Different aspects of nonlinear stochastic filtering theory
Riadh Kaddachi · MADOC (University of Mannheim) · 2006
This thesis studies different aspects of the linear and the nonlinear stochastic filtering problem. It consists of four chapters. In the first chapter we derive the Kalman and the extended Kalman filter algorithms and we study some of their qualitative properties. In the second chapter we present a unified general framework on particle filter methods. In particular, we show how the particle filter methods surmount the difficulties due to the Kalman approach to filtering and we compare different particle filter algorithms. In the third chapter we study a real life example, tracking the position and the speed of a car, then we compare the extended Kalman filter and the particle filter methods. Finally, in the fourth chapter we generalize the formulation of the filtering with the Zakai equation to the case of multidimensional systems with unbounded observation functions and an Ornstein-Uhlenbech type noise.