GNSS Ambiguity-Resolved Detector: Implementation With a Lookup Table

The ambiguity-resolved detector (ARD) is developed for the validation of high-precision Global Navigation Satellite Systems (GNSS) mixed-integer observation models. The ARD releases the high success rate restriction of resolving the float ambiguities to integers, enabling ambiguity resolution to contribute to model validation even if the resolution success rate is not close to one. However, there are no closed-form expressions for the distribution of the ARD test statistic. The ARD critical value can only be obtained by Monte Carlo simulation, which requires heavy computations. To reduce the effort of applying the ARD, we provide a lookup table for the critical value of the ARD that utilizes the integer least-squares (ILS) estimator to resolve the ambiguities (ARDILS). We obtain 263 408 ARDILS critical values corresponding to GNSS observation models that vary in the precision of observables, satellite geometry, constellation, and the number of signal frequencies. We treat critical values as functions of the integer bootstrapping success rate and conduct curve fitting with second-order polynomials. The polynomial parameters are provided in the lookup table with which the ARDILS critical values can be simply computed rather than simulated. Numerical experiments demonstrate that the critical values computed with the lookup table provide significance levels close to the specified ones. The ARDILS can be implemented easily and efficiently with the lookup table. The lookup table with the polynomial coefficients to compute the ARD critical values can be downloaded from (Yin, 2024).