A multi-variable frequency-domain maximum likelihood estimator is proposed to identify the modal parameters together with confidence intervals directly from the input-output Fourier data. The use of periodic excitation signals enables the use of a so-called non-parametric errors-in-variables noise model for an accurate description of the measurement set-up. The combination with a maximum likelihood identification approach yields a solver that is extremely robust to errors in the data, such as noise and leakage and hence results in accurate models. Since the maximum likelihood approach involves an optimization problem, a least-squares estimator is proposed as well, with the availability of a stabilization diagram. Both algorithms have been optimized for modal analysis applications by a significant reduction of the computation time and memory requirements. In the case when random noise excitation is required, the proposed method allows a parametric compensation for effects of leakage.