The paper presents a methodology that combines geometry-based models and geometric constraints for improved three carrier ambiguity resolution (TCAR). First of all, a general modelling strategy using three or more phase-based ranging signals is presented. The strategy can generally identify three best "virtual" signals to allow for more reliable AR under certain observational conditions characterised by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The

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... selected virtual signals often have minimum or comparatively low ionospheric effects, and thus are known as ionosphere-reduced virtual signals. As a result, the ionospheric parameters in the geometry-based observation models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. Secondly, the general formulation of the equation system for the ambiguity resolution problem is examined. This general formulation enables the combination of apriori position and ambiguity and ionosphere information, to achieve reliable integer solutions or high availability of Real-Time Kinematic (RTK) solutions. Thirdly, numerical experiments have been performed and three sets of dual-frequency GPS data have been collected over baselines of length 21km, 56km and 74km and the performance benefits of the proposed algorithms have been investigated. Results confirm that the AR with the ionosphere-reduced NL signals, instead of the original L1 and L2 signals, performs better over longer baselines. For instance, the AR success rate for the 74km data set is improved from 88% to 93%. Introducing geometric constraints, particularly, apriori position and ionospheric corrections predicted from the previous epochs, AR reliability is further improved, to 98% for the above data set.