Optimal GPS Satellite Selection using Stochastic Optimization and Volumes of Tetrahedrons for High Precision Positioning

Abstract

A possibility of utilizing the Global Positioning System (GPS) depends on the positioning accuracy. Two decisive factors of position accuracy are User Range Error (URE) value and dimensionless Dilution of Precision (DOP), related to number of visible satellites. Several error modeling and correction techniques are available to improve the accuracy by optimizing the errors. While finding the GDOP at every instant, satellite selection plays predominant role. Satellite geometry with more satellites gives the good GDOP. However, due to limited receiver tracking channels and smaller size memories and other problems, it may not be possible to use all satellites in view for positioning. In GPS navigation, position of user requires minimum of four visible satellites. The selection of four satellites has a considerable impact on the position accuracy and GDOP shows the order of this impact. By using the concept of relation between GDOP and volume of tetrahedron optimal four satellites are selected to improve the position accuracy. Genetic Algorithm is used to select best ten combinations based on GDOP. For experimental validation the data collected at Andhra University, Visakhapatnam, located at (706970.9093, 6035941.0226, 1930009.5821) (m) is used. It is observed that selected satellites which are arranged in tetrahedron by following the work done by M Kihara on satellite selection method and accuracy for the GPS, using GA gives the best position values.