Geomagnetically induced currents (GICs) can cause half-cycle saturation of transformers, which increases harmonic currents and reactive power losses in the high voltage transmission grid. This paper focuses on estimating the geomagnetically induced electric field that causes these GICs. To improve the electric field estimation, the electric field dependence on previous observations is recognized, and a dynamic model for the electric field estimation is developed. The developed model is integrated into a Kalman filter providing for a more accurate estimation. The advantage of the proposed estimation technique over the conventional least squares estimation is validated numerically through simulation.