Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications

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.

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

Zhang

et al. 2015

J Geod

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In the high-precision application of Global Navigation Satellite System (GNSS), integer ambiguity resolution is the key step to realize precise positioning and attitude determination. As the necessary part of quality control, integer aperture (IA) ambiguity resolution provides the theoretical and practical foundation for ambiguity validation. It is mainly realized by acceptance testing. Due to the constraint of correlation between ambiguities, it is impossible to realize the controlling of failure rate according to analytical formula. Hence, the fixed failure rate approach is implemented by Monte Carlo sampling. However, due to the characteristics of Monte Carlo sampling and look-up table, we have to face the problem of a large amount of time consumption if sufficient GNSS scenarios are included in the creation of look-up table. This restricts the fixed failure rate approach to be a post process approach if a look-up table is not available. Furthermore, if not enough GNSS scenarios are considered, the table may only be valid for a specific scenario or application. Besides this, the method of creating look-up table or look-up function still needs to be designed for each specific acceptance test. To overcome these problems in determination of critical values, this contribution will propose an instantaneous and CONtrollable (iCON) IA ambiguity resolution approach for the first time. The iCON approach has the following advantages: (a) critical value of acceptance test is independently determined based on the required failure rate and GNSS model without resorting to external information such as look-up table; (b) it can be realized instantaneously for most of IA estimators which have analytical probability formulas. The stronger GNSS model, the less time con-B Jingyu Zhang sumption; (c) it provides a new viewpoint to improve the research about IA estimation. To verify these conclusions, multi-frequency and multi-GNSS simulation experiments are implemented. Those results show that IA estimators based on iCON approach can realize controllable ambiguity resolution. Besides this, compared with ratio test IA based on look-up table, difference test IA and IA least square based on the iCON approach most of times have higher success rates and better controllability to failure rates.

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Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications

Cited by 4 publications

References 14 publications

Generalized integer aperture estimation for partial GNSS ambiguity fixing

Generalized integer aperture estimation for partial GNSS ambiguity fixing

Integer aperture ambiguity resolution based on difference test

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

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