Rigorous and integrated self-calibration model for a large-field-of-view camera using a star image

Abstract

This paper proposes a novel self-calibration method for a large-FoV (Field-of-View) camera using a real star image. First, based on the classic equisolid-angle projection model and polynomial distortion model, the inclination of the optical axis is thoroughly considered with respect to the image plane, and a rigorous imaging model including 8 unknown intrinsic parameters is built. Second, the basic calibration equation based on star vector observations is presented. Third, the partial derivative expressions of all 11 camera parameters for linearizing the calibration equation are deduced in detail, and an iterative solution using the least squares method is given. Furtherly, simulation experiment is designed, results of which shows the new model has a better performance than the old model. At last, three experiments were conducted at night in central China and 671 valid star images were collected. The results indicate that the new method obtains a mean magnitude of reprojection error of 0.251 pixels at a 120° FoV, which improves the calibration accuracy by 38.6% compared with the old calibration model (not considering the inclination of the optical axis). When the FoV drops below 20°, the mean magnitude of the reprojection error decreases to 0.15 pixels for both the new model and the old model. Since stars instead of manual control points are used, the new method can realize self-calibration, which might be significant for the long-duration navigation of vehicles in some unfamiliar or extreme environments, such as those of Mars or Earth’s moon.