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

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