Real time kinematic, or RTK, is a high-accuracy GPS relative positioning technique, which allows to measure positions in real time with an accuracy usually better than 1 decimeter. Ionospheric small-scale variability can strongly degrade RTK accuracy. In this paper, we present a method allowing to assess in a direct quantitative way the influence of the ionospheric activity on RTK accuracy. We apply this method to two different ionospheric situations: a day where strong travelling ionospheric disturbances (TIDs) were detected (December 24, 2004) and a day where a severe geomagnetic storm was observed (November 20, 2003). We show that on a 4 km baseline, strong TIDs have the same influence as the ionospheric variability induced by a geomagnetic storm on RTK accuracy: in both cases errors of more than 1.5 m are observed.