Abstract: To avoid the difficulty from laser spot alignment of existing laser collimation system in calibration process, a system composition is simplified, the efficiency and accuracy of calibration are improved, and the adaptability of calibration system is enhanced. A transformation matrix between calibration system and ballistic range system is presented by using the coordinates of three non-collinear points in calibration system and ballistic range system. The mean value and the variance-covariance matrix of the final measuring error are studied by an error model founded by Jacobian matrix between the measuring and various error sources.The self-covariance of measuring error is studied based on the Cauchy-Schwarz inequality and the relationship between vector and matrix norms. An firing experiment of live ammunition is performed to verify the three-point calibration method of ballistic range. The research results show that the mean vector length of final measuring error about a point in ballistic range system is equal to the mean vector length of measuring error associated with same point in the calibration system; the larger the distance and the area surrounded by three non-collinear points which links the calibration system and ballistic range system together are, the smaller the self-covariance of the final measuring error is; the self-covariance decreases when the transition coordinate origin which is defined by the three non-collinear points is close to a projected trajectory line; based on the measurement method and the error of the three-point coordinates in ballistic system, the self-covariance of measuring error are changed when the calibration system origin moves away from the ballistic range system origin; and the calibration system based on the three-point method can be build-up by general instruments, and the quality of measured data is better.

Key words: ordnance science and technology, calibration of ballistic range, ballistic range experiment, error control, error analysis