We consider the problem of estimating the steering vectors of an uncalibrated diversely polarized array. The array elements are assumed to consist of several groups. In each group the elements have the same polarization sensitivity and the same unknown gain pattern, up to an unknown multiplicative factor. The phases of the elements are arbitrary and unknown. We identify a cost function whose minimizer is a statistically consistent and efficient estimate of the unknown parameters. An iterative algorithm for finding the minimum of that cost function is presented. The proposed algorithm is guaranteed to converge. The estimated steering vectors are used for constructing a matrix whose multiplication with the observed data yields an estimate of each of the signals. A comparison of Monte Carlo experiments and theoretical bounds is used to validate the analysis.