Global optimization applied to GPS positioning by ambiguity functions

Abstract

Differential GPS positioning with carrier-phase observables is commonly done in a process that involves determination of the unknown integer ambiguity values. An alternative approach, named the ambiguity function method, was already proposed in the early days of GPS positioning. By making use of a trigonometric function ambiguity unknowns are eliminated from the functional model before the estimation process. This approach has significant advantages, such as ease of use and insensitivity to cycle slips, but requires such high accuracy in the initial approximate coordinates that its use has been practically dismissed from consideration. In this paper a novel strategy is proposed so that the need for highly accurate initial coordinates disappears: the application of a global optimization method to the ambiguity functions model. The use of this strategy enables the ambiguity function method to compete with the present prevailing approach of ambiguity resolution.