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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-Ramírez. We apply a similar strategy to estimate these parameters by using modulating functions method. The convergence of the noise error part due(More)
Recent algebraic parametric estimation techniques (see [10,11]) led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal (see [24,25]). In this paper, we extend such differentiation methods by providing a larger choice of parameters in these integrals: they can be reals. For this, the extension is done via a(More)
In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then,(More)
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's(More)
This paper investigates the behavior of central Jacobi differentiator in robot identification applications. Jacobi differentiator is a Jacobi orthogonal based algebraic differentiator. It is applied to compute acceleration from noisy position measurements. Moreover, its frequency domain property is analyzed via a finite impulse response (FIR) filter point(More)
The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess [1], [2]. We are going to generalize this method from the integer order to the fractional order so as to estimate the fractional order derivatives of noisy signals. For sake of clarity, this(More)
Christian GOUT Professeur à l'INSA de Rouen Rapporteur Gildas BESANCON Professeur à l'Université de Grenoble Rapporteur Mamadou MBOUP Professeur à l'Université de Reims Invité Alban QUADRAT Chargé de Recherche INRIA Saclay Examinateur Sette DIOP Chargé de Recherche CNRS à l'Université de Paris Sud Examinateur Stéphane DE BIEVRE Professeur à l'USTL(More)