Sturkell et al. (2008) present GPS measurements on nunataks exposed on Katla’s caldera edge between 1999 to 2004 and show  steady inflation of the volcano. The “measurements show uplift and horizontal displacement of the nuntatak benchmarks at a rate of up to 2 cm a
1 , together with horizontal displacement of far-field stations (>11 km) at about 0.5 cm a
1 away from the caldera centre. Using a point-source model, these data place the center of the magma chamber at 4.9 km depth beneath the northern part of the caldera. However […] the depth may be only 2–3 km. About 0.01 km3 of magma has accumulated between 1999 and 2004”.
Parks et al. (2014) present “long-term deformation time-series spanning > 20 years for Hekla, Katla, Eyjafjallajökull and Askja volcanoes, based on a variety of geodetic techniques including InSAR, GPS and tilt measurements”. 
The authors state that “InSAR and GPS observations at Katla volcano (between 2001 and 2009) suggest no indication of magma induced deformation outside the ice-cap, it is possible that a small flood at Mýrdalsjökull in July 2011, followed by an increase in micro-seismic earthquakes, was related to magmatic activity”.