This paper presents an adaptive-observer-based robust estimation methodology of the amplitudes, frequencies, and phases of biased multi-sinusoidal signals in the presence of bounded perturbations on the measurement. The parameters of the sinusoidal components are estimated online, and the update laws are individually controlled by an excitation-based switching logic enabling the update of a parameter only when the measured signal is sufficiently informative. This way doing, the algorithm is able to tackle the problem of overparameterization (i.e., when the internal model accounts for a number of sinusoids that is larger than the true spectral content) or temporarily fading sinusoidal components. The stability analysis proves the existence of a tuning parameter set, for which the estimator's dynamics are input-to-state stable with respect to bounded measurement disturbances. The performance of the proposed estimation approach is evaluated and compared with the other existing tools by extensive simulation trials and real-time experiments.