Recursive method for optimum GPS satellite selection

Abstract

The author addresses the problem of selecting an optimum n-satellite subset from m visible satellites (m>n). The optimality criteria is minimum geometric dilution of precision (GDOP) subject to the integrity constraint. To solve this problem an efficient algorithm is developed using a revolving door method and matrix inversion lemma. The revolving door method generates each n-subset from its immediate predecessor by deleting some single element and adjoining some other single element. Then using the matrix inversion lemma, the GDOP for each new n-subset is recursively calculated from the incoming and outgoing elements. The matrix inversion lemma is also used to check the satisfaction of the integrity constraint.