The authors consider the identification problem for linear combined deterministic-stochastic systems for which special cases, both deterministic and stochastic, use a subspace identification method with regularization. It is well known that in common subspace identification methods, the system matrices are estimated by the least squares method, but for a finite number of data points, the estimated matrix is not guaranteed to be stable. Thus, they suggest using a regularization method. The regularization term they use is the trace of a matrix that involves the dynamical system matrix and a non-negative definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski can be interpreted as iteratively applying regularization with specific choices for the weighting matrix.