RECIPROCAL PROCESSES: IDENTIFICATION AND COVARIANCE EXTENSION
Modeling and identification of finite support signals (for example signals depending on one or two spatial coordinates like images) has traditionally been approached by describing these signals as truncations of stationary signals defined on the whole time axis. This approach leads to wellknown problems and drawbacks related to truncations, border effects etc. A class of statistical models called reciprocal processes which intrinsecally live on a finite support set has recently been popularized in a series of papers by A. Krener, B. Levy and coworkers. We believe that stationary reciprocal processes are a very natural class of models for treating estimation and processing of signals defined on a finite set. In particular the identification of these processes is an important open problem which we have just started to look at [I18],[I 19]. Its solution would surely lead to a significant advance in several areas of signal processing and control.
MODELING AND IDENTIFICATION OF LINEAR MECHANICAL SYSTEMS
The identification of linear models for large mechanical systems is a very important research area with diverse applications such as the analysis, design and nondestructive testing of large compliant structures. The parameters of interest (e.g. mass and stiffness matrices) are defined in terms of continuoustime models but identification algorithms are invariably based on discrete data and produce discretetime models. Quite often the recovery of a continuoustime model from a discretization is a very illconditioned problem and therefore one needs special discretization techniques which permit an accurate recovery of the continuoustime parameters from the identified discretetime model. One would also like to preserve the physical meaning of basic mechanical quantities such as total energy etc. The theory of variational integrators, a new discretization technique of the Lagrange equation of motion of a mechanical system, leads to simple and wellconditioned transformation formulas for the recovery of the continuous time parameters from the discretized model. We plan to use this theory in identification. Preliminary results [I 22] seem encouraging.
