Mathematical Methods for the Approximation of Radar Traces

  • 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.

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Metadaten
Author:Thilo Schneider
URN:urn:nbn:de:bvb:739-opus4-3269
Advisor:Tomas Sauer, Tom Lyche
Document Type:Doctoral Thesis
Language:English
Year of Completion:2015
Date of Publication (online):2015/10/28
Date of first Publication:2015/10/28
Publishing Institution:Universität Passau
Granting Institution:Universität Passau, Fakultät für Informatik und Mathematik
Date of final exam:2015/05/22
Release Date:2015/10/28
Tag:DBSCAN; Huber-Approximation; Non-Linear Least-Squares; Non-linear IRLS; Robust Smooth Regression
GND Keyword:Spline-Approximation; Numerisches Verfahren; Nichtlineare Optimierung; Radar
Page Number:114
Institutes:Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung