This master thesis deals with the study of a major problem in control and system theory, the filtering problem, from a deterministic point of view. This problem consists of estimating the trajectories of a dynamical system (input - state - output), given some noised measures.
We start the analysis with a brief reminder of useful concepts and results of control and system theory.
In the second chapter, we define the filtering problem, under the form of an optimization problem: minimizing an uncertainty measure involving the estimated state and input trajectories.
Subsequently, we distinguish between two kinds of filtering: time-varying filtering and time-i,nvariant filtering. Chapters III and IV are devoted to the resolution of these problems, as well as the development of dynamic filtering algorithms.
Finally, in chapter V, the theoretical results are applied to the estimation problem of the position of a geostationnary satellite.