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。

Based on the error relation of a group of typical characteristic points, the most favorable function relation between indirect measurement and direct measurement was established, and the error influence of other characteristic points was synthesized according to the error propagation theory. Finally, a new method of error step-by-step analysis of the PNP problem with complete azimuth, pitch, and tilt angle error analysis model was proposed. Taking the P4P problem as an example, the analytical formulas of the error functions of the related parameters and variables in monocular vision measurement were derived, and the error rules affecting the attitude measurement were revealed. The correctness of the error mathematical model and the validity of the step-by-step error analysis method based on error propagation theory were verified by the simulation of P4P attitude calculation. Under the determined measurement parameters of monocular vision condition, the error analysis model shows that the azimuth angle measurement error is independent of the azimuth angle value, and the error is proportional to the ratio of camera height to cooperative mark size. The pitch/tilt angle has little effect on the measurement error in a larger range. The pitch/tilt angle measurement error is related to pitch/tilt angle value, and the error is proportional to the square of the ratio of camera height to cooperative mark size. The measurement error of the azimuth angle is less than that of the pitch/tilt angle. The analysis method and error function analytical formulas can provide guidance for the design of a monocular vision measurement system.