Fourier Ambiguity Validation for Carrier-Phase GNSS

Carrier-phase ambiguity validation is essential to ensure the reliability of integer ambiguity resolution in high-precision GNSS positioning. Although integer equivariant (IE) estimators provide optimal integer candidates within their class, noise and model limitations may lead to incorrect fixing. Validation procedures are therefore crucial for safeguarding the transition from float to fixed solutions, particularly in high-precision and safety-critical applications. In this contribution we introduce the concept of Fourier ambiguity validation and show how it is rooted in the principles of integer aperture (IA) estimation and its periodic representation. Unlike classical integer estimators that always return an integer solution, IA estimators introduce adjustable acceptance regions in the float ambiguity domain and fix ambiguities only when sufficient statistical evidence is present. As a result we present a general Fourier representation of IA estimators and provide an analytical description of the probabilistic properties of integer-aperture bootstrapping. We also present a hybrid description and show how the spatial and frequency representations can be mixed so as to do justice to the practical situation when carrier-phase ambiguities have a wide range of varying precision.