Identification of multi-sinusoidal signals with direct frequency estimation: An adaptive observer approach

This paper addresses the problem of estimating the frequencies, amplitudes and phases of the n sinusoidal components of a possibly biased multi-sinusoidal signal. The proposed adaptive observer allows the direct adaptation of the frequency estimates with a relatively low dynamic order 3n+1 (3n for an unbiased signal). The stability analysis proves the global exponential convergence of the estimation error and the robustness to additive norm-bounded measurement perturbations.

[1]  Thomas Parisini,et al.  An Adaptive Observer-Based Switched Methodology for the Identification of a Perturbed Sinusoidal Signal: Theory and Experiments , 2014, IEEE Transactions on Signal Processing.

[2]  Alireza R. Bakhshai,et al.  Estimation of $n$ Frequencies Using Adaptive Notch Filter , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  A. Bakhshai,et al.  Processing of Harmonics and Interharmonics Using an Adaptive Notch Filter , 2010, IEEE Transactions on Power Delivery.

[4]  Giuseppe Fedele,et al.  A Frequency-Locked-Loop Filter for Biased Multi-Sinusoidal Estimation , 2014, IEEE Transactions on Signal Processing.

[5]  Biqing Wu,et al.  A magnitude/phase-locked loop approach to parameter estimation of periodic signals , 2003, IEEE Trans. Autom. Control..

[6]  Marc Bodson,et al.  Analysis and Implementation of an Adaptive Algorithm for the Rejection of Multiple Sinusoidal Disturbances , 2009, IEEE Transactions on Control Systems Technology.

[7]  Giuseppe Fedele,et al.  Editorial for the special issue on recent advances in adaptive methods for frequency estimation with applications , 2016 .

[8]  Romeo Ortega,et al.  A globally convergent frequency estimator , 1999, IEEE Trans. Autom. Control..

[9]  Indra Narayan Kar,et al.  Design of Asymptotically Convergent Frequency Estimator Using Contraction Theory , 2008, IEEE Transactions on Automatic Control.

[10]  Ming Hou,et al.  Parameter Identification of Sinusoids , 2012, IEEE Transactions on Automatic Control.

[11]  Barbara F. La Scala,et al.  Design of an extended Kalman filter frequency tracker , 1996, IEEE Trans. Signal Process..

[12]  Masoud Karimi-Ghartemani,et al.  A nonlinear time-frequency analysis method , 2004, IEEE Transactions on Signal Processing.

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

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

[15]  M. Karimi-Ghartemani,et al.  Addressing DC Component in PLL and Notch Filter Algorithms , 2012, IEEE Transactions on Power Electronics.

[16]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

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

[18]  Alexey A. Bobtsov,et al.  A method for increasing the rate of parametric convergence in the problem of identification of the sinusoidal signal parameters , 2017, Autom. Remote. Control..

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

[20]  K. Hirai,et al.  Upper and lower bounds on the solution of the algebraic Riccati equation , 1979 .

[21]  Alessandro Astolfi,et al.  Robust hybrid estimation and rejection of multi-frequency signals , 2016 .

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

[23]  Sergey A. Kolyubin,et al.  Estimation of polyharmonic signal parameters , 2015, Autom. Remote. Control..

[24]  Giuseppe Fedele,et al.  Non Adaptive Second-Order Generalized Integrator for Identification of a Biased Sinusoidal Signal , 2012, IEEE Transactions on Automatic Control.