On the error sensitivity of the GPS ambiguity success rate

GPS ambiguity resolution is the process of resolving the unknown cycle ambiguities of the double-difference (DD) 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 are resolved, the carrier phase measurements will start to act as if they were high-precision pseudo range measurements, thereby allowing the remaining parameters, such as the baseline coordinates, to be estimated with a comparable high precision. High ambiguity success rates are required for GPS ambiguity resolution to be successful. These success rates, as measured by the probabilities of correct integer estimation, depend on the various assumptions underlying the mathematical model used. Mis-specifications or errors in either the functional or stochastic model will generally result in lower success rates. It is therefore of importance to be able to diagnose the sensitivity of ambiguity resolution for such type of errors. In this contribution we will analyse the sensitivity of GPS ambiguity resolution for various type of modeling errors. The analysis is based on an analytical, closed form formula for the probability of correct integer estimation. This formula is generally valid and may be applied to any of the GPS models currently in use. In the present contribution it will be used to study the error sensitivity of the GPS geometry-free model.