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One of the challenges in the design of the LOFAR radio telescope is the calibration of the ionosphere which, at low frequencies, is not uniform and can change within minutes. The number of unknown parameters quickly approaches the number of measurements and hence, structural assumptions on the ionosphere must be made, in time, frequency, and space. Using general models for the second-order statistics, we propose to use maximum a posteriori (MAP) estimators combined with Karhunen-Loeve basis functions. The resulting estimation algorithm is shown in simulated LOFAR data to be superior to currently considered techniques. A significant advantage is that it is robust to overestimation of the number of free parameters.