Deadbeat kernel-based frequency estimation of a biased sinusoidal signal

Robust finite-time estimation of biased sinusoidal signals: A volterra operators approach

“…In the spirit of prior work presented by the authors on the sole frequency estimation problem (see [33]), this paper deals with a finite-time convergent estimation scheme in which the frequency, amplitude and phase (AFP) of a noisy sinusoidal signal are estimated in finite-time. As shown in the very recent paper [32] dealing with non-asymptotic continuous-time systems identification, Volterra operators induced by suitably defined bivariate kernels, turn out to be an enabling tool for finite-time estimation.…”

“…Later, in Section 5, we will show that the frequency adaptation algorithm (32) is able to identify the squaredfrequency in finite-time in a noise-free scenario, while the estimation error is ISS in presence of measurement noise. Compared to the preliminary work [33] that exploits a first order sliding mode-based adaptation law, the use of a second order sliding mode (see [27] and [44]) allows a significant suppression of the chattering phenomenon, which will be highlighted in the simulation results provided in Section 6. Moreover, the time-based switching condition in [33] is enhanced by a more robust switching mechanism that depends on a known signal and the above excitation condition.…”

“…Compared to the preliminary work [33] that exploits a first order sliding mode-based adaptation law, the use of a second order sliding mode (see [27] and [44]) allows a significant suppression of the chattering phenomenon, which will be highlighted in the simulation results provided in Section 6. Moreover, the time-based switching condition in [33] is enhanced by a more robust switching mechanism that depends on a known signal and the above excitation condition. Now, with the aim of estimating the amplitude of the sinusoid in finite time, we will exploit a further structural constraint verified by the derivatives of the measured signal.…”

“…(36) When only the estimatesΩ(t) of Ω,Â(t) of A * , and y (i) (t) of y (i) (t) are available (the estimated derivatives can be obtained from (33) by usingΩ(t) in place of Ω * , thus becoming exact in finite time afterΩ has converged to Ω * ), we have that the constraint (36) is not met in general unlessÂ(t) = A * , in general, so that we can introduce a time-varying residual that depends on the frequency estimateΩ(t) and on the estimates y (1) (t) and y (2) (t) obtained by (33):…”

“…and y (1) (t), y (2) (t), computed by (33) with the substitution ofρ h (Ω, t) κ a,h (t) +Ω(t)κ d,h (t), h = 1, 2, 3 in place of ρ h (Ω * , t).…”