What is the zakai equation

Url: http://ub-madoc.bib.uni-mannheim.de/1391URN: urn: nbn: de: bsz: 180-madoc-13911Document type: dissertation Publishing year: 2006 publishing company: University of Mannheim Appraiser: Potthoff, Jürgen Date of oral exam: July 26, 2006 Language of publication: English Facility: Faculty of Business Informatics and Business Mathematics> Mathematics V (Potthoff)Area of ​​Expertise: 510 mathStandardized keywords (SWD): Filter theory stochastics Free keywords (English): Stochastic filtering, Kalman, Zakai, Monte Carlo Abstract: 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. Translated title: Different aspects of the nonlinear stochastic filter theory (German) Translation of the abstract: This dissertation studies different aspects of the linear and non-linear 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 overcome the difficulties due to The Extended kalman approach and we compare different particle filter algorithms. In the third chapter we study a real life example, estimate the position and 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 filter problem with the Zakai equation for the case of multidimensional systems with unlimited observation functions and an Ornstein-Uhlenbech type of noise. (German) Additional Information:

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