Approximating a matrix as the square of a skew-symmetric matrix, with application to estimating angular velocity from acceleration data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912330644717568 |
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| author | Wan, Yang Grossman-Ponemona, Benjamin E. Kesari, Haneesh |
| author_facet | Wan, Yang Grossman-Ponemona, Benjamin E. Kesari, Haneesh |
| contents | In this paper we study the problem of finding the best approximation of a real square matrix by a matrix that can be represented as the square of a real, skew-symmetric matrix. This problem is important in the design of robust numerical algorithms aimed at estimating rigid body kinematics from multiple accelerometer measurements. We give a constructive proof for the existence of a best approximant in the Frobenius norm. We demonstrate the construction with some small examples, and we showcase the practical importance of this work to the problem of determining the angular velocity of a rotating rigid body from its acceleration measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating a matrix as the square of a skew-symmetric matrix, with application to estimating angular velocity from acceleration data Wan, Yang Grossman-Ponemona, Benjamin E. Kesari, Haneesh Optimization and Control Mathematical Physics In this paper we study the problem of finding the best approximation of a real square matrix by a matrix that can be represented as the square of a real, skew-symmetric matrix. This problem is important in the design of robust numerical algorithms aimed at estimating rigid body kinematics from multiple accelerometer measurements. We give a constructive proof for the existence of a best approximant in the Frobenius norm. We demonstrate the construction with some small examples, and we showcase the practical importance of this work to the problem of determining the angular velocity of a rotating rigid body from its acceleration measurements. |
| title | Approximating a matrix as the square of a skew-symmetric matrix, with application to estimating angular velocity from acceleration data |
| topic | Optimization and Control Mathematical Physics |
| url | https://arxiv.org/abs/2504.11590 |