作　　者： ; ; ;

机构地区： 同济大学中德学院

出　　处： 《计算机工程与应用》 2008年第35期25-27,共3页

摘　　要： 计算机图形学中物体三维旋转通常用矩阵、欧拉角、四元数表示,用矩阵及欧拉角存在计算繁琐、旋转不均匀性及平衡环锁定等局限,四元数可以避免这些局限,并且几何意义明确,计算简单。研究用四元数表示物体的姿态,在四元数基本运算法则基础上提出并证明了"基于四元数的多个旋转运动合成规则",然后将此规则为依据,推导出一种用来计算姿态非线性状态方程系数的方法,对非线性状态转移函数进行线性化,并且研究了测量方程函数的确定及线性化,借助扩展Kalman滤波实现了对姿态的跟踪。最后给出一滤波跟踪实例,验证此种方法是有效的。 The matrix representation,Euler angles and quaternions are commonly used in computer graphics.There are weaknesses by matrix representation and Euler angles,such as high computational cost,gimbal lock and so on.Quaternions are well-suited for the representation of rotations as they are free from singularities, numerically well-conditioned.In this paper,pose representation by quatemions are researched.With the basic quaternion algebra,the ＂quaternion based rotations combination theorem＂ is introduced and proved theoretically.On the basis of this theorem,a method for compute of pose nonliear state transfer function and its linearization is purposed.Then,the computing of the measurement function and the linearization is studied.With the Extended Kalman Filter （EKF）,the pose is tracked and estimated.Finally,the experiment results show this quaternion-based algorithm for pose nonliear tracking is effective.

关 键 词： 四元数 姿态跟踪 非线性 滤波 旋转运动合成

领　　域： [自动化与计算机技术] [自动化与计算机技术]