An Efficient Implementation of Fixed Failure-Rate Ratio Test for GNSS Ambiguity Resolution

Area of Science:

• Geomatics Engineering
• Satellite Navigation Systems
• Geodetic Surveying

Background:

• Accurate Global Navigation Satellite System (GNSS) positioning relies on successful integer ambiguity resolution (AR).
• Incorrectly fixed ambiguities lead to significant positioning errors, necessitating robust validation methods.
• The traditional ratio test is widely used but lacks adaptability to specific failure rate tolerances.

Purpose of the Study:

• To introduce easy-to-implement fitting functions for calculating critical values in the Fixed Failure-rate Ratio Test (FFRT).
• To enable users to define tolerable failure rates for AR validation.
• To provide fitting functions for evaluating the conditional success rate of AR.

Main Methods:

• Massive Monte Carlo simulations were conducted to generate fitting functions for various tolerable failure rates.
• Fitting functions for the fix rate were developed to assess conditional success rates.
• Simulations and a real-world experiment were used to compare FFRT with the traditional ratio test.

Main Results:

• Provided fitting functions for calculating FFRT critical values across a range of user-defined failure rates.
• Enabled the evaluation of conditional success rates for the first time.
• FFRT demonstrated superior control over failure rates and reduced false alarms compared to the traditional ratio test.
• Real-world data showed FFRT achieved up to 30% higher fix rates with comparable positioning accuracy over a 182.7 km baseline.

Conclusions:

• FFRT offers enhanced reliability in GNSS positioning by providing adaptable critical values for AR.
• The developed fitting functions simplify the application of FFRT, allowing for tailored AR validation.
• FFRT significantly improves fix rates and prevents false alarms, leading to more dependable precise positioning solutions.