基于误差传播理论的PnP问题姿态精度分析

提出了一种在辨识一组典型特征点误差关系的基础上,建立间接测量值与直接测量值之间的最有利函数关系,并根据误差传播理论综合其他特征点的误差影响,最终获得完整的方位、俯仰和倾斜角误差数学模型的PnP问题误差分步分析新方法。以P4P问题研究为例,推导得到了单目视觉测量中相关参数和变量的误差函数解析式,揭示了影响姿态测量精度的误差规律。经P4P姿态解算仿真,验证了误差数学模型的正确性,以及基于误差传播理论的误差分步方法的有效性。分析误差数学模型可以看出:在单目视觉测量参数确定的条件下,方位角测量误差与方位角值无关,与相机高度和合作标志尺寸的比值成正比,在较大范围内俯仰和倾斜角变化对方位角测量误差影响小;俯仰/倾斜角的测量误差与俯仰/倾斜角值有关,与相机高度和合作标志尺寸比值的平方成正比;方位角测量误差小于俯仰/倾斜角测量误差。给出的分析方法和误差解析数学模型对单目视觉测量系统设计有指导作用。

Attitude accuracy analysis of PnP based on error propagation theory

Based on the error relation of a group of typical characteristic points, the most favorable function relation between indirect measurement and direct measurement is established, and the error influence of other characteristic points is synthesized according to the error propagation theory. Finally, the error of PnP problem in mathematical model of azimuth, pitch and tilt angle accuracy analysis is obtained. The new method is analyzed step by step. Taking the P4P problem as an example, the analytical formulas of the error functions of the related parameters and variables in monocular vision measurement are derived, and the error rules affecting the attitude measurement accuracy are revealed. The correctness of error mathematical model and the validity of error step-by-step method based on error propagation theory are verified by the simulation of P4P attitude calculation. The error mathematical model shows that the measurement accuracy of azimuth has nothing to do with the azimuth value and has a linear relationship with the ratio of the camera height to the cooperative target size under the condition that the measurement parameters of monocular vision are determined, and the pitch/tilt angle has little influence on the measurement accuracy in a larger range. The tilt angle is related to the square of the ratio of the camera height to the cooperative target size, and the measurement accuracy of azimuth is better than that of pitch/tilt angle. The analytical method and the mathematical model of error analysis are important to the design of monocular vision measurement system.