Abstract: Based on the shadowgraphy system and the calibration of camera intrinsic and extrinsic parameters, the measuring errors associated by image recognition errors are studied, and an error model is built by using Taylor series expansion. Assuming that the image recognition errors are of independent identical distribution (IID), the mathematical expressions of the first moment and the second moment are presented for the measuring errors. Furthermore, the probabilistic properties of the measuring errors are studied according to the hypothesis that the distance between the cameras and the calibration surface are equal. The symbolic analysis and the numerical validation results show that each component of the measuring error is not independent; the recognition errors act as a factor to influence the measuring error; the first moment coefficient of measuring error changes linearly with the distance from object point to calibration surface, but there exists a nonlinear relationship between the auto-covariance coefficient of measuring error and the coordinate of the object point; and both the first moment coefficient and the auto-covariance coefficient are decreased if the object point is close to camera.

Key words: ordnance science and technology, measuring error model, error analysis, camera calibration, ballistic range