Total Least Squares

Comparing Least Squares Methods for Signal Reconstruction

Bachelor thesis (2023)

Authors

J. Houben Electrical Engineering, Mathematics and Computer Science

Contributors

M.B. van Gijzen Numerical Analysis - EEMCS (mentor)
H.N. Kekkonen Statistics - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Jort Houben
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Published Date

12-07-2023

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

A common problem in wireless communication is the existence of multipath propagation. This means that a transmitted signal is received multiple times because of reflections caused by the environment. We present two ways of modeling multipath propagation of an acoustic underwater signal. We discretise these models to solve them numerically. During the solving process, we are presented with inconsistent, overdetermined systems of linear equations. We investigate two methods to go about these systems: the ordinary least squares method and the total least squares method. We reconstruct a signal using both of these methods and compare their results. The method of least squares reconstructs the signal moderately well. For the total least squares method this is not the case. It turns out that it is not straightforward to formulate a total least squares problem in the corresponding model. We suspect that, in part, this is why the signal reconstruction does not work well for the total least squares method.

Files

TLS_Bep.pdf
(pdf | 5.19 Mb)