Astronomical Calibration of a Strapdown Astroinertial Navigation System: Part 1. Calibration of Mutual Attitude of Digital Cameras

Astronomical calibration refers to determination of the constant mutual attitude of digital cameras and the inertial measurement unit using ground-based star observations. The first part of this paper considers calibrating the attitude of all cameras relative to the selected one. The calibrated vector contains the useful parameters (three attitude angles of each camera relative to the selected one) and interfering parameters (three attitude angles of the selected camera in the Earth-fixed frame at the time of shooting each frame). The system of nonlinear equations for determining the calibrated vector is based on the differences in the coordinates of images of the identified stars, which are calculated in the image planes of different cameras for each frame and then combined into a common residual vector. Atmospheric refraction and velocity aberration of light are considered when projecting the identified stars from the star catalog onto the image plane. Before solving the system of equations, intrinsic parameters of each camera are determined. Calibrating the relative attitude of real cameras provides a virtual camera with an extended field of view, which significantly reduces the error in star-based attitude determination. A virtual camera error model is provided that takes into account the errors in astronomical calibration. The results from experimental verification show that the error in astronomical calibration of the cameras’ relative attitude does not exceed 2 arcsec for each useful parameter.