We report on the first wide-field , high-precision astrometric analysis of the 13 extragalactic radio sources of the complete S5 polar cap sample at 15.4 GHz . We describe new algorithms developed to enable the use of differenced phase delays in wide-field astrometric observations and discuss the impact of using differenced phase delays on the precision of the wide-field astrometric analysis . From this global fit , we obtained estimates of the relative source positions with precisions ranging from 14 to 200 \mu as at 15.4 GHz , depending on the angular separation of the sources ( from \sim 1.6 to \sim 20.8 degrees ) . These precisions are \sim 10 times higher than the achievable precisions using the phase-reference mapping technique .