Generalised Ambiguity Resolution Approaches to Processing Multiple GNSS Signals
Global Navigation Satellite System (GNSS) provides global, real time and continuous positioning services, which include metre-level standard positioning service down to centimetre-level precise positioning service. The key of precise positioning service is making use of high precision carrier phase observations. However, only a fractional part of a carrier phase observation can be precisely measured, while the remaining full cycle part is unknown. Determining the unknown full cycle number is known as ambiguity estimation problem in context of GNSS positioning. Only if the unknown integer cycle number is correctly resolved, centimeter level positioning accuracy becomes achievable. Meanwhile, incorrectly fixed ambiguity may cause a large bias in positioning results without notice. Therefore, reliability of GNSS integer ambiguity is of great importance for precise positioning services.
This study focuses on the issues related to the reliability control of GNSS ambiguity resolution and aims to improve the reliability of the GNSS ambiguity resolution by adopting the most reliable integer estimator and ambiguity acceptance tests. Reliable ambiguity resolution requires an unbiased function model and a realistic stochastic model, which are addressed in the study. The reliability of ambiguity estimation is investigated from integer estimation and integer acceptance test aspects. The major contributions of the research are summarized as follows:
1. This research systematically reviews the integer aperture (IA) estimation theory and compares performance of IA estimators with extensive simulation. The IA estimators are classified into four categories according to their characteristics. This classification reveals similarities and differences between different IA estimators, which also inspires new ideas on how to construct the test statistics for the ambiguity acceptance test.
2. A weighted integer aperture bootstrapping (WIAB) estimator is proposed, which has a better performance than existing integer aperture bootstrapping (IAB) estimator. Success and failure rates of the WIAB estimator are easy to evaluate.
3. A likelihood ratio integer aperture estimation (LRIA) is investigated and compared with the optimal integer aperture (OIA). The LRIA has the same acceptance region shape as the OIA, but uses a different threshold determination method. The comparison shows the threshold of the LRIA is more reasonable in extreme cases. The LRIA employs likelihood as reliability measure rather than failure rate. The success fix rate can be guaranteed by the LRIA.
4. The threshold determination methods are systematically reviewed. Under the integer aperture framework, the threshold determination method is discussed as a separate topic. The existing threshold determination methods are summarized as four categories.
5. A new threshold determination method for the ambiguity acceptance test, called threshold function method, is proposed. This method preserves controllable failure rate nature of the fixed failure rate (FF-) approach, but no simulation is required. The threshold function method enables direct calculation of the FF-threshold with given formulas and integer bootstrapping (IB) success rate, thus significantly reducing complexity of the FFthreshold calculation.
6. The fixed failure rate approach is applied to the real data process. Performance of the threshold function method is assessed with real GNSS data, which demonstrates feasibility of the FF-approach in the real data processing.