Abstract
For a biased multi-sinusoidal signal an estimator of order 5 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> +1 is designed to identify all the 3 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> +1 parameters including the frequency, amplitude and phase for each of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> 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.
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