R-ratio test threshold selection in GNSS integer ambiguity resolution

Abstract Ensuring that ambiguity cycles are correctly fixed as integers is a critical prerequisite for ensuring the reliability of GNSS high-precision carrier positioning results. As a result, it is both theoretically and practically important to investigate the performance of the ambiguity validation test by selecting an appropriate threshold. To begin, two statistics are proposed in this paper to quantitatively describe the performance of the validation test, namely the true negative rate and the false positive rate, which are based on the percentage of Type I errors (discarded-truth) in the total number of failed tests and the percentage of Type II errors (false positive) in the total number of passed tests. Following that, this paper employs the false positive rate and the true negative rate as primary and secondary criteria for evaluating the performance of the R-ratio test, respectively, and develops simulation experiments to evaluate the performance of different thresholds under different ambiguity dimensions and data accuracy, and finally provides decisions for test threshold selection: (1) For ambiguities with 4 to 9 dimensions, a reference table for the selection of thresholds is given. (2) For ambiguities of 10 dimensions or more, the threshold value should be no less than 2.0 (where data with a mean value of more than 3.7 for the main diagonal elements of the variance matrix should not be fixed).