Ambiguity Acceptance Testing: A Comparison of the Ratio Test and Difference Test

Abstract

Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing ambiguity validation tests and provides a new prospective to review existing methods, which enables us to have a better understanding on the ambiguity validation problem. This contribution analyses two simple but efficient ambiguity validation test methods, ratio test and difference test, from three aspects: acceptance region, probability basis and numerical results. The major contribution of this paper can be summarized as: (1) The ratio test acceptance region is overlap of ellipsoids while the difference test acceptance region is overlap of half-spaces. (2) The probability basis of these two popular tests is firstly analyzed. The difference test is an approximation to optimal integer aperture, while the ratio test follows an exponential relationship in probability. (3) The limitations of the two tests are firstly identified. The two tests may under-evaluate the failure risk if the model is not strong enough or the float ambiguities fall in particular region. (4) Extensive numerical results are used to compare the performance of these two tests. The simulation results show the ratio test outperforms the difference test in some models while difference test performs better in other models. Particularly in the medium baseline kinematic model, the difference tests outperforms the ratio test, the superiority is independent on frequency number, observation noise, satellite geometry, while it depends on success rate and failure rate tolerance. Smaller failure rate leads to larger performance discrepancy.

A Self-Organizing Spatial Clustering Approach to Support Large-Scale Network RTK Systems

“…The long baseline length between the NTRIP clients and VRS introduces additional propagation path-specified error, which affects the positioning performance by reducing the reliability of ambiguity resolution. The reliability of ambiguity resolution is often tested by various ambiguity acceptance test and the most popular test is called ratio test, which is defined as in [ 34 ]: where is the float solution of ambiguity parameter, and and are the best and second best integer candidates, respectively. is the squared Mahalanobis distance.…”

Improving GNSS Ambiguity Acceptance Test Performance with the Generalized Difference Test Approach

“…Both employ two squared Mahalanobis distances for construction of test statistics with the difference in their test statistics formation. According to a previous comparison between the ratio test and the difference, the difference test is theoretically better than the ratio test [ 26 , 27 ], so we focus on the difference test in the remaining discussion. In this section, we compare the difference test and the OIA to reveal the sub-optimality of the difference test.…”

“…A comparison among the OIA, the ratio test and the difference test indicates that the OIA is theoretically optimal, although it is not computationally efficient. Meanwhile, the ratio test and the difference test are efficient but suboptimal [ 26 ]. The difference test is a rough approximation of the OIA and can be generalized to bridge the gap between the difference test and the OIA.…”

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

“…Verhagen and Teunissen (2006) give an initial investigation about the comparison of IA estimators and finding the good performance of RTIA and DTIA estimators. Furthermore, in Wang and Verhagen (2014), DT and RT are compared in detail. However, those comparisons only give initial explanations to the phenomena in simulation experiments.…”