{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:213"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:213","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Maximum likelihood estimation in dynamical systems","abstract":"Short description of contents:
Dynamical systems are frequently used to model the time evolution of a system.
Typically, they depend on unknown parameters and their trajectories
are only partially observed.
Here maximum likelihood methods are used for the estimation of the
parameters from noisy measurements and to construct the unobserved
components of a system.
These methods take into account the entire information about the
deterministic nature of the underlying true trajectory.
To circumvent the problem of local minima in the space of parameters,
multiple shooting methods are used.
In particular, this thesis contains:
- an examination of the strengths and limits of the maximum likelihood
approach for time-discrete systems, using the logistic map as an example;
- an application to measured data from a CO2 laser, using a
five-dimensional ordinary differential equation;
- an extension of the multiple shooting method to delay differential
equations with applications to the Mackey-Glass system and to measured
data from an electronic circuit;","abstract_html":"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;","abstract_has_math":false,"creators":["Horbelt, Werner"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Honerkamp, Josef"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:21:30Z","subjects":["Identifizierung","Modellierung","unbeobachtete Komponenten","hidden variables","vector field reconstruction","parameter identification, multiple shooting"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/213","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Honerkamp, Josef"]},{"key":"dc:creator","label":"Author","values":["Horbelt, Werner"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Identifizierung","Modellierung","unbeobachtete Komponenten","hidden variables","vector field reconstruction","parameter identification, multiple shooting"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Short description of contents:
Dynamical systems are frequently used to model the time evolution of a system.
Typically, they depend on unknown parameters and their trajectories
are only partially observed.
Here maximum likelihood methods are used for the estimation of the
parameters from noisy measurements and to construct the unobserved
components of a system.
These methods take into account the entire information about the
deterministic nature of the underlying true trajectory.
To circumvent the problem of local minima in the space of parameters,
multiple shooting methods are used.
In particular, this thesis contains:
- an examination of the strengths and limits of the maximum likelihood
approach for time-discrete systems, using the logistic map as an example;
- an application to measured data from a CO2 laser, using a
five-dimensional ordinary differential equation;
- an extension of the multiple shooting method to delay differential
equations with applications to the Mackey-Glass system and to measured
data from an electronic circuit;"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Maximum likelihood estimation in dynamical systems","Maximum-Likelihood-Schätzung in dynamischen Systemen"]}]}],"canonical_facts":{"dc:contributor":["Honerkamp, Josef"],"dc:creator":["Horbelt, Werner"],"dc:description.abstract":["Short description of contents:
Dynamical systems are frequently used to model the time evolution of a system.
Typically, they depend on unknown parameters and their trajectories
are only partially observed.
Here maximum likelihood methods are used for the estimation of the
parameters from noisy measurements and to construct the unobserved
components of a system.
These methods take into account the entire information about the
deterministic nature of the underlying true trajectory.
To circumvent the problem of local minima in the space of parameters,
multiple shooting methods are used.
In particular, this thesis contains:
- an examination of the strengths and limits of the maximum likelihood
approach for time-discrete systems, using the logistic map as an example;
- an application to measured data from a CO2 laser, using a
five-dimensional ordinary differential equation;
- an extension of the multiple shooting method to delay differential
equations with applications to the Mackey-Glass system and to measured
data from an electronic circuit;"],"dc:format.medium":["application/pdf"],"dc:subject":["Identifizierung","Modellierung","unbeobachtete Komponenten","hidden variables","vector field reconstruction","parameter identification, multiple shooting"],"dc:title":["Maximum likelihood estimation in dynamical systems","Maximum-Likelihood-Schätzung in dynamischen Systemen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:30Z"}