Estimation of Damped Sinusoidal Signals: an Observer-Based Approach

This paper presents a novel observer-based method for estimating the parameters of an exponentially damped sinusoid, including the frequency, amplitude, phase and the damping factor. A second-order sliding-mode-based adaptation law is designed for estimating the frequency and the damping factor, while amplitude and phase are obtainable from the said parameters by straightforward algebra. The stability and robustness analysis in presence of an additive disturbance proves the existence of a tuning parameter set for which the estimator’s dynamics are asymptotic stable and the estimation error asymptotically converges to a residual set whose size depends on the amplitude of the disturbance. Numerical and comparative examples show the effectiveness of the proposed estimation approach.