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An important cause of performance loss in source localization in underwater acoustics is that towed flexible antennas deviate from the assumed rectilinear shape. In this work, the localization of sources in presence of phase errors is studied. Cancellation of phase errors is necessary to solve the source-localization problem. A previous work led to interesting results for antennas composed of a few sensors. We propose here a novel algorithm which is adapted to the antennas composed of a large number of sensors, keeping a small computational load. Our method is based on an orthogonality property between signal and noise subspaces and a novel optimization method: the robust dividing rectangles algorithm accelerated by spline interpolation. The performances of the proposed method are illustrated by applying it to the characterization of three sources.