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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Wahba's problem ： ウィキペディア英語版 Wahba's problem In applied mathematics, Wahba's problem, first posed by Grace Wahba in 1965, seeks to find a rotation matrix (special orthogonal matrix) between two coordinate systems from a set of (weighted) vector observations. Solutions to Wahba's problem are often used in satellite attitude determination utilising sensors such as magnetometers and multi-antenna GPS receivers. The cost function that Wahba's problem seeks to minimise is as follows: : $J(\backslash mathbf)\; =\; \backslash frac\; \backslash sum\_^\; a\_k||\; \backslash mathbf\_k\; -\; \backslash mathbf\; \backslash mathbf\_k\; ||^2$ where $\backslash mathbf\_k$ is the ''k''-th 3-vector measurement in the reference frame, $\backslash mathbf\_k$ is the corresponding ''k''-th 3-vector measurement in the body frame and $\backslash mathbf$ is a 3 by 3 rotation matrix between the coordinate frames. $a\_k$ is an optional set of weights for each observation. A number of solutions to the problem have appeared in literature, notably Davenport's q-method, QUEST and singular value decomposition-based methods. == Solution by Singular Value Decomposition == One solution can be found using a singular value decomposition as reported by (Markley ) 1. Obtain a matrix $\backslash mathbf$ as follows: $\backslash mathbf\; =\; \backslash sum\_^\; a\_i\; \backslash mathbf\_i\; ^T$ 2. Find the singular value decomposition of $\backslash mathbf$ $\backslash mathbf\; =\; \backslash mathbf\; \backslash mathbf\; \backslash mathbf^T$ 3. The rotation matrix is simply: $\backslash mathbf\; =\; \backslash mathbf\; \backslash mathbf\; \backslash mathbf^T$ where 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wahba's problem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.