Implementation of Ambiguity-Resolved Detector for High-Precision GNSS Fault Detection

Ambiguity resolution plays a critical role in fast and high-precision applications of the Global Navigation Satellite System (GNSS). The parameter estimation of high-precision GNSS can benefit from ambiguity resolution when its success rate is very close to 1 (e.g., larger than 0.995); otherwise it is better, in order to avoid a substantial probability of incorrect resolution, to ignore the integer property of the ambiguity, and use the float solution. Nonetheless, model validation and fault detection can still benefit from the integer property of the ambiguity with relatively low ambiguity resolution success rates (e.g. between 0.8 and 0.995) by applying the ambiguity-resolved (AR) detector test statistic based on the ambiguity-resolved residual. Due to the integer property of the resolved (so-called fixed) ambiguity estimator, the distribution of the ambiguity-resolved residual cannot be evaluated analytically. Consequently, the critical value of the AR detector has to be obtained numerically via Monte Carlo simulation of the quantile. Due to the inherent uncertainty in the Monte Carlo simulation process, the implementation of the AR detector also needs to evaluate the uncertainty associated with the simulated critical value. If the simulation uncertainty is large, the actual significance level of the detector may deviate significantly from the target value. In this study, we first describe the process of simulating the samples of the AR test statistic and obtaining the AR critical value for a given significance level through Monte Carlo simulation of the quantile. A histogram of the AR test statistic samples will be shown as an example to illustrate the irregular shape of the distribution of this test statistic. Furthermore, we introduce three methods that can be used to evaluate the uncertainty of the simulated critical value: 1) variance based on the asymptotic normality of the Monte Carlo quantile estimator, 2) confidence interval based on a distribution-free approach, and 3) variance obtained numerically by repeating the simulation. We conduct experiments to compare the above three methods in terms of the consistency between the simulation uncertainties reported by these methods. It will also be shown how the uncertainty of the critical value simulation is affected by the specified significance level. Moreover, we provide the uncertainties of the critical value simulations for nine observation models with various numbers of simulation samples and significance levels, offering insights into the number of samples that should be used for simulating the ARD critical value with the desired uncertainty when applying the AR detector.