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The paper deals with the problem of developing a multi-output soft sensor for the industrial reactive distillation process of methyl tert-butyl ether production. Unlike the existing soft sensor approaches, this paper proposes using a soft sensor with filters to predict model errors, which are then taken into account as corrections in the final predictions of outputs. The decomposition of the problem of optimal estimation of time delays is proposed for each input of the soft sensor. Using the proposed approach to predict the concentrations of methyl sec-butyl ether, methanol, and the sum of dimers and trimers of isobutylene in the output product in a reactive distillation column was shown to improve the results by 32%, 67%, and 9.5%, respectively.