Streamlining Dilution of Precision Analysis for GPS Constellations

B.J. Stanton, C. Jones, J.C. Flom

Abstract:	One of the major contributors to navigation position errors is a measurement of constellation geometry called Dilution of Precision (DOP). DOP and various summary statistics of DOP, such as, worst case “xth” percentile, global average, etc., have contributed to the formulation of requirements for the Navstar Global Positioning System (GPS). Previous analyses have derived DOP statistics based on standardized 24-satellite/6-plane (24SV6P) and hypothetical 27-satellite/6-plane (27SV6P) GPS constellations and have determined deviations in statistics for the worst case of two-satellites-excluded (TSE) from these constellations. The calculation of global DOP values can pose a formidable challenge depending on the grid spacing separating each data point on the Earth’s surface. One part of the problem is to determine the balance between computational complexity and granularity of the analysis that will provide reasonable results. The other part of the problem is to manage the volume of analysis which is driven by the number of possible TSE combinations, and to determine a method for obtaining reasonable results as quickly as possible. This paper explores heuristics for managing the computational complexity of calculating global DOP values while seeking the TSE combinations that create the worst-case DOP deviations from the full constellation. A method is described that first calculates global DOP values using coarse grid point spacing for all possible TSE combinations. These initial results are then used to rank-order the TSE combinations such that the combinations most likely to produce the largest statistical deviations are analyzed first. The method provides a good likelihood of obtaining the final results long before all TSE combinations are exhaustively analyzed. This paper also reports the summary metrics of DOP analyses on hypothetical 27-satellite/6-plane (27SV6P) and 30- satellite/6-plane (30SV6P) GPS constellations.
Published in:	Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009) September 22 - 25, 2009 Savannah International Convention Center Savannah, GA
Pages:	140 - 146
Cite this article:	Stanton, B.J., Jones, C., Flom, J.C., "Streamlining Dilution of Precision Analysis for GPS Constellations," Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009, pp. 140-146.
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