GNSS Integer Ambiguity Validation Procedures: Sensitivity Analysis

Abstract

Global Navigation Satellite Systems (GNSS) have been widely used for many precise positioning and navigation applications. In satellite-based precise positioning, as carrier phase measurements are used, the determination of correct integer carrier phase ambiguities is a key issue in obtaining accurate and reliable positioning results. Therefore much effort has been investigated in developing a robust quality control procedure which can effectively validate the ambiguity resolution results. Such a quality control procedure has been traditionally based on the so-called F-ratio and R-ratio tests. A major shortcoming of these two ratio tests is that their probability distributions, which are normally considered to be Fisher distributed, are still unknown, which precludes the possibility to evaluate the confidence level for the ambiguity validation test. To overcome such a shortcoming, an alternative ambiguity validation test based on the so-called W-ratio has been proposed, which allows for a more rigorous quality control procedure under the assumption that the fixed integer ambiguities are constant. The W-ratio test has been widely used by many researchers. Like any other quality control procedures, there are assumptions to be made, for example, it is assumed that both functional and stochastic models are correct, in the W-ratio test. This paper presents a sensitivity analysis for the new ambiguity validation test based on the W-ratio as well as the other two ratio tests. The analysis will cover the sensitivities of the ratio tests to undetected gross errors (outliers), stochastic models, and geometry strengths relating to a variety of satellite constellations, such as GPS, GPS/GLONASS integration with real data sets. While the performances of different ratio tests are analyzed in terms of the so-called ambiguity “correct” rates based on the ground truth integer ambiguity values.