Astronomical Calibration of a Strapdown Astroinertial Navigation System. Part II. Calibration of Mutual Attitude of Inertial and Astronomical Sensors

Astronomical calibration is defined as determination of the constant attitude of digital cameras relative to the inertial measurement unit (IMU) using ground-based star observations. The first part of [1] focuses on the calibration of relative attitude of all cameras, which provides combination of their separate measurements into the observations of one virtual camera. The second part examines the calibration of virtual camera attitude relative to the IMU. The calibration is performed on a simple test bench, which is unable to set the accurate attitude of the calibrated unit relative to the stars. Therefore, the calibrated parameters are estimated by the attitude increments over a time period between the astronomical measurements. Formulas for calculating the attitude increments from the inertial and astronomical measurements and their covariance matrices have been obtained. It has been shown that not all calibration trajectories provide unambiguous estimation of the calibrated parameters based on the attitude increments. The necessary condition for selecting the required trajectories has been formulated. The formula for finding the error covariance matrix of IMU attitude by the astronomical measurements has been received. This formula considers the star configuration observed with the virtual camera, its calibration errors described in the first part of the paper, and calibration errors in its attitude relative to the IMU obtained in the second part. The RMS error of the attitude calibration is experimentally found to be about 6 arcsec.