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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 Triad method ： ウィキペディア英語版 Triad method Triad is one of the earliest and simplest solutions to the spacecraft attitude determination problem, due to Harold Black. Black played a key role in the development of the guidance, navigation and control of the U.S. Navy's Transit satellite system at Johns Hopkins Applied Physics Laboratories. As evident from the literature, TRIAD represents the state of practice in spacecraft attitude determination, well before the advent of the Wahba's problem and its several optimal solutions. Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD algorithm obtains the direction cosine matrix relating both frames. Covariance analysis for Black's classical solution was subsequently provided by Markley. ==Summary== We consider the linearly independent reference vectors $\backslash vec\_$ and $\backslash vec\_2$. Let $\backslash vec\_1,\; \backslash vec\_2$ be the corresponding measured directions of the reference unit vectors as resolved in a body fixed frame of reference. Then they are related by the equations, for $i\; =\; 1,2$, where $A$ is a rotation matrix (sometimes also known as a proper orthogonal matrix, i.e., $A^A\; =\; I,\; det(A)\; =\; +1$). $A$ transforms vectors in the body fixed frame into the frame of the reference vectors. Among other properties, rotational matrices preserve the length of the vector they operate on. Note that the direction cosine matrix $A$ also transforms the cross product vector, written as, Triad proposes an estimate of the direction cosine matrix $A$ as a solution to the linear system equations given by where $\backslash vdots$ have been used to separate different column vectors. The solution presented above works well in the noise-free case. However, in practice, $\backslash vec\_1,\; \backslash vec\_2$ are noisy and the orthogonality condition of the attitude matrix (or the direction cosine matrix) is not preserved by the above procedure. Triad incorporates the following elegant procedure to redress this problem. To this end, we define unit vectors and to be used in place of the first two columns of (). Their cross product is used as the third column in the linear system of equations obtaining a proper orthogonal matrix for the spacecraft attitude given by While the normalizations of Equations () - () are not necessary, they have been carried out to achieve a computational advantage in solving the linear system of equations in (). Thus an estimate of the spacecraft attitude is given by the proper orthogonal matrix as Note that computational efficiency has been achieved in this procedure by replacing the matrix inverse with a transpose. Equation() shows that the matrices used for computing attitude are each composed of an orthogonal triad of basis vectors. "TRIAD" derives its name from this observation. 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「Triad method」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.