Semi-global direct estimation of multiple frequencies with an adaptive observer having minimal parameterization

Abstract

This paper deals with the problem of estimating the frequencies of the n sinusoidal components of a multisinusoidal signal. A distinctive feature of the proposed method is that the frequencies are directly adapted, thus not requiring further steps of eigenvalue extraction or polynomial rootfinding to retrieve the frequencies from the characteristic polynomial, as typically done in the literature. The frequency estimation problem is approached by formulating a new statespace realization of the signal generator (oscillatory internal model) which is characterized by a minimal parameterization in the sense that only n parameters are used to assign the spectrum of the generator, i.e., the n frequencies of the components. In contrast with other existing adaptive observer-based methods that provide direct estimates of the frequencies, the proposed technique does not require state augmentation, making the overall dynamic order (internal model's state+parameters) equal to 3n.

Improved Transients in Multiple Frequencies Estimation via Dynamic Regressor Extension and Mixing

“…In our paper we follow this approach and assume that the frequencies are estimated if the vector θ is obtained. The problem of direct frequency identification is considered, for example, in [13].…”

“…, q−1} verifying (IV-A). Define the vector R e and the matrix M e as given in (13). Next consider the estimatoṙ…”

Parameters estimation of multi-sinusoidal signal in finite-time

“…Thus, to construct frequency estimates, it is necessary to find the roots of a polynomial with dynamically changing coefficients, which significantly increases the computational complexity of the algorithm in the presence of a large number harmonics in the measured signal. The papers [Chen, 2014], [Wang, 2015], [Pin, 2019] propose new adaptive observers that make it possible to eliminate the aforementioned shortcoming and obtain a frequency estimate directly without any need of further processing.…”

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

“…As a consequence, the computational burden may increase significantly in the presence of a large number of sinusoids. In order to alleviate the drawback of the afore-described methods, two novel adaptive-observer algorithms have been recently proposed in [8] and [24], that allow to adapt the frequencies directly without the need of further processing.…”

“…Based on the preliminary results presented in [24], this paper deals with a full AFP methodology, characterized by a direct adaptation mechanism for the squares of the frequencies. In contrast with the recently presented adaptive observer with the same notable feature [8], the devised method removes the requirement of state augmentation, reducing the dimensionality of the observer.…”