Parameter identification of a discretized biased noisy sinusoidal signal

A discrete time, on-line approach is proposed for the simultaneous identification of the frequency, the amplitude and the phase parameters in continuous noisy sinusoidal signals. The proposed technique takes the exact discretization of a continuous sinusoidal signal and generates exact computation formulas for the frequency, bias, amplitude and phase parameters, calculated in terms of quotients involving functions of the output and of some of its delayed values. The formula yields exact parameter calculations in the noiseless case, and it can be synthesized by means of time-varying filters whose outputs are obtained on-line. When the treated signal is affected by additive noises, a least squares-based “invariant filtering” is proposed, resulting in an enhancement of the signal to noise ratio of the factors conforming the basic algorithm. The scheme is proven and analysed by means of a laboratory experiment, a noise analysis and a comparison against other existing methods, where the proposed method shows accurate results with fast convergence rates.