This article proposed an iterative pose estimation for the planar object to deal with the pose ambiguity in the Perspective n Points (PnP) problem. Specifically, by utilizing the unit virtual sphere, the PnP pose estimation problem can be performed as a minimization of the error function with three independent transitional parameters, referred to as the coupling position. Then, Levenberg–Marquardt (LM) optimization algorithm is applied to acquire the coupling position of the first local minimum. Furthermore, the coupling position is represented as the two Euler angles and the vector length, which are combined with the planar points to compute the second local minimum approximation as the initialization of the second LM algorithm. Consequently, once the global coupling position in the two local minimum is decided by the lower error, the orientation and position are directly decoupled by using the singular value decomposition. It is shown that the designed pose estimation is able to achieve prescribed performance for locating and distinguishing two local minimum, and meanwhile guarantee the superior computation behavior under the pose ambiguity for the planar object. Finally, numerical simulation and physical experiment are conducted to validate the effectiveness of the proposed method, compared with the state-of-the-art PnP methods.

中文翻译：

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使用虚拟球体的平面对象的迭代姿态估计

本文提出了一种平面物体的迭代姿态估计来处理Perspective n Points中的姿态模糊(PnP) 问题。具体来说，通过利用单位虚拟球体，PnP 姿态估计问题可以作为具有三个独立过渡参数的误差函数的最小化来执行，称为耦合位置。然后，应用 Levenberg-Marquardt (LM) 优化算法来获取第一个局部最小值的耦合位置。此外，耦合位置表示为两个欧拉角和向量长度，它们与平面点结合计算第二个局部最小近似值，作为第二个LM算法的初始化。因此，一旦两个局部最小值中的全局耦合位置由较低的误差决定，则通过使用奇异值分解将方向和位置直接解耦。结果表明，所设计的位姿估计能够达到定位和区分两个局部最小值的规定性能，同时保证平面物体在位姿模糊下的优越计算行为。最后，通过数值模拟和物理实验验证了所提方法的有效性，并与最先进的 PnP 方法进行了比较。