W-Ratio Test as an Integer Aperture Estimator: Pull-in Regions and Ambiguity Validation Performance

Abstract

Global Navigation Satellite Systems (GNSS) carrier phase integer ambiguity resolution is an indispensible step in generating highly accurate positioning results. As a quality control step, ambiguity validation, which is an essential procedure in ambiguity resolution, allows the user to make sure the resolved ambiguities are reliable and correct. Many ambiguity validation methods have been proposed in the past decades, such as R-ratio, F-ratio, W-ratio tests, and recently a new theory named integer aperture estimator. This integer aperture estimator provides a framework to compare the other validation methods with the same predefined fail-rate, even though its application in practice can only be based on simulations.

As shown in literature, the pull-in regions of different validation methods may have a variety of shapes which may dictate the closeness of such validation methods to the optimal integer least-squares method. In this contribution, the W-ratio is shown to be connected with the integer aperture theory with an exact formula. The integer least-squares pull-in region for W-ratio is presented and analysed. The results show that the W-ratio’s pull-in region is close to the integer least-squares pull-in region. We have performed numerical experiments which show that the W-ratio is a robust way of validating the resolved ambiguities.