Integer aperture estimation comparison between ratio test and difference test: from theory to application

Abstract

Acceptance testing or ambiguity validation is a key step in global navigation satellite system (GNSS) ambiguity resolution, which combined with integer estimator is the so-called integer aperture (IA) estimator. The difference test and ratio test are the two most popular tests. In order to compare the performances of both IA estimators, their differences in different GNSS models are analyzed from algebraic and geometrical perspectives. Furthermore, both tests are connected by comparing with the optimal acceptance test, and then, they can be transformed each other based on certain numerical conditions. As to the instantaneous applications, both tests are first compared with their corresponding instantaneous approaches, including the fixed failure rate approach for ratio test IA (RTIA) and the instantaneous and controllable approach for difference test IA (DTIA). Advantages and drawbacks of both IA estimators in theory and application are analyzed based on these comparisons. In order to verify these conclusions, typical multi-frequency, multi-GNSS situations are constructed to evaluate the performances of DTIA and RTIA ambiguity resolution. Then, both IA estimators are compared based on their instantaneous approaches in the field test. All the simulation experiments and field test results indicate that DTIA has more advantages and is better than RTIA not only in theory, but also in the practical applications.