Teunissen (J Geod 98(83):1–16, 2024) proposed the ambiguity-resolved (AR) detection theory for GNSS mixed-integer model validation. In this contribution, we study the performance of the AR detector through analysis and simulation experiments and compare it with the ambiguity-float (AF) and ambiguity-known (AK) detectors. We describe how the detectors can be implemented and how to evaluate their performance by computing the power as functions of the model misspecifications’ size. We present two simulation experiments with single- and dual-frequency GPS models and demonstrate that the AR detector can provide a larger detection power than the AF detector, even if the success rate is not close to one. Then, we obtain power functions over 25 user locations with five observation models and 72 satellite geometries per location per model. We find that the AR detector increases the detection probability of ionosphere and troposphere delays by 47% and 60% on average when the success rate is larger than 97.5% and the level of significance is 0.01. We also find the AR detection power to be larger than that of the AF detector in case of multi-dimensional misspecifications.

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.