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Using an antenna array at the base station in a mobile communication system can lead to benefits such as increased capacity and coverage. Experimental results have shown that a further increase in diversity gain can be accomplished if the antenna not only consists of several elements, but also if the elements are diversely polarized. However, employing diversely polarized arrays complicates the estimation of parameters such as the directions of arrival, as the number of unknown parameters increases, and thereby the complexity of the estimator. Previous work has presented solutions to take the polarization parameters into account, but the necessary constraint used is in a sense restrictive. Instead, a constrained relaxed minimization procedure is proposed that eliminates this restriction. In essence, each propagation path is constrained separately. The proposed technique is applied to real GSM data from a dually polarized antenna array.