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 in:International journal of navigation and observation 2011, Vol.2011 (2011), p.1-10
Main Authors: Nieminen, Tuukka, Kangas, Jari, Kettunen, Lauri
Format: Article
Language:English
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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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.
ISSN:1687-5990
1687-6008
DOI:10.1155/2011/450269