Theory of carrier phase ambiguity resolution
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Carrier phase ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. A proper handling of carrier phase ambiguity resolution requires a proper understanding of the underlying theory of integer inference. In this contribution a brief review is given of the probabilistic theory of integer ambiguity estimation. We describe the concept of ambiguity pullin regions, introduce the class of admissible integer estimators, determine their probability mass functions and show how their variability affect the uncertainty in the socalled ‘fixed’ baseline solution. The theory is worked out in more detail for integer leastsquares and integer bootstrapping. It is shown that the integer leastsquares principle maximizes the probability of correct integer estimation. Sharp and easytocompute bounds are given for both the ambiguity success rate and the baseline’s probability of concentration. Finally the probability density function of the ambiguity residuals is determined. This allows one for the first time to formulate rigorous tests for the integerness of the parameters.
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