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Fourier Ambiguity Validation for Carrier-Phase GNSS.
Peter J G Teunissen1,2,3,4
1Department of Geoscience and Remote Sensing, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands.
Sensors (Basel, Switzerland)
|April 14, 2026
Summary
Fourier ambiguity validation enhances high-precision GNSS positioning by improving integer ambiguity resolution. This method uses integer aperture estimation, offering adjustable acceptance regions for more reliable float-to-fixed solutions.
Area of Science:
- Geomatics Engineering
- Signal Processing
- Satellite Navigation Systems
Background:
- Carrier-phase ambiguity validation is critical for reliable integer ambiguity resolution in high-precision GNSS positioning.
- Integer equivariant (IE) estimators, while optimal, can fail due to noise and model limitations, necessitating robust validation.
- Safety-critical applications demand stringent validation for the transition from float to fixed GNSS solutions.
Purpose of the Study:
- Introduce Fourier ambiguity validation based on integer aperture (IA) estimation.
- Provide a general Fourier representation for IA estimators.
- Analyze the probabilistic properties of integer-aperture bootstrapping.
Main Methods:
- Developed a novel Fourier ambiguity validation technique.
- Utilized principles of integer aperture (IA) estimation and its periodic representation.
- Presented a hybrid spatial-frequency representation for mixed precision ambiguities.
Main Results:
- Introduced a general Fourier representation of IA estimators.
- Provided analytical descriptions of integer-aperture bootstrapping probabilities.
- Demonstrated a hybrid approach combining spatial and frequency domains for practical scenarios.
Conclusions:
- Fourier ambiguity validation offers a principled approach to enhance GNSS positioning reliability.
- IA estimators with adjustable acceptance regions improve integer fixing accuracy.
- Hybrid representations effectively handle varying precision of carrier-phase ambiguities.
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