Le filtrage linéaire et non linéaire à temps discret et à temps continu et applications

Abstract

The object of this work concerns on the estimate of the state of linear and nonlinear dynamic system and some applications of the problem of filtering in various fields. After a concise talk of the basic concepts of stochastic calculation, various approaches to the problem of filtering have been considered according to temporal nature and the linear or not linear aspect of the system. In the case of a linear dynamic system, we use the approach innovation to find the optimal kalman filter and in particular we find the kalman-Bucy filter in the case of the Gaussian systems. When the dynamic system is nonlinear, the discrete time filter is deduced from the Kalman filter after linearizing of the system and in the case of continuous time, the optimal filter is obtained according to the approach change of measurement initially and then the approach innovation. Three applications to illustrate the interest and the effectiveness of filtering theory were initiated in signal processing, navigation and finance.