Abstract: in 　this　papersin gle －point －positioning　confi gurations　with　minimum　gdop　emplo ying　orthogonal 　tri gonometric 　functions 　are 　presented．the 　preconditions 　for　minimizing　the　gdop　are 　intro－ducedand　the 　set 　composed　of 　all 　confi gurations　with　minimal　gdop　is 　defined．some　properties 　ofthe　minimum　gdop　confi gurationsincluding　the 　invariance 　of 　rotation　and　super position are 　de－tailed．for 　arbitrar y　given　number　n　of 　control 　pointsre gular 　pol ygon　solutions 　are 　immediately　deduced　from　the　orthogonal 　tri gonometric 　functions．based　on　the 　two　dimensional 　confi gurations　with minimum　gdopthree　kinds 　of 　three　dimensional 　confi gurations　with　minimum　gdopincluding　the cone 　confi guration　with　cone 　angle 　108．48°the　descartes　confi gurationand　the　walker　confi gurationwith 　inclination 　angle 　54．74°are 　discussed．the 　geometrical 　conditions 　of 　these 　confi gurations　provide 　us 　some　knowledge　for　gnss　constellation　design