellite Position Computation

Sameet Deshpande, Shubham Kumar, and Yogesh Shekar

Abstract:	Multi-constellation receivers are coming of age with GPS and GLONASS having reached their full constellations. Combined GPS and GLONASS constellation has about 50 operational satellites which is proving to be a boon for users to get better position accuracy and availability anywhere in the world. This has increased the processing requirement for GNSS receivers. Hence, there is a need to perform the user position computation intelligently to optimize the processing requirement while achieving better accuracy and availability. Satellite position computation is an important operation in the user position computation process. Different constellations have their own format for transmitting the orbital information. GPS transmits a Keplerian model for satellite orbit which is useful over 2 to 4 hours. GLONASS transmits satellite state vector (position, velocity and acceleration) at a particular time and is valid over +/-15 minutes interval. Hence, GLONASS satellite position computation requires a numerical integration of an orbital force model with satellite state vector. In this paper, different approaches were evaluated to compare their accuracy, processing requirements and effect of integration step size. Two factors influence the accuracy of numerical integration methods. The first one is force model accuracy over the integration period and second one is the integration duration. These two factors cause the error in satellite state vector to accumulate over time resulting in poor user accuracy. A lesser integration duration with smaller step size is ideal for limiting error growth in the satellite state vector. This requires the receiver to integrate every second for all the satellites to be used in position which puts a considerable burden on the processor. Numerical integrators were evaluated to measure the integration error growth over 1-hour duration at different strides. Different stride approaches were analyzed to determine the combination of lesser error growth with efficient processing. Stride lengths ranging from 1 to 30 seconds were analyzed over the desired time interval. A GLONASS simulator as well as open-sky signal was used to generate the ephemeris for test purpose. The true satellite positions at desired time instants were also obtained from the simulator.
Published in:	Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011) September 20 - 23, 2011 Oregon Convention Center, Portland, Oregon Portland, OR
Pages:	775 - 779
Cite this article:	Deshpande, Sameet, Kumar, Shubham, Shekar, Yogesh, "Efficient Numerical Integration Method of GLONASS Satellite Position Computation," Proceedings of the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 775-779.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In