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

Robust online estimation of an oscillation frequency belongs to classical problems of the system identification and adaptive control. The given harmonic signal can be noisy and amplitude-varying, at the same time, like e.g. in case of the damped oscillations. A novel robust frequency estimation algorithm is proposed, 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 is insensitive to the amplitude variations, which comes in favor of applications with damped oscillations or additionally shaped harmonic signals. The proposed analysis is simple and discloses 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 amplitude-varying and noisy signals.