A computational method for detecting near-zero apparent motion of objects on the series of CCD-frames using the XY-wise and coordinate-wise decision rules is developed. The method is based on checking the statistical significance of the factor of speed of the object apparent motion on the studied series of measurements using the Student's t-test for coordinate-wise decision rules and F-test for XY-wise decision rules. This is the main feature of the developed computational method compared with the conventional decision rules based on the maximum likelihood criterion. The developed computational method for detecting near-zero apparent motion of the objects was tried and tested, and embedded in the block of inter-frame processing of the CoLiTec software package for the operational automated detection of new and tracking of the known asteroids, comets and faint celestial bodies. Using the CoLiTec software package and the proposed embedded computational method, the comet C/2012 S1 (ISON) — long-period sungrazing comet was discovered, which at the time of discovery was the object with near zero apparent motion.

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

The CoLiTec software for the automated search for small celestial objects of the solar system on a series of CCD frames has been developed within the Ukrainian virtual observatory project. Four comets and more than a thousand asteroids were discovered using the software. It was also used to send approximately 700000 positional CCD measurements to the Minor Planet Center. In this paper, accuracy factors of positional CCD measurements using the CoLiTec software are analyzed according to data from the Minor Planet Center. The comparative analysis of these factors according to the results of the processing of the same frames using CoLiTec and Astrometrica software is also conducted. In the case of low signal to noise ratios, the standard deviation of positional CCD measurements using the Astrometrica software is 30–50% greater than that of the CoLiTec software.

Comparative analysis of the positional accuracy of CCD measurements of small bodies in the solar system software CoLiTec and Astrometrica

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 observation al 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-Marquar dt 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.

/pdf/a-new-method-based-on-the-subpixel-gaussian-model-for-48ep82pzmp.pdf

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

In this paper we presented the new algorithm for astrometric reduction of the images received from modern large telescopes with very wide field of view. This algorithm is based on the iterative using of the method of ordinary least squares (OLS) and statistical Student t-criterion. The paper contains information about selecting the appropriate reduction model and system of conditional equations for determination of the reduction model parameters with the aim to solve it using the OLS method. The proposed algorithm also provides the automatic selection of the most probabilistic reduction model. At the first iteration the fifth degree polynomial is used, which provides 21 constant plates. The reduction error from the each iteration is used in the next iteration to eliminate reference objects whose residuals more than three sigma. In the developed algorithm the statistical Student t-criterion of reliability is applied after several iterations of getting rid of the noisy objects. This approach allows us to eliminate almost all systematic errors that are caused by imperfections of the optical system of modern large telescopes. The developed software based on the proposed algorithm was applied to perform the astrometric reduction of all measured positions of objects on the digitized photographic plates of SuperCOSMOS data. The research results showed that the new proposed algorithm allows performing the reduction into the system of reference catalogue with the highest accuracy level.

Astrometric Reduction of the Wide-Field Images

In this paper we presented the results of cloud computing and analysis of orbital parameters of the satellite fragments that formed by first India anti-satellite (ASAT) missile against a "live" Microsat-R satellite launched by them on January 24, 2019. Based on the cloud computing we calculated the orbital parameters and distribution of impulse values obtained by Microsat-R fragments that were formed after the impact of ASAT missile and tracked by NASA. All results in this paper and detailed analysis of this event are based on the orbital data taken in form of NORAD two-line element (TLE) dataset from space-track.org and by own calculation of the CoLiTec group in EOS Data Analytics using own cloud server. The test parameters were chosen with extreme caution to minimize the hazard of debris after the impact. However, the results of our research showed the significant differences from expected "head-on collision" of rocket with Microsat-R satellite.

Cloud Computing Analysis of Indian ASAT Test on March 27, 2019

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.

N. Sokovikova

Papers

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

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

Automated software for CCD-image processing and detection of small Solar System bodies