Pierre Vilbé

Online optimization of the time scale in adaptive Laguerre-based filters

A new online method to optimize the free parameter in adaptive Laguerre-based filters is presented, it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error. The proposed technique presents a fast convergence and a good robustness.

Optimum choice of free parameter in orthonormal approximations

This correspondence investigates the choice of a free parameter, usually related to time scale, that minimizes the error energy when approximating a given signal with some widely used orthonormal basis functions. The proposed solution is the best that can be achieved with the limited required knowledge of the signal. It is appealing for experimental data for which no exact mathematical expression is available. >

Mine classification using a hybrid set of descriptors

This paper is concerned with the problem of recognition of objects laying on the sea-bed. A high resolution sonar provides high-quality acoustic images of the sea-bed, allowing the classification of objects from their cast shadow. After the segmentation step, a set of features is extracted from the shadow. We propose an approach based on a hybrid set of descriptors, combining features of different origins. We first compute topological parameters: the extent and the elongation. In addition to these classical features, affine moment invariants seem suitable for sonar images. Indeed, under weak perspective conditions, the perspective transformation is well approximated by an affine transformation. A four-dimensional vector is then computed characterizing the shadow. The method has been tested on simulated sonar images.

Pertinent choice of parameters for discrete Kautz approximation

Kautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled.

Laguerre-Gram reduced-order modeling

We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the L/sub /spl infin///sup 2/(/spl Ropf//sup +/) criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in L/sub /spl infin///sup 2/(/spl Ropf//sup +/). The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to multiple-input-multiple-output systems is also given.

Improved method for optimum choice of free parameter in orthogonal approximations

We report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions. This method requires limited knowledge of the signal to be approximated and has a low computational cost.

A new discrete impulse response Gramian and its application to model reduction

Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure.

An alternative method for numerical inversion of Laplace transforms

Based on least-squares approximation of the rectangular pulse (Vilbeacute , 1999) by exponential functions, this brief presents an alternative method for performing numerical inversion of the Laplace transform. It compares favourably with the celebrated Vlachs method

Novel interpretation of the pencil-of-functions approximation/identification method

Jains pencil-of-functions method based on the linear dependence/independence of a set of functions is revisited. It is shown that no matter what model order is chosen, every estimated denominator coefficient may be regarded as the geometric mean of two values obtained in a least-squares sense.