Integer ambiguity estimation and validation for precise GNSS positioning

Global Navigation Satellite Systems (GNSSs) have been widely used in surveying, geodesy and navigation as well as other fields. By 2020, there will be four constellations for global usage, namely the American Global Positioning System (GPS), Russian GLObal NAvigation Satellite System (GLONASS), European Union Galileo and Chinese BeiDou. The first two constellations possess the full operational capability at the moment and the last two are hopefully to be fully operational by 2020. The Japanese regional Quasi-Zenith Satellite System (QZSS) and Indian Regional Navigation Satellite System (IRNSS) are all under developing. Multi-constellations will benefit global positioning, navigation and timing (PNT) users not only in terms of satellite availability, but also precision, integrity and reliability. However, to achieve centimeter to millimeter-level accuracy, resolving the integer ambiguities in the carrier phase measurements is indispensable. As soon as the integer ambiguities are correctly resolved, the carrier phase measurements begin to measure the distance in centimeter to millimeter-level accuracy.The integer ambiguity resolution and validation have been major issues for high precision GNSS positioning over the past two decades. In general, there are three steps required for reliable integer ambiguity resolution and validation. The first step is to estimate the float solution and its variance-covariance matrix by the standard least-squares, regardless of the integer constraint for the ambiguities. Then, the second step is to resolve the integer ambiguities by the integer least-squares with the float ambiguity vector and the variance-covariance matrix. The last step is to constrain the coordinates with the resolved integer ambiguities to achieve centimeter to millimeter-level accuracy. To ensure the reliability of the resolved integer ambiguities and the position, specific modeling and quality control procedures, especially for the integer ambiguity validation, are indispensable. In this research, modeling and quality control procedures for precise and reliable GNSS positioning have been researched. Most importantly, the challenging integer ambiguity resolution and validation issues have been explicitly investigated for both relative positioning and precise point positioning. The major contributions are specified as follows:a) Mathematical modeling aspects for GPS, GLONASS and QZSS constellation integration are investigated. Numerical and theoretical comparative studies are conducted. The results indicate that the identified model outperforms the other models in terms of high integer ambiguity resolution success-rates.b) Mathematical modeling and quality control aspects for precise point positioning are examined. An improved model for triple-frequency precise point positioning is developed and a new procedure of integer ambiguity resolution and validation in precise point positioning is proposed. Success-rate is introduced as an essential factor to evaluate the integer ambiguity resolution performance. Simulation results indicate the effectiveness of the proposed models and procedures.c) Sensitivity analysis of integer ambiguity validation with regard to the outliers, stochastic models and satellite geometries is discussed. Details on the construction of the acceptance regions for the classical integer ambiguity validation statistics are given. Comparative studies for integer ambiguity validation methods are presented under the framework of integer aperture estimation. The advantages and limitations of the integer aperture estimation have been researched.d) The upper bound and lower bound for the integer aperture estimation fail-rate are addressed. By virtue of these bounds, the critical value upper bounds for the classical integer ambiguity validation statistics are derived. The correctness of these derived upper bounds has been proved by experimental results. As a consequence, these classical integer ambiguity validation statistics need further rigorous analysis on their distributions. Alternatively, the pre-defined fail-rate should be used to generate the corresponding critical value