Stochastic Modelling of the Ionosphere for Fast GPS Ambiguity Resolution

Integer carrier phase ambiguity resolution is the key to precise GPS positioning. For baselines over 10km the errors due to the ionosphere limit the ability to resolve the integer ambiguities within short observation time spans. Of course, one can estimate the ionospheric delays, but the additional unknowns in the model limit the use of very short time spans. On the other hand, very short time spans can be successfully used by not estimating the delays at all, but only if the ionospheric delays in the data are within certain bounds. In this contribution the effect of a priori weighting of the ionosphere is investigated on integer least-squares estimation with the LAMBDA method. Stochastic modelling of the ionosphere can mathematically be regarded as the addition of pseudo-observations to the model of GPS obervation equations, together with a variance-covariance matrix (vc-matrix) in which the uncertainty of the ionospheric delays is accounted for. Note, on the one hand, if "infinite" weights are used for these ionospheric pseudo-observables, the model degenerates to the one in which no ionospheric delays are estimated at all. On the other hand, if these observables are not weighted at all, the model in which the ionospheric delays are estimated is obtained. Stochastic modelling in a way interpolates between these two "extreme" models. For a medium-length baseline it can be shown that with this technique it is possible to determine the correct integer ambiguities within a shorter time span than with the model in which the ionospheric delays are considered as completely unknown parameters.