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Relaxation for online frequency estimator of bias‐affected damped sinusoidal signals based on Dynamic Regressor Extension and Mixing
Author(s) -
Vedyakov Alexey A.,
Vediakova Anastasiia O.,
Bobtsov Alexey A.,
Pyrkin Anton A.
Publication year - 2019
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3034
Subject(s) - estimator , signal (programming language) , mixing (physics) , extension (predicate logic) , control theory (sociology) , mathematics , relaxation (psychology) , amplitude , regression , set (abstract data type) , estimation theory , algorithm , computer science , statistics , physics , artificial intelligence , psychology , social psychology , control (management) , quantum mechanics , programming language
Summary This paper considers the problem of continuous‐time online frequency estimation for a biased damped sinusoidal signal. The previous result for a sinusoidal signal with time‐varying amplitude requires a persistency of excitation condition for regressor, which is not satisfied in the considered case. To relax this condition, we propose to use Dynamic Regressor Extension and Mixing method on the first step to replace n th‐order regression with n first‐order regression models. On the second step, two simple relaxation methods are proposed to establish necessary excitation for the first‐order gradient‐based estimator. The efficiency of the proposed approach is demonstrated through the set of numerical simulations for the exponentially damped sinusoidal signal.