The paper deals with a computational method for detection of the solar systemminor bodies (SSOs), whose inter-frame shifts in series of CCD-frames duringthe observation are commensurate with the errors in measuring their positions.These objects have velocities of apparent motion between CCD-frames notexceeding three RMS errors ($3\sigma$) of measurements of their positions.About 15\% of objects have a near-zero apparent motion in CCD-frames, includingthe objects beyond the Jupiter's orbit as well as the asteroids headingstraight to the Earth. The proposed method for detection of the object's near-zero apparent motionin series of CCD-frames is based on the Fisher f-criterion instead of using thetraditional decision rules that are based on the maximum likelihood criterion.We analyzed the quality indicators of detection of the object's near-zeroapparent motion applying statistical and in situ modeling techniques in termsof the conditional probability of the true detection of objects with anear-zero apparent motion. The efficiency of method being implemented as a plugin for the CollectionLight Technology (CoLiTec) software for automated asteroids and cometsdetection has been demonstrated. Among the objects discovered with this plugin,there was the sungrazing comet C/2012 S1 (ISON). Within 26 minutes of theobservation, the comet's image has been moved by three pixels in a series offour CCD-frames (the velocity of its apparent motion at the moment of discoverywas equal to 0.8 pixels per CCD-frame; the image size on the frame was aboutfive pixels). Next verification in observations of asteroids with a near-zeroapparent motion conducted with small telescopes has confirmed an efficiency ofthe method even in bad conditions (strong backlight from the full Moon). So, werecommend applying the proposed method for series of observations with four ormore frames.
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