查询词典 quaternion

After analysing the existing smooth orientation interpolation methods we proposed a smooth orientaion interpolation method based on cubic cardinal spline in quaternion space. This method possesses the following advantages: interpolation, C〓 continuity, accurate evaluation of the quaternion value at arbitrary parameter, transparent to the users, adjustable parameters for controlling the velocity of orientation change.

在分析现有的朝向光滑插值方法基础上，提出了基于四元数空间三次C样条的朝向光滑插值方法，该方法具有插值、C〓连续、任一参数处的四元数值可精确求得、对用户透明、可以用参数调节关键帧处物体朝向变化的速度等优点。

Utilizing the real representation of quaternion matrices and its characters discusses the reversibility of quaternion matrices and a account way of athwart matrix in this article.

3，利用四元数矩阵的实表示及其性质讨论了四元数矩阵的可逆性以及逆矩阵的一种计算方法

The research on the CCD sensor information is used to determinate the satellite attitude system without gyroscope .(1) Using quaternion and MRP as attitude representation , the attitude kinematics function are established . The satellite attitude dynamics function is established,that is disturbed by the first-order Markov force moment.(2) Using the quaternion as attitude representations, the attitude determination state estimator EKF and UKF are designed , numerical simulation is done .

基于CCD星敏感器的无陀螺测量卫星姿态确定系统的研究(1)针对地球同步轨道卫星，分别建立了以姿态四元数和修正罗德里格参数为卫星姿态描述参数的姿态运动方程；建立了卫星受一阶马尔柯夫干扰力矩时的卫星姿态动力学方程；(2)设计了采用姿态四元数为卫星姿态描述参数的EKF和UKF估计器，设计了分别以姿态四元数和修正罗德里格参数为卫星姿态描述参数的UKF估计器，并进行了数学仿真。

The quaternion calculation for spacecraft attitude determination is investigated in this paper,including the transformation between quaternion and the direction cosine matrix,the quaternion differential equation,the selection of time steps for integrating the quaternion equation,and the compensation methods for the noncommutativity error in high dynamic motion.

介绍了四元数计算中的相关问题，包括四元数与方向余弦阵之间的转换、四元数运动方程、求解四元数运动方程时积分步长的选取和高动态应用中非互易误差的补偿，此外还介绍了对偶四元数的发展。

The research of matrixes is continuously an important aspect of the quaternion division algebra. The purpose of this paper is to discuss the property of skew self-conjugate matrix. The definition of skew self-conjugate matrix on real quaternion division algebra is given.

四元数体上矩阵的研究是四元数代数理论中的一个重要方面，本文研究实四元数体上斜自共轭矩阵的性质，给出实四元数体上斜自共轭矩阵的定义。

The reason why quaternion is used in flight simulation of fighter aircraft and the geometric meaning of quaternion are described,according to axis system used in flight simulation of fighter aircraft in China,three problems are introduced as follows:(1) quaternion kinematic equations,(2) relationship of quaternion and coordinate transformation matrix,(3) Euler angles in terms of quaternion.

阐述了在战斗机的飞行仿真中采用四元数的原因和四元数的几何意义，并按照中国战斗机飞行仿真中采用的坐标系，介绍了三个问题：四元数运动学方程；四元数与坐标变换矩阵的关系；用四元数表示的欧拉角。

Hamilton discovered the quaternion ,to the middle period of last century,the application of the quaternion and the quaternion matrix are discovered widely in geostatics,the theory of ped-top using, strap-down inertial ,naviation, enginery and organ,robot technology and artificial satellite attitude control,and so on.

R。 Hamilton发现四元数到上世纪中叶，四元数和四元数矩阵方法在刚体动力学、陀螺使用理论、捷联惯性导航、机器与机构、机器人技术、人造卫星姿态控制等领域应用非常广泛。

Rotation matrix s representation with the unit quaternion has no singular points, so the unit quaternion-based estimation method is of more practical importance, and the algorithm in this paper does not need iteration computation compared to those unit quaternion-based method proposed by Horn(1987) and Su, et al.

单位四元数表示旋转矩阵时不存在奇异点，故基于单位四元数的运动估计方法具有更大的实用价值，而本文算法无需Horn(1987)和Su等人(1989)提出的单位四元数方法的迭代运算。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

In the last two chapters, this thesis first develops two quaternion-based color image filtering methods that are based on the quaternion rotation theory and quaternion unit transform, respectively, then analyzes the fulfillment algorithm of the QSVD (Quaternion Singular Value Decomposition) and its applications to color image processing, and expands the real number-valued PCA to quaternion-valued PCA.

在论文的最后二章，通过利用四元数旋转和色调抵消机制以及四元数单位变换来表达二个彩色像素的色调差异，提出了二个基于四元数理论的彩色图像滤波的新方法；并分析了四元数奇异值分解QSVD (Quaternion Singular Value Decomposition)的实现算法及其在彩色图像处理中的应用；同时将实数域上的主成份分析扩展到四元数域，形成了四元数版本的主成份分析QPCA (Quaternion Principal Component Analysis)。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。