STAR CENTROID ON THE F-RADIUS SPHERE USING VON MISES-FISHER PROBABILITY DISTRIBUTION

This paper proposes two methods to perform star centroid particularly suitable when using wide field-of-view star trackers with small focal lengths, such as micro and nano star trackers. These sensor cameras are those where the physical dimensions of the imager (CCD or CMOS) and PSF (point spread function) are large in comparison to the system focal length. The proposed methods avoid the gnomonic distortion affecting projections of observed data into a planar imager by working on a fictitious spherical imager, the f-radius sphere. The gray tones and areas mapping between imager pixels and f-radius sphere pixels are derived for both, continuous and discrete (real) imagers. The first method is an extension of the center of mass method to the f-radius sphere, whereas the second method performs an iterative nonlinear least-squares best fit to the observed data, by considering the von Mises-Fisher probability distribution from directional dispersion statistics. Methodologies to perform Montecarlo numerical tests are proposed to validate these methods and compare them to the classical 2D center of mass method.

STAR CENTROID ON THE F-RADIUS SPHERE USING VON MISES-FISHER PROBABILITY DISTRIBUTION Conference Paper