{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:326"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:326","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Mathematical Methods for the Approximation of Radar Traces","abstract":"Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account. In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently. In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables.","abstract_html":"Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account. In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently. In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables.","abstract_has_math":false,"creators":["Schneider, Thilo"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Sauer, Tomas","Lyche, Tom"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-22","date_published":"2015-05-22","updated_at":"2026-07-24T03:45:00Z","subjects":["Non-Linear Least-Squares","Non-linear IRLS","Huber-Approximation","DBSCAN","Robust Smooth Regression"],"languages":[],"rights":["Standardbedingung laut Einverständniserklärung"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/326","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sauer, Tomas","Lyche, Tom"]},{"key":"dc:creator","label":"Author","values":["Schneider, Thilo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Passau"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Non-Linear Least-Squares","Non-linear IRLS","Huber-Approximation","DBSCAN","Robust Smooth Regression"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Standardbedingung laut Einverständniserklärung"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account. In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently. In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Mathematical Methods for the Approximation of Radar Traces"]}]}],"canonical_facts":{"dc:contributor":["Sauer, Tomas","Lyche, Tom"],"dc:creator":["Schneider, Thilo"],"dc:description.abstract":["Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account. In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently. In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Standardbedingung laut Einverständniserklärung"],"dc:subject":["Non-Linear Least-Squares","Non-linear IRLS","Huber-Approximation","DBSCAN","Robust Smooth Regression"],"dc:title":["Mathematical Methods for the Approximation of Radar Traces"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:00Z"}