The imaging of fast-moving electron-density Structures in the polar cap presents a unique set of challenges that are not encountered in other ionospheric imaging problems. GPS observations of total electron content in the polar cap are sparse compared to other regions in the Northern Hemisphere. Furthermore, the slow relative motion of the satellites across the sky complicates the problem since the velocity of the plasma can be large in comparison and traditional approaches could result in image blurring. This paper presents a Kalman-filter based method that incorporates a forward projection of the solution based on a model plasma drift velocity field. This is the first time that the plasma motion, rather than just integrations of electron density, has been used in an ionospheric imaging algorithm. The motion is derived from the Weimer model of the electric field. It is shown that this novel approach to the implementation of a Kalman filter provides a detailed view of the polar cap ionosphere under severe storm conditions. A case study is given for the October 2003 Halloween storm where verification is provided by incoherent scatter radars.