Oleksandr Briukhovetskyi

Active space debris removal operations require a priori knowledge of the target objects’ rotation parameters, i.e., information on their rotation speed and current orientation in space. This can be achieved through appropriate observations designed to determine these parameters. Recording and subsequent analysis of light curves is the most common method for monitoring space objects’ rotation using optical means. This paper examines the results of long-term photometric observations of a large space debris object — the third stage of the SL-14 rocket (international COSPAR number 1987-074G, USSTRATCOM ID 18340). It shows how this resident space object’s (RSO) rotation speed around its center of mass repeatedly changed between 2006 and 2025. To understand the cause of this behavior of RSO 18340, it is necessary to study the relationship between its different rotation speed states and the corresponding orientation of its rotation axis in inertial space. In paper, we consider the observed light curves of RSO 18340, recorded in 2024 at different observatories, analyze their structure and identify similar photometric patterns in different light curves. These photometric patterns are used to determine the spatial direction of the object’s rotation axis in two short (1–3 days) time intervals in late February – early March 2024. As a result of this analysis of the light curves, four estimates of the average direction of the rotation axis and its evolution over a two-week interval were obtained. Using two light curves obtained during flybys over different observing points on February 27, 2024, we obtained the current direction of the rotation axis in the inertial coordinate system: RA = 10°, Decl. = -66°. And based on six light curves obtained on March 9, 10 and 11, 2024, the following average coordinates were determined: RA = 06°, Decl. = -39°. We estimate the internal error of these results to be ±(5–10)°. Based on these results, we hypothesize that there are no rapid shifts in the rotation axis of RSO 18340.

The astronomical images are made by cameras with the charge-coupled device (CCD). They can be received from the different sources, like servers, clusters, predefined series, archives or “live” (online) data streams. The astronomical images processing is focused on but not limited to the following tasks: data mining, knowledge discovery, big astronomical data processing, filtering, background alignment, brightness equalization, segmentation, classification, image recognition, object's image detection, object's astrometry and photometry, moving object detection, parameters determination of the object's image and apparent motion, reference objects selection and others. The modern Lemur software of the Collection Light Technology (CoLiTec) project (https://colitec.space) was developed using the described above technologies and approaches. The Lemur software is designed to perform a sequence of the following main steps: pre-processing (astronomical information collection -> worst data rejection -> useful data extraction -> data mining -> classification -> background alignment -> brightness equalization), image processing (segmentation -> typical form analysis -> recognition patterns applying -> detection of the object's image -> astrometry -> photometry -> objects identification -> tracks detection), knowledge discovery (Solar System objects or artificial satellites to be discovered, tracks parameters for the investigation, light curves of the variable stars, scientific reports in the international formats). The paper describes the modern features for the astronomical image processing implemented in the Lemur software. It has assisted in making over 1700 discoveries of asteroids, including 5 NEOs, 21 Trojan asteroids of Jupiter, 1 Centaur. In total it has been used in about 800 000 observations, during which five comets were discovered. All such observations and discoveries have official observational circulares from the Minor Planet Center (MPC) of the International Astronomical Union (IAU).

Violating the observation conditions for the investigated objects leads to the formation of diverse typical forms of objects throughout the frame in the series. As a consequence, determining the exact position of the object on the frame becomes difficult. To this end, a method was devised to determine the position of an object using the typical form of its image on a series of frames. This method is based on the formation of a typical form of a digital image of an object based on data from all frames of the series. This makes it possible to take into account the peculiarities of the very formation of the digital image of an object on each frame of the original series. Based on this, a more accurate assessment of the initial approximation of the parameters of all Gaussians of the object's image is performed. Adapting the method specifically for the typical form allows for a more accurate assessment of the positional parameters (coordinates) of the object in comparison with the analytically set profile. The estimation of the position of an object was obtained using the method of least squares. After that, minimization was performed using the Levenberg-Marquardt algorithm. Also, the use of the method makes it possible to improve identification with reference objects and reduce the number of false detections. The study showed a reduction in the standard deviation of frame identification errors by 7–10 times when using a typical digital image shape. The method devised for determining the position of an object using the typical form of its image was tested in practice within the framework of the CoLiTec project. It was implemented in the intraframe processing unit of the Lemur software to automatically detect new objects and track known ones. Owing to the use of Lemur software and the proposed computational method implemented in it, more than 700,000 measurements of various objects under study were successfully processed and identified

