An adaptive observer-based estimator for multi-sinusoidal signals

2015 54th IEEE Conference on Decision and Control (CDC)

et al. 2015

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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.

Section: Introductionmentioning

confidence: 98%

“…On the other hand, the method [20] requires the augmentation of the state dynamics with auxiliary linear filters, that caus the dynamic order of the algorithm to be non-minimal.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

2015 54th IEEE Conference on Decision and Control (CDC)

et al. 2015

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“…In the spirit of the preliminary results presented in [23], the robustness in presence of structured and unstructured uncertainties are addressed by Input-to-state stability (ISS) arguments. A notable feature of adaptive observer schemes is the possibility of carrying out multi-sinusoidal estimation by expanding the dynamic model with a suitable system transformation (see, for example, [19,21,25,26]). …”

Section: Introductionmentioning

confidence: 99%

A parallel prefiltering approach for the identification of a biased sinusoidal signal: Theory and experiments

Adaptive Control & Signal

et al. 2015

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SUMMARYThe problem of estimating the amplitude, frequency and phase of an unknown sinusoidal signal from a noisy biased measurement is addressed in this paper by a family of parallel pre-filtering schemes. The proposed methodology consists in using a pair of linear filters of specified order to generate a suitable number of auxiliary signals that are used to estimate -in an adaptive way -the frequency, the amplitude and the phase of the sinusoid. Increasing the order the pre-filters improves the noise immunity of the estimator, at the cost of an increase of the computational complexity. Among the whole family of estimators realizable by varying the order of the filters, the simple parallel pre-filters of order 2+2 and 3+3 are discussed in detail, being the most attractive from the implementability point of view. The behavior of the two algorithms with respect to bounded external disturbances is characterized by Input-to-State Stability arguments. Finally, the effectiveness of the proposed technique is shown both by comparative numerical simulations and by a real experiment addressing the estimation of the frequency of the electrical mains from a noisy voltage measurement.

“…In contrast with other methods that are either indirectly identifying the frequency contents or are characterized by local stability only, the present paper deals with a direct adaptation mechanism for the squares of the frequencies with semi-global stability based on the recent preliminary results presented in [35]. Moreover, the robustness to the bounded measurement noise, that is likely to appear in real-world applications, is addressed by Inputto-State-Stability (ISS) arguments.…”

Section: Introductionmentioning

confidence: 99%

“…It is shown that the ISS property with respect to the additive measurement noise is ensured by suitably choosing a few suitable tuning parameters. In comparison with [35], the proposed novel estimator adopts a n-dimensional excitation-based switching signal to separately control the multiple frequency adaptation in all directions by means of suitable matrix decomposition techniques, thus enhancing the practical implementation and avoiding unnecessarily disabled adaptation in the scenario that only parts of the directions fulfill the excitation condition (e.g., overparametrization scenarios).…”

Section: Introductionmentioning

confidence: 99%

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

IEEE Trans. Automat. Contr.

et al. 2018

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Abstract-This paper presents an adaptive observer-based robust estimation methodology of the amplitudes, frequencies and phases of biased multi-sinusoidal signals in presence of bounded perturbations on the measurement. The parameters of the sinusoidal components are estimated on-line and the update laws are individually controlled by an excitation-based switching logic enabling the update of a parameter only when the measured signal is sufficiently informative. This way doing, the algorithm is able to tackle the problem of over-parametrization (i.e., when the internal model accounts for a number of sinusoids that is larger than the true spectral content) or temporarily fading sinusoidal components. The stability analysis proves the existence of a tuning parameter set for which the estimator's dynamics are input-to-state stable with respect to bounded measurement disturbances. The performance of the proposed estimation approach is evaluated and compared with other existing tools by extensive simulation trials and real-time experiments.