Probabilistic Evaluation of the Integer Least-Squares and Integer Aperture Estimators

The carrier phase observations start to act as very precise pseudorange observations once the ambiguities are resolved as integers. However, the integer ambiguity estimates should only be used if the reliability of the integer solution is high. The question is then how to assess this reliability. A well-known a-priori reliability measure is the ambiguity success rate. But even with a high success rate, integer ambiguity validation remains indispensable in order to check whether or not a specific integer solution is sufficiently more likely than any other integer candidate. A solution to the integer validation problem is the use of integer aperture estimation. With this approach an aperture space is defined such that only float samples that fall into this space are fixed to the corresponding integer estimates, otherwise the float solution is maintained. The aperture space is built up of translationally invariant aperture pull-in regions centered at all integers. The size of these pull-in regions is determined by the condition of a fixed failure rate.