Integer aperture ambiguity resolution based on difference test

Abstract

Carrier-phase integer ambiguity resolution (IAR) is the key to highly precise, fast positioning and attitude determination with Global Navigation Satellite System (GNSS). It can be seen as the process of estimating the unknown cycle ambiguities of the carrier-phase observations as integers. Once the ambiguities are fixed, carrier phase data will act as the very precise range data. Integer aperture (IA) ambiguity resolution is the combination of acceptance testing and integer ambiguity resolution, which can realize better quality control of IAR. Difference test (DT) is one of the most popular acceptance tests. This contribution will give a detailed analysis about the following properties of IA ambiguity resolution based on DT:1. The sharpest and loose upper bounds of DT are derived from the perspective of geometry. These bounds are very simple and easy to be computed, which give the range for the critical values of DT. 2. The definition of DT integer aperture bootstrapping (IAB) estimator is firstly given. The relationships between DT-IAB and DT-IA are deeply investigated, which also firstly give a new perspective to review the IAB and IA least square (IALS) estimators. 3. Based on the properties of the second best integer candidates in integer least square and integer bootstrapping estimators, the definition of DT-IA is given from another perspective, which is mathematically equivalent to its original definition.4. The analytical expressions of the success rate lower bound and upper bound of DT-IA estimator are firstly derived. Then, the quality measure for DT-IA estimator can be completely calculated as integer estimator without measurements. Both sharp and loose bounds of DT-IA success rate are given so that the success rates are easily evaluated, which also can provide reasonable approximation for DT-IA estimator.All these conclusions are verified based on the single and combination GNSS simulation experiments. The experiment results indicate the correctness of these conclusions. These properties demonstrate the special properties of DT-IA estimator, and also provide the research frame to investigate other IA estimators. They are helpful to realize better use of IA estimators in quality control and precise positioning in future.

Instantaneous and controllable integer ambiguity resolution: review and an alternative approach

“…The range of μ DT based on LAMBDA method has the easy-to-compute [0, 1 d(1,1) ), in which d(1, 1) is the first element of D in the LDL-decomposition of the decorrelated matrix Qˆzˆz. This is proved in Zhang et al (2015).…”

“…Since its IA pull-in region is linearly scaled based on integer pull-in estimator in each dimension, the success rate of DTIA estimator can be directly approximated based on the corresponding scaling ratio. The details about DTIA estimator can be referred to Zhang et al (2015). Besides the approximation method, Monte Carlo sampling method can also be used in the computation of IA success rate.…”

“…However, we can give indirect evaluation by various bounds. The first results for the lower bound and upper bound of the success rate of DTIA are derived and proved in Zhang et al (2015).…”

“…The success rate of DTIA can be approximated by that of DTIAB in decorrelated space. The definition and properties of DTIAB can be referred to Zhang et al (2015).…”

Data-driven generalized integer aperture bootstrapping for real-time high integrity applications

“…These methods include the ratio test [8], the difference test [9], and an optimal test [10]. Unlike IA bootstrapping and ellipsoidal IA, none of these methods' test statistics has an analytical probability distribution or decision threshold [11].…”