A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates

Abstract

We describe a new iteration method to estimate asteroid coordinates, which is based on the subpixel Gaussian model of a discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational space (the set of pixels potential) of the CCD frame. In this model, a kind of the coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The developed method, being more flexible in adapting to any form of the object image, has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure, which is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquardt algorithm for the minimisation of the quadratic form.Since 2010, the method was tested as the basis of our CoLiTec (Collection Light Technology) software, which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of CCD frames. As the result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON), and P/2013 V3 (Nevski)) as well as more than 1500 small Solar System bodies (including five NEOs, 21 Trojan asteroids of Jupiter, and one Centaur object) were discovered. We discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency.In 2014, the CoLiTec software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.

Development of computational method for detection of the object’s near-zero apparent motion on the series of ccd-frames

“…Комета ISON была выделена блоком обнаружения объектов с околонулевым видимым движением про-граммного комплекса CoLiTec [15,20]. В данном блоке использовался разработанный вычислительный метод обнаружения околонулевого видимого движения объ-ектов на серии ПЗС-кадров (рис.…”

“…С помощью программного комплекса CoLiTec [12,20] и внедрённого в него предложенного вычисли-тельного метода была обнаружена комета C/2012 S1 (ISON) [18] -долгопериодическая околосолнечная ко-мета, которая на момент открытия являлась объектом с околонулевым видимым движением.…”

A method of immediate detection of objects with a near-zero apparent motion in series of CCD-frames

“…In 2009, the authors of this paper developed the CoLiTec (Collection Light Technology) software for the automated detection of the solar system minor bodies in CCD-frames series 1 (see, in detail, Savanevych 1999Savanevych , 2006Savanevych et al 2012Savanevych et al , 2015aVavilova et al 2012aVavilova et al ,b, 2017Vavilova 2016;Pohorelov et al 2016). Since 2009 it has been installed at several observatories: Andrushivka Astronomical Observatory (A50, Ukraine; Ivashchenko et al 2013), ISON-NM Observatory (H15, the US; Elenin et al 2013), ISON-Kislovodsk Observatory (D00, Russia;ISON-Kislovodsk 2016), ISON-Ussuriysk Observatory (C15, Russia;Elenin et al 2014), Odessa-Mayaki (583, Ukraine;Troianskyi et al 2014), Vihorlat Observatory (Slovakia; Dubovsky et al 2017).…”

“…Such accumulation is reached by the method of the multivalued transformation of the object coordinates that is equivalent to the Hough transformation (Savanevych 2006;Savanevych et al 2012). In general, CoLiTec software allows detecting of the objects with different velocities of the apparent motion by individual plugins for fast and slow objects, and objects with the near-zero apparent motion.…”

“…CoLiTec software is widely used in a number of observatories. In total, four comets (C/2011 X1 (Elenin), P/2011 NO1 (Elenin), C/2012 S1 (ISON) and P/2013 V3 (Nevski)) and more than 1560 asteroids including 5 NEOs, 21 Trojan Jupiter asteroids and one Centaur were discovered using CoLiTec software as well as more than 700 000 positional CCD-measurements were sent to the Minor Planet Center (Ivashchenko et al 2013;Elenin et al 2013Elenin et al , 2014Savanevych et al 2015a). Our comparison of statistical characteristics of positional CCD-measurements with CoLiTec and Astrometrica 2 (Miller et al 2008;Raab 2012) software in the same set of test CCD-frames has demonstrated that the limits for reliable positional CCD-measurements with CoLiTec software are wider than those with Astrometrica one, in particular, for the area of extremely low signal-to-noise ratio (S/N; Savanevych et al 2015a).…”