  The paper deals with a computational method for detection of the solar system
minor bodies (SSOs), whose inter-frame shifts in series of CCD-frames during
the observation are commensurate with the errors in measuring their positions.
These objects have velocities of apparent motion between CCD-frames not
exceeding three RMS errors ($3\sigma$) of measurements of their positions.
About 15\% of objects have a near-zero apparent motion in CCD-frames, including
the objects beyond the Jupiter's orbit as well as the asteroids heading
straight to the Earth.
  The proposed method for detection of the object's near-zero apparent motion
in series of CCD-frames is based on the Fisher f-criterion instead of using the
traditional decision rules that are based on the maximum likelihood criterion.
We analyzed the quality indicators of detection of the object's near-zero
apparent motion applying statistical and in situ modeling techniques in terms
of the conditional probability of the true detection of objects with a
near-zero apparent motion.
  The efficiency of method being implemented as a plugin for the Collection
Light Technology (CoLiTec) software for automated asteroids and comets
detection has been demonstrated. Among the objects discovered with this plugin,
there was the sungrazing comet C/2012 S1 (ISON). Within 26 minutes of the
observation, the comet's image has been moved by three pixels in a series of
four CCD-frames (the velocity of its apparent motion at the moment of discovery
was equal to 0.8 pixels per CCD-frame; the image size on the frame was about
five pixels). Next verification in observations of asteroids with a near-zero
apparent motion conducted with small telescopes has confirmed an efficiency of
the method even in bad conditions (strong backlight from the full Moon). So, we
recommend applying the proposed method for series of observations with four or
more frames.
