Changes beneath a volcano can be observed through position changes in a GPS network, but distinguishing the source of site motion is not always straightforward. The records of continuous GPS sites provide a favorable data set for tracking magma migration. Dense campaign observations usually provide a better spatial picture of the overall deformation field, at the expense of an episodic temporal record. Combining these observations provides the best of both worlds. A Kalman filter provides a means for integrating discrete and continuous measurements and for interpreting subtle signals. The unscented Kalman filter (UKF) is a nonlinear method for time‐dependent observations. We demonstrate the application of this technique to deformation data by applying it to GPS data collected at Okmok volcano. Seven years of GPS observations at Okmok are analyzed using a Mogi source model and the UKF. The deformation source at Okmok is relatively stable at 2.5 km depth below sea level, located beneath the center of the caldera, which means the surface deformation is caused by changes in the strength of the source. During the 7 years of GPS observations more than 0.5 m of uplift has occurred, a majority of that during the time period January 2003 to July 2004. The total volume recovery at Okmok since the last eruption in 1997 is ∼60–80%. The UKF allows us to solve simultaneously for the time‐dependence of the source strength and for the location without a priori information about the source. 2009 by the American Geophysical Union.
