In this research study, a single axis (inner azimuth gimbal) of a four-axis gyro-stabilized electro optic gimbal system is modelled through experimental investigation in the frequency domain, and the results of this investigation are presented. The dynamic behaviour of the mechanical system is obtained from input and output signals, strictly speaking, nonparametric measurements. Detecting and measuring the nonlinear distortions allows a better understanding and gives an intuitive insight into the error sources on frequency response function measurements. In this study, a nonparametric frequency response function and its uncertainty (noise) are measured; nonlinear distortions are quantified on a real-time system. The dynamic system is modelled by its parametric transfer function with various different estimation techniques and their efficiencies, convergence properties, and bias errors are compared and discussed. It turns out that, the nonparametric noise model allows the estimator to weight the cost function and reach statistically better results. As an original contribution, a common problem encountered with gimbals having small rotational movement capacity (in this case study, +/- 5 degrees for the inner gimbals) is formulated as an optimization problem. An optimization procedure is studied to achieve a better signal-to-noise ratio in the frequency band of interest, while satisfying device-specific constraints.