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The amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far-field sources is investigated. The authors prove that the presence of a doublet and use of fourth-order cumulants is sufficient to accomplish this task. Their approach is based on the interpretation of cumulants for array processing. The cumulant-based algorithm is computationally efficient and more general than constrained covariance-based algorithms. Simulations indicate excellent results by the proposed algorithm.