Use of Tikhonov Regularization to Improve the Accuracy of Position Estimates in Inertial Navigation

Inertial navigation problems are often understood as initial value problems. However, there are many applications where boundary value problems naturally arise. In these situations, it has been shown that the finite element method can be efficiently used to compute accurate position and velocity est...

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Bibliographic Details
Published inInternational journal of navigation and observation Vol. 2011; no. 2011; pp. 1 - 10
Main Authors Nieminen, Tuukka, Kangas, Jari, Kettunen, Lauri
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Puplishing Corporation 2011
Hindawi Publishing Corporation
Hindawi Limited
Subjects
Accuracy
Boundary value problems
Estimates
Finite element method
Inertial navigation
Inverse
Inverse problems
Mathematical analysis
Mathematical models
Navigation
Problems
Regularization
Studies
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ISSN1687-5990
1687-6008
DOI10.1155/2011/450269

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Summary:Inertial navigation problems are often understood as initial value problems. However, there are many applications where boundary value problems naturally arise. In these situations, it has been shown that the finite element method can be efficiently used to compute accurate position and velocity estimates. We will propose that finite element method complemented with Tikhonov regularization—a basic tool for inverse problems—is a powerful combination for further accuracy improvements. The proposed method provides a straightforward way to exploit prior information of various types and is subject to rigorous optimality results. Use and accuracy of the proposed method are demonstrated with examples.
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ISSN:1687-5990
1687-6008
DOI:10.1155/2011/450269