GNSS Ambiguity Resolution: When and How to Fix or not to Fix?

Abstract

In order to facilitate rapid and precise GNSS positioning, the integer carrier phase ambiguities need to be resolved. Since wrong integer ambiguity estimates may result in fixed position estimates which are worse than their float counterparts, very high success rates (i.e. high probabilities of correct integer estimation) or very low failure rates are required when performing ambiguity resolution. We discuss two different approaches of ambiguity resolution, a model-driven approach and a data-driven approach. The first is linked to the theory of integer estimation and the second is linked to the theory of integer aperture estimation. In the first approach, the user chooses an integer estimator and computes on the basis of his/her model the corresponding failure rate. The decision whether or not to use the integer ambiguity solution is then based on the thus computed value of the failure rate. This approach is termed model-driven, since the decision is solely based on the strength of the underlying model and not dependent on the actual ambiguity float estimate. This approach is simple and provides a priori information on the outcome of the decision process. A disadvantage of the model-driven approach is that it does not provide the user of any control over the failure rate. This disadvantage is absent when one uses the more elaborate data-driven approach of integer aperture estimation. 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. Although more elaborate, the data-driven approach is more flexible than the model-driven approach and can provide a guaranteed failure rate as set by the user.

In this contribution we compare the model-driven and data-driven approaches, describe the decision making process of when and how to fix (or not to fix) and also give the optimal data-driven approach. We also show how the so-called ‘discrimination tests’, in particular the popular ‘ratio test’, fit into this framework. We point out that the common rationales for using these ‘tests’ are often incorrectly motivated in the literature and we show how they should be modified in order to reach an overall guaranteed failure rate for ambiguity resolution.