Parameter identification of unknown biased sinusoid

Abstract

An algorithm composed of a normalised frequency estimator and a first-order low-pass filter is introduced to identify online the unknown values of bias, amplitude, frequency and phase angles of a sinusoid signal. Slow integral manifold technique and averaging method are used to educe a non-linear autonomous system for frequency estimation. The global exponential stability of isolated equilibrium point and the ultimate boundedness under unknown bounded disturbance are investigated respectively. The identification and the estimation errors of bias, amplitude and phase angle under bounded disturbance are also formulated and exhibited by simulation.