One-parameter robust global frequency estimator for slow-varying amplitude and noisy oscillations.

Robust online estimation of the oscillation frequency belongs to classical problems of the system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as for example in the case of damped oscillations. A novel robust frequency estimation algorithm is proposed, being motivated by the existing globally convergent frequency estimator. Advantage of the proposed estimator is in requiring one design parameter only and being robust against the measurement noise and initial conditions. The proven global convergence allows also for slow-varying amplitudes that comes in favor of the applications with damped oscillations or additionally shaped harmonic signals. The proposed analysis is simple and relies on averaging theory of the periodic signals. The developments disclose an exponential convergence rate, which depends analytically from the sought frequency, adaptation gain, and oscillations amplitude. Numerical and experimental examples demonstrate robustness and efficiency of the proposed estimator for the signals with slow-varying amplitude and noise.