A Probabilistic Evaluation of Correct GPS Ambiguity Resolution

GPS ambiguity resolution is the process of resolving the unknown cycle ambiguities of double differenced carrier phase data as integers. It is the key to highprecision relative GPS positioning when only short observation time spans are used. Once the integer ambiguities have been resolved, the carrier phase measurements will start to act as if they were highprecision pseudorange measurements, thereby allowing the remaining parameters (e.g. baseline coordinates) to be estimated with a comparable high precision. The chance of successful ambiguity resolution can be inferred once the probability mass function of the integer ambiguities is known. In this contribution we will present and evaluate the probability of correct integer ambiguity estimation. This will be done for two different integer estimators. They are the integer rounding estimator and the integer bootstrapped estimator, both of which are of relevance to ambiguity resolution, in particular after the decorrelation process of the LAMBDA method has been applied, Teunissen (1993). As a result easy-to-use probability measures are presented which as diagnostics complement existing methods of ambiguity resolution. These measures will be used to evaluate the strength of the geometry-free GPS model for different measurement scenarios.