Ambiguity-Free Method for Fast and Precise GNSS Differential Positioning

Abstract

Methods based on integer ambiguity determination, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) method, are currently used for precise global navigation satellite system (GNSS) differential positioning. In the present paper, the author proposes an ambiguity-free method based on a dedicated mixed (stochastic/deterministic) optimization algorithm that, unlike the LAMBDA method, is capable of providing reliable and accurate results using few observation epochs (e.g., 1-cm accuracy with just two epochs), having the additional advantages of insensitivity to cycle slips and impossibility of wrong ambiguity fixation. In addition, it is demonstrated that the application of the linear (deterministic) part of this algorithm yields the correct baseline results much more easily and quickly than methods requiring integer ambiguity determination, provided the initial approximate coordinates are accurate to a few centimeters. However, the use of ambiguity-free methods requires that the integer character of the ambiguities be preserved so that they can be eliminated; therefore no ionosphere-free combination can be computed and the methods are valid only for short baselines (e.g., less than 10 km).