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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)
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)
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)
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)
In this paper, we are interested in the estimation of the source term for a space fractional advection dispersion equation using concentration and flux measurements at final time. An example of application is the identification of contamination source in groundwater transport. We propose to use the so called modulating functions method which has been(More)
This paper aims to study the existence of a change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form. Moreover, an algorithm used to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This paper is(More)