Parameter Identification of Sinusoids

For a biased multi-sinusoidal signal an estimator of order 5n+1 is designed to identify all the 3n+1 parameters including the frequency, amplitude and phase for each of n sinusoids, and the overall offset. As an alternative, a fifth-order parameter estimator is also derived for a biased single sinusoid. The derivations of the estimators are straightforward by using some treatments in the existing frequency estimators and the standard gradient algorithm. Global asymptotic convergence of the parameter estimation is verified. The originality of the work is the proposal of a first solution to the problem of identifying full parameters of a biased multi-sinusoidal signal with globally asymptotic convergence of the parameter estimation.

[1]  Riccardo Marino,et al.  Global estimation of n unknown frequencies , 2002, IEEE Trans. Autom. Control..

[2]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[3]  Ming Hou,et al.  Estimation of Sinusoidal Frequencies and Amplitudes Using Adaptive Identifier and Observer , 2007, IEEE Transactions on Automatic Control.

[4]  Scott C. Douglas,et al.  Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency , 1996, Autom..

[5]  Petre Stoica.  List of references on spectral line analysis , 1993, Signal Process..

[6]  Sergio M. Savaresi,et al.  On the parametrization and design of an extended Kalman filter frequency tracker , 2000, IEEE Trans. Autom. Control..

[7]  Barry G. Quinn,et al.  The Estimation and Tracking of Frequency , 2001 .

[8]  Peter Händel,et al.  Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm , 2000, IEEE Trans. Instrum. Meas..

[9]  Riccardo Marino,et al.  Output regulation for linear systems via adaptive internal model , 2003, IEEE Trans. Autom. Control..

[10]  K. Narendra,et al.  Persistent excitation in adaptive systems , 1987 .

[11]  X. Xia,et al.  Global frequency estimation using adaptive identifiers , 2002, IEEE Trans. Autom. Control..

[12]  Artem Kremlev,et al.  Identification of Frequency of Biased Harmonic Signal , 2007, Eur. J. Control.

[13]  Alexander G. Loukianov,et al.  A globally convergent estimator for n-frequencies , 2002, IEEE Trans. Autom. Control..

[14]  Jayme Garcia Arnal Barbedo,et al.  Estimating Frequency, Amplitude and Phase of Two Sinusoids with Very Close Frequencies , 2009 .