GNSS Phase Ambiguity Validation: A Review

The LAMBDAmethod is very suitable for Multi-Carrier Ambiguity Resolution (MCAR), which is of interest with the coming of Galileo and the modernisation of GPS. Ambiguity resolution involves, however, not only integer estimation, but often also a decision on whether or not to accept the estimated integers. In this contribution, we show the relevance of this decision-step and show that integer aperture estimation is the proper theory for handling the combined integer estimation/acceptance problem. With this approach the user sets his/her own failure rate (irrespective of the strength of the underlying model), thus generating an aperture space which forms the basis of the decision process: the integer solution is chosen as output if the float solution resides inside the aperture space, otherwise the float solution is maintained. We show how the various approaches as used in the literature fit in the framework of integer aperture estimation and we also present the optimal integer aperture estimator. We also show how the popular ratio test fits in this framework. The weak point of this test, as it is currently used in practice, is the choice of the threshold value which determines whether or not the fixed solution will be accepted. Mostly a fixed value is used, not depending on the model under consideration. It will be shown here that this approach will often be too conservative, meaning that the fixed solution is rejected while the probability of being wrong is actually very low. This implies that the time to first fix may be unnecessarily long.