85 research outputs found
Numerical differentiation with annihilators in noisy environment
International audienceNumerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented
Numerical differentiation on irregular grids
International audienceIn this article, we propose a multidimensional numerical differentiation method from irregularly sampled data, in a noisy environment. The method extends to irregular grids our previous work and it relies on the same spirit as the algebraic numerical differentiators due to M. Mboup et al. ("Numerical differentiation with annihilators in noisy environment," Numerical Algorithm, 50, pp. 439-457, 2009). We provide a least squares interpretation of the developed estimators as well as a discrete implementation scheme. Several numerical simulations are presented to asses the performance of the proposed differentiators
Non-asymptotic fractional order differentiators via an algebraic parametric method
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 modified
Riemann-Liouville derivative [14]. Exact and simple formulae for these
differentiators are given where a sliding integration window of a noisy signal
involving Jacobi polynomials is used without complex mathematical deduction.
The efficiency and the stability with respect to corrupting noises of the
proposed fractional order differentiators are shown in numerical simulations
Algebraic parameter estimation of a biased sinusoidal waveform signal from noisy data
International audienceThe amplitude, frequency and phase of a biased and noisy sum of two complex exponential sinusoidal signals are estimated via new algebraic techniques providing a robust estimation within a fraction of the signal period. The methods that are popular today do not seem able to achieve such performances. The efficiency of our approach is illustrated by several computer simulations
Fractional order differentiation by integration with Jacobi polynomials
The differentiation by integration method with Jacobi polynomials was
originally introduced by Mboup, Join and Fliess. This paper generalizes this
method from the integer order to the fractional order for estimating the
fractional order derivatives of noisy signals. The proposed fractional order
differentiator is deduced from the Jacobi orthogonal polynomial filter and the
Riemann-Liouville fractional order derivative definition. Exact and simple
formula for this differentiator is given where an integral formula involving
Jacobi polynomials and the noisy signal is used without complex mathematical
deduction. Hence, it can be used both for continuous-time and discrete-time
models. The comparison between our differentiator and the recently introduced
digital fractional order Savitzky-Golay differentiator is given in numerical
simulations so as to show its accuracy and robustness with respect to
corrupting noises
Algebraic estimation in partial derivatives systems: parameters and differentiation problems
International audienceTwo goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix
Some remarks on wheeled autonomous vehicles and the evolution of their control design
Recent investigations on the longitudinal and lateral control of wheeled
autonomous vehicles are reported. Flatness-based techniques are first
introduced via a simplified model. It depends on some physical parameters, like
cornering stiffness coefficients of the tires, friction coefficient of the
road, ..., which are notoriously difficult to identify. Then a model-free
control strategy, which exploits the flat outputs, is proposed. Those outputs
also depend on physical parameters which are poorly known, i.e., the vehicle
mass and inertia and the position of the center of gravity. A totally
model-free control law is therefore adopted. It employs natural output
variables, namely the longitudinal velocity and the lateral deviation of the
vehicle. This last method, which is easily understandable and implementable,
ensures a robust trajectory tracking problem in both longitudinal and lateral
dynamics. Several convincing computer simulations are displayed.Comment: 9th IFAC Symposium on Intelligent Autonomous Vehicles (Leipzig,
Germany, 29.06.2016 - 01.07.2016
On short-term traffic flow forecasting and its reliability
Recent advances in time series, where deterministic and stochastic modelings
as well as the storage and analysis of big data are useless, permit a new
approach to short-term traffic flow forecasting and to its reliability, i.e.,
to the traffic volatility. Several convincing computer simulations, which
utilize concrete data, are presented and discussed.Comment: 8th IFAC Conference on Manufacturing Modeling, Management & Control
(Troyes, France, June 2016
Fractional order differentiation by integration: an application to fractional linear systems
International audienceIn 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 calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method
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