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Multichannel interferometric synthetic aperture radar (InSAR) systems allow the estimation of the height profile of the Earth's surface, exploiting the availability of multiple radar acquisitions, obtained via different baselines/frequencies. Statistical approaches, in particular maximum a posteriori technique and Markov random-field image models, can be exploited for such estimation problem, which proved to be effective. However, despite the particular solution method used, the problem with multichannel interferometry is that interferograms can be affected from the presence of undetermined phase offsets, which makes it difficult to get correct height estimation in any case. In this letter, we present a procedure to estimate these phase offsets using statistical estimation; we test the procedure on both simulated and real data. For the latter, we show how an optimal estimation of the phase offsets can be used to improve the resolution of an available Shuttle Radar Topography Mission digital elevation model. The obtained results prove the effectiveness of the method and assess the overall quality of the height estimation procedure.