The appearance of "blurred" digital images is a consequence of the violation of the immobility of the camera during the shooting of the objects under study. To this end, a procedure was devised for matched filtering of the blurred digital image of the object using its typical image form in a series of frames. This procedure is based on the automated formation of a typical form of a digital image, as well as on the choice of special parameters for the transfer function of the matched filter. Adapting the procedure specifically to the typical form makes it possible to perform a more accurate assessment of the required parameters of the blurred digital image compared to the analytically set profile. The formation of a typical form makes it possible to take into account the features of the very formation of the blurred image on each frame of the original series. Based on this, a more accurate assessment of the initial approximation of the parameters of all Gaussians of the object image is performed. In practice, matched filtering makes it possible to highlight blurred images of objects against the background of substrate noise. Also, using the matched filtering procedure makes it possible to improve the segmentation of images of reference objects and reduce the number of false detections. The devised procedure for the matched filtering of a blurred digital image using its typical form has been tested in practice as part of the research in the framework of the CoLiTec project. It was implemented in the intraframe processing unit of the Lemur software for the automated detection of new and tracking of known objects. Owing to the use of Lemur software and the proposed computational procedure introduced into it, more than 700,000 measurements of various objects under study were successfully processed and identified

A computational method for the automated formation of a typical form of a digital image of the investigated objects on a series of digital frames has been developed. Due to the imperfection of the mounting of digital cameras, as well as their automated mounts, their immobility at shooting during exposure time can be disturbed, which leads to the formation of "blurred" images of objects of various forms. Due to such inaccuracies in the tracking of objects on digital frames, even in one series, the typical form of the image of objects can vary from frame to frame. This fact of the difference in the standard form significantly complicates the execution of various image processing tasks. In order to simplify the evaluation of the image parameters of objects in a series of digital frames, it has been proposed to use a typical image on a digital frame corresponding to the average image of objects as a model of object images. In this case, the appearance of the image of the object, its form, the distribution of brightness in the image will be determined only by the typical image. This paper proposes a computational method for the automated formation and evaluation of the typical form of the image of an object in a digital frame based on the initial data – the actual given digital frame. This computational method is based on the selection of single images of objects and the formation of their rectangular area. Next, the offset is evaluated, and the selected single images of objects are normalized to calculate the typical form of the object image. Using the method makes it possible to highlight objects against the background of noise and reduce the number of false detections. It is recommended to apply the method only in the case when the frames have defects and "blurs" during the shooting, otherwise there will be unreasonable additional computational costs. The developed computational method was successfully tested in practice within the framework of the CoLiTec project and implemented in the intraframe processing unit of the Lemur software.

A computational method for matched filtration with analytical profile of the blurred digital image of the investigated objects on digital frames has been developed. Such «blurred» objects can be the result of an involuntary shift of a fixed camera, an incorrect choice of the mode of guiding the telescope (diurnal or object tracking) or a failure of the diurnal tracking. This computational method is based on the analytical selection of the typical form of the object’s image, as well as on the choice of special parameters for the transfer function of the matched filter for the blurred digital image, which makes it possible to evaluate the required parameters of the blurred digital image. In addition, determining the number of Gaussians of the object’s image makes it possible to perform the most accurate assessment of the initial approximation of the parameters of their shape. Thus, matched filtration makes it possible to highlight the investigated objects with a blurred image of a typical shape against the background of substrate noise. Using the computational method of matched filtration makes it possible to improve the segmentation of images of reference objects on the frame and reduce the number of false detections. The developed computational method for matched filtration with analytical profile of the blurred digital image of the investigated objects on the frames was tested in practice as part of the research of the CoLiTec project. It was implemented in the intraframe processing unit of the Lemur software for the operational automated detection of new and observation of known objects with a weak brightness. Owing to the Lemur software using and the proposed computational method introduced into it, more than 500,000 measurements of the various investigated objects were successfully processed and identified.