Integer least-squares statistics for three frequency GPS/GNSS ambiguity resolution

Global Navigation Satellite System (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of double difference (DD) carrier phase data as integers. It is the key to fast and high precision kinematic satellite positioning. Ambiguity resolution applies to a great variety of current and future GNSS models. Apart from the current dual-frequency Global Positioning System (GPS) models, it also applies to the future triple-frequency GNSS models, such as those of the modernized GPS and the European Galileo system. In order to judge the third civil signal on its merit for long baseline ambiguity resolution, the integer least-squares statistics for three frequency GPS/GNSS ambiguity resolution will be presented and discussed in this paper. In particular the probability of correct integer ambiguity estimation, or the success-rate, will be compared for the current GPS two frequency and the future three frequency set-up. This will be done for a variety of different measurement scenarios. In addition, the effect on the success-rate of varying the spacing between the three frequencies will be considered.