Attitude Reconstruction from Inertial Measurement: Mitigating Runge Effect for Dynamic Applications
Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper rev...
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| Published in | arXiv.org |
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| Language | English |
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10.07.2021
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| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.2107.04722 |
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| Abstract | Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions. |
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| AbstractList | Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions. IEEE Transactions on Aerospace and Electronic Systems, 2021 Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions. |
| Author | Wu, Yuanxin Zhu, Maoran |
| Author_xml | – sequence: 1 givenname: Yuanxin surname: Wu fullname: Wu, Yuanxin – sequence: 2 givenname: Maoran surname: Zhu fullname: Zhu, Maoran |
| BackLink | https://doi.org/10.1109/TAES.2021.3111839$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.2107.04722$$DView paper in arXiv |
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| DOI | 10.48550/arxiv.2107.04722 |
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| Snippet | Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the... IEEE Transactions on Aerospace and Electronic Systems, 2021 Time-equispaced inertial measurements are practically used as inputs for motion determination.... |
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| SubjectTerms | Attitudes Computation Computer Science - Robotics Computer Science - Systems and Control Coning motion Inertial navigation Interpolation Iterative methods Numerical stability Polynomials Time measurement |
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| Title | Attitude Reconstruction from Inertial Measurement: Mitigating Runge Effect for Dynamic Applications |
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