In the framework of the operational modal analysis (OMA), several approaches have been developed for estimating the modal parameters, i.e., natural frequencies, damping ratios, and mode shapes. In this paper, two methods for the estimate of the modal parameters from ambient responses are proposed. The first one estimates the modal parameters directly from the correlation functions, the other from the power spectral densities. The main purpose is to increase the reliability of the results and to speed up the estimation procedure: two fundamental tasks in dealing with flight tests. In the first case the Hilbert transform allows the reconstruction of the analytical signal of the correlation functions and then the exponential least square fitting can be implemented for the evaluation of the modal parameters. On the other side, a similar procedure recovers the causality of the power spectral densities by applying the Hilbert transform and then the least square polynomial ratio technique gives the modal estimates. The validation of these methodologies against standard input-output tests is performed on simple cantilever beam. Then, the capabilities of the proposed approaches to identify the dynamic properties of a flying system, represented by a Savannah ultra-light aircraft, are reported. For this purpose, the evolution of the poles of the dynamic system to the change of the flight conditions are investigated.