Parameters estimation of a noisy sinusoidal signal with time-varying amplitude

In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introduced by Fliess and Sira-Ramirez. We apply a similar strategy to estimate these parameters by using modulating functions method. The convergence of the noise error part due to a large class of noises is studied to show the robustness and the stability of these methods. We also show that the estimators obtained by modulating functions method are robust to "large" sampling period and to non zero-mean noises

A Fast On-Line Estimator of the Two Main Vibration Modes of Flexible Structures From Biased and Noisy Measurements

Vibrations are present in many mechanical structures and machines, and are often associated with their elastic parts. Characterizing these vibrations, i.e., obtaining their frequencies, amplitudes and phases, is of most interest in many applications ranging from the maintenance of civil structures to motion control. This article presents a method for the on-line and reliable identification of the defining parameters of two unknown sinusoidal signals through the use of their measured sum in the presence of noise and an offset. It is based on the algebraic derivative approach, defined in the frequency domain, which yields exact calculation formulae for the unknown parameters of the signal, i.e., the amplitudes, phases and frequencies of the two sinusoids and the value of the constant term. The on-line estimation is performed in a time interval which is only a fraction of the first full cycle of the slower component of the measured signal. This feature allows the algorithm to be used to monitor time varying parameters in these vibration signals. This algorithm has been used in experiments with a flexible beam, which is a representative platform of a vibrating mechatronic system. It estimated all the vibration signal parameters quickly and accurately, proved to be insensitive to high frequency noises, and accurately tracked the time variations of the signal parameters

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Systematic and multifactor risk models revisited

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments.Comment: First Paris Financial Management Conference, Paris : France (2013

Critique du rapport signal à bruit en communications numériques

International audienceThe signal to noise ratio, which plays such an important rôle in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus, differential algebra, noncommutative algebra and nonstandard analysis are the main mathematical tools.On démontre que le rapport signal à bruit, si important en théorie de l’information, devient sans objet pour des communications numériques où la démodulation s’effectue selon des techniques nouvelles d’estimation rapide. Calcul opérationnel, algèbre différentielle, algèbre non commutative et analyse non standard sont les principaux outils mathématiques

A property of the elementary symmetric functions”,

Abstract In this paper, a relation between the elementary symmetric functions on the frequencies of multi-sine wave signal and its multiple integrals is proposed. In particular, such relation is useful to obtain a closed-form expression for the frequencies estimation. The approach used herein is based on the algebraic derivative method in the frequency domain, which allows to yield exact formula in terms of multiple integrals of the signal when placed in the time domain. Moreover, it allows to free oneself from the hypothesis of uniform sampling. Two different ways to approach the estimation are advised, the first is based on least-squares estimation, while the second one is based on the solution of a linear system of dimension equal to the number of sinusoidal components involved. For an easy time realization of such formula, a time-varying filter is proposed. Due to use of multiple integrals of the signal, the resulting parameters estimation is accurate in the face of large measurement noise. To corroborate the theoretical analysis and to investigate the performance of the developed algorithm, computer simulated and laboratory experiments data records are processed

A Model-Free Approach for Accurate Joint Motion Control in Humanoid Locomotion

A new model-free approach to precisely control humanoid robot joints is presented in this article. An input&-output online identification procedure will permit to compensate neglected or uncertain dynamics, such as, on the one hand, transmission and compliance nonlinear effects, and, on the other hand, network transmission delays. Robustness toparameter variations will be analyzed and compared to other advanced PID-based controllers. Simulations will show that not only good tracking quality can be obtained with this novel technique, but also that it provides a very robust behavior to the closed-loop system. Furthermore, a locomotion task will be tested in a complete humanoid simulatorto highlight the suitability of this control approach for such complex systems.This work has been supported by the CAM Project S2009/DPI-1559/ROBOCITY2030 II, developed by the research team RoboticsLab at the University Carlos III of Madrid.Publicad