绝对方位问题封闭形式最优估计的快速算法

提出一种快速的绝对方位问题算法,通过最小二乘法构造目标函数,对目标函数中的旋转矩阵和平移向量进行分离,利用矩阵的Fobenius范数、行列式以及伴随矩阵等构造旋转矩阵和平移向量封闭形式的最优估计。这种算法具有较高的计算精度和抗噪声性能,并且避免了目前常用算法中的奇异值分解运算,从而提高了计算速度。数学实验结果表明,在计算精度与抗噪声能力上与目前性能最优的Umeyama算法相当,同时计算速度较之有大幅提升,尤其适用于对实时性要求较高的领域。

Fast and Close-Form Optimal Estimation of Absolute Orientation Problem

A fast algorithm to solve the absolate orientation problem is proposed. The algorithm first formulates objective function by least square method. Then it decouples the rotation and translation. Finally it uses the Fobenius norm, determinant and adjoint matrix to formulate the close-form optimal estimation of the rotation and translation. The proposed algorithm has high accuracy and noise-resistance, especially high computation speed because of the absence of singular value decomposition, which is commonly used in current employed algorithms. Results of numerical experiment show that, compared with Umeyama algorithm, one of the best absolute orientation algorithms, the proposed algorithm performs the same level of accuracy and noise-resistance and extremely faster speed, and it is suitable for the areas which require high real-time performance.