Maximum likelihood estimation in dynamical systems

Short description of contents: <br> <br>Dynamical systems are frequently used to model the time evolution of a system. <br>Typically, they depend on unknown parameters and their trajectories <br>are only partially observed. <br>Here maximum likelihood methods are used for the estimation of the <br>parameters from noisy measurements and to construct the unobserved <br>components of a system. <br>These methods take into account the entire information about the <br>deterministic nature of the underlying true trajectory. <br>To circumvent the problem of local minima in the space of parameters, <br>multiple shooting methods are used. <br> <br>In particular, this thesis contains: <br> <br>- an examination of the strengths and limits of the maximum likelihood <br>approach for time-discrete systems, using the logistic map as an example; <br> <br>- an application to measured data from a CO2 laser, using a <br>five-dimensional ordinary differential equation; <br> <br>- an extension of the multiple shooting method to delay differential <br>equations with applications to the Mackey-Glass system and to measured <br>data from an electronic circuit;

Author dc:creator

• Horbelt, Werner

Contributors dc:contributor

• Honerkamp, Josef

• Identifizierung
• Modellierung
• unbeobachtete Komponenten
• hidden variables
• vector field reconstruction
• parameter identification, multiple shooting

Repository record source_url

https://freidok.uni-freiburg.de/data/213

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:213