In this paper, we present a new method for frequency domain identification of discrete linear time-invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems. KEYWORDSfrequency domain, mixed noises, orthogonal basis, rational function, shifted Cauchy kernel MSC CLASSIFICATION A1420; 26C15Math Meth Appl Sci. 2019;42:7285-7295.wileyonlinelibrary.com/journal/mma

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