2026-09-20T21:45:13Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:326 2025-08-13 bibliography:false doc-type:PhDThesis open_access ddc ddc:510

Mathematical Methods for the Approximation of Radar Traces Thilo Schneider 510 Spline-Approximation Numerisches Verfahren Nichtlineare Optimierung Radar Non-Linear Least-Squares Non-linear IRLS Huber-Approximation DBSCAN Robust Smooth Regression 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. Universität Passau Passau Innstrasse 29, 94032 Passau Tomas Sauer Tom Lyche 2015-05-22 2015-10-28 PhDThesis Text urn:nbn:de:bvb:739-opus4-3269 application/pdf eng Standardbedingung laut Einverständniserklärung thesis.doctoral Universität Passau Passau Fakultät für Informatik und Mathematik 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/326 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/326