Unbiased Estimation of Sinusoidal Signal Parameters via Discrete-Time Frequency-Locked-Loop Filters

A novel class of discrete-time frequency-locked-loop nonlinear (FLL) filters is introduced and their relevance for the on-line estimation of the parameters of a possibly time-varying sinusoidal signal is discussed. Continuous-time nonlinear FLL filters have been proposed in the literature because of their circuital simplicity and ability to provide unbiased estimates of the instantaneous frequency, phase and amplitude of a time-varying sinusoidal signal simultaneously. It is shown in this note that standard discretization techniques may fail to generate discrete-time FLL filters exhibiting the same good properties of the continuous-time domain. In particular, biased frequency estimates are usually produced by these discrete-time filters. In this note, such a drawback is overcome because the proposed discrete-time FLL filters are proved to enjoy semi-globally exponential stability and their estimates are unbiased. A final example is presented for assessment purposes where also comparisons with other discrete-time filters, among which some synthesized by means of standard discretization techniques, are provided.