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The theoretical usefulness of volume as a predictor of fetal weight was assessed on 25 dead neonates with weight ranges between 364 and 3,650 gm. The correlation between volume, measured by water displacement, and weight was r = 0.999, with a standard error of 37 gm. A method is described for using volume, calculated from three-dimensional ultrasonic head… (More)

- Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti, Taous-Meriem Laleg-Kirati, D Y Liu, T M Laleg-Kirati +2 others
- 2013

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)

- Driss Boutat, Da-Yan Liu
- 2015

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)

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)

— Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the… (More)

- D Y Liu, T M Laleg-Kirati, O Gibaru
- 2012

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by… (More)

- Da-Yan Liu
- 2011

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)

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