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.
Author: | Thilo Schneider |
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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): | Standardbedingung laut Einverständniserklärung |