Based on the linearization of the structure’s vibration equation in the state space, the stochastic subspace (SSI) approach is often used for system identification in the time domain of structures. As a consequence of using singular value decomposition (SVD) and QR factorization, the non-linear optimization solution may be avoided, and the identification issue can be solved as a linear least-squares problem. Although SSI does not explicitly minimize a cost function to produce the system matrices, the statistical analysis is significantly more involved for subspace approaches. Alternatively, in system identification, one might choose an output-error method (OEM), whereby the model parameters are repeatedly tweaked to match the outputs of the simulated model and the observed system. The purpose of this study is to modify the OEM to obtain structural features in the following manner: First, to reduce the number of optimization iterations, the initial term is derived using the SSI. Second, the objective function’s nonlinearity is reduced by considering the second-order derivatives as a linear system to optimize parameters using the Gauss-Newton approach. Finally, perform a gradient project minimization in state-space systems to prevent non-injectivity. After applying OEM to the results of a model of a three-story structure activated by seismic acceleration at SNR=1dB, the model’s damping ratio and mode shapes became more precise.