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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| Published in | International journal of navigation and observation Vol. 2011; no. 2011; pp. 1 - 10 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Puplishing Corporation
2011
Hindawi Publishing Corporation Hindawi Limited |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1687-5990 1687-6008 |
| DOI | 10.1155/2011/450269 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Kettunen, Lauri Nieminen, Tuukka Kangas, Jari |
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| Cites_doi | 10.1155/2010/869127 10.1007/s002110050078 10.1145/321105.321114 10.1137/1034115 10.1109/TAC.1969.1099196 10.1137/0917062 10.1080/00401706.1970.10488699 10.1109/42.700740 10.2514/3.3166 10.1016/S0010-4655(01)00217-X 10.1080/00401706.1979.10489751 10.1088/0957-0233/21/10/105204 10.1016/0022-247X(70)90017-X 10.1111/j.1365-246X.1979.tb03777.x |
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| Contributor | Kettunen, Lauri Kangas, Jari |
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| Copyright | Copyright © 2011 Tuukka Nieminen et al. Copyright © 2011 Tuukka Nieminen et al. Tuukka Nieminen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| Snippet | Inertial navigation problems are often understood as initial value problems. However, there are many applications where boundary value problems naturally... Inertial navigation problems are often understood as initial value problems . However, there are many applications where boundary value problems naturally... |
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| SubjectTerms | 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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| Title | Use of Tikhonov Regularization to Improve the Accuracy of Position Estimates in Inertial Navigation |
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