Relaxation for online frequency estimator of bias‐affected damped sinusoidal signals based on Dynamic Regressor Extension and Mixing

Abstract

SummaryThis 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 nth‐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.