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A study of QR decomposition and Kalman filter implementations
KTH, School of Electrical Engineering (EES), Signal Processing.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

With the rapid development of new technologies during the last decades,

the demand of complex algorithms to work in real-time applications has increased

considerably. To achieve the real time expectations and to assure

the stability and accuracy of the systems, the application of numerical methods

and matrix decompositions have been studied as a trade-off between

complexity, stability and accuracy. In the first part of this thesis, a survey

of state-of-the-art QR Decomposition methods applied to matrix inversion

is done. Stability and accuracy of these methods are analyzed analytically

and the complexity is studied in terms of operations and level of parallelism.

Besides, a new method called Modified Gaussian Elimination (MGE) is proposed.

This method is shown to have better accuracy and less complexity

than the previous methods while keeping good stability in real time applications.

In the second part of this thesis, different techniques of extended

Kalman Filter implementations are discussed. The EKF is known to be numerically

unstable and various methods have been proposed in the literature

to improve the performance of the filter. These methods include square-root

and unscented versions of the filter that make use of numerical methods such

as QR, LDL and Cholesky Decomposition. At the end of the analysis, the

audience/reader will get some idea about best implementation of the filter

given some specifications.

Place, publisher, year, edition, pages
2014. , 73 p.
Series
EES Examensarbete / Master Thesis, XR-EE-SB 2014:010
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-165624OAI: oai:DiVA.org:kth-165624DiVA: diva2:808731
Examiners
Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2015-04-29Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf