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Angles-only initial orbit determination (AIOD) methods have been used to find the orbit of satellites since the beginning of the Space Race. Given the ever increasing number of objects in orbit today, the need for accurate space situational awareness (SSA) data has never been greater. Small aperture (< 0.5m) optical systems, increasingly popular in...
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... Raw images must be processed to reduce noise and increase chances of successfully detecting RSOs [16,17]. Images are processed using Gaussian filtering, threshold filtering, and intensity based centroiding [50,51]. Raw images from telescope imaging systems are typically imported as flexible image transport system (FITS) files, a format designed for scientific imaging that preserves raw image data and allows the storage of custom image metadata. ...
... The smoothed image I s (x, y) is given by the 2D convolution of the filter kernel with the image [51]: ...
... Classically the problem is solved given observations at three times because the measurement consists of two angles at each time which corresponds to the minimum number of observations to find an orbiting object's six orbital states [68]. Gooding's method of IOD will only be summarized here; for further details of the implementation of Gooding's method see references [51,57]. Gooding assumes that measurements are available at three times, and also requires a guess for the range to the satellite at each time. ...
Space is becoming increasingly congested every day and the task of accurately tracking satellites is paramount for the continued safe operation of both manned and unmanned space missions. In addition to new spacecraft launches, satellite break-up events and collisions generate large amounts of orbital debris dramatically increasing the number of orbiting objects with each such event. In order to prevent collisions and protect both life and property in orbit, accurate knowledge of the position of orbiting objects is necessary. Space Domain Awareness (SDA) used interchangeably with Space Situational Awareness (SSA), are the names given to the daunting task of tracking all orbiting objects. In addition to myriad objects in low-earth-orbit (LEO) up to Geostationary (GEO) orbit, there are a growing number of spacecraft in cislunar space expanding the task of cataloguing and tracking space objects to include the whole of the earth-moon system.
This research proposes a series of algorithms to be used in autonomous SSA for earth-orbiting and cislunar objects. The algorithms are autonomous in the sense that once a set of raw measurements (images in this case) are input to the algorithms, no human in the loop input is required to produce an orbit estimate. There are two main components to this research, an image processing and satellite detection component, and a dynamics modeling component for three-body relative motion.
For the image processing component, resident space objects, (commonly referred to as RSOs) which are satellites or orbiting debris are identified in optical images. Two methods of identifying RSOs in a set of images are presented. The first method autonomously builds a template image to match a constellation of satellites and proceeds to match RSOs across a set of images. The second method utilizes optical flow to use the image velocities of objects to differentiate between stars and RSOs. Once RSOs have been detected, measurements are generated from the detected RSO locations to estimate the orbit of the observed object. The orbit determination component includes multiple methods capable of handling both earth-orbiting and cislunar observations. The methods used include batch-least squares and unscented Kalman filtering for earth-orbiting objects. For cislunar objects, a novel application of a particle swarm optimizer (PSO) is used to estimate the observed satellite orbit. The PSO algorithm ingests a set of measurements and attempts to match a set of virtual particle measurements to the truth measurements. The PSO orbit determination method is tested using both MATLAB and Python implementations.
The second main component of this research develops a novel linear dynamics model of relative motion for satellites in cislunar space. A set of novel linear relative equations of motion are developed with a semi-analytical matrix exponential method. The motion models are tested on various cislunar orbit geometries for both the elliptical restricted three-body problem (ER3BP) and the circular restricted three-body problem (CR3BP) through MATLAB simulations. The linear solution method's accuracy is compared to the non-linear equations of relative motion and are seen to hold to meter level accuracy for deputy position for a variety of orbits and time-spans.
Two applications of the linearized motion models are then developed. The first application defines a differential corrector to compute closed relative motion trajectories in a relative three-body frame. The second application uses the exponential matrix solution for the linearized equations of relative motion to develop a method of initial relative orbit determination (IROD) for the CR3BP.
... 8,9 When imaging RSOs, there are two main approaches: (a) images are taken in an "inertial stare" mode where stars will appear as point-sources, and RSOs will appear as streaks in an image, or (b) images are taken in an "RSO-Tracking" mode where stars will all streak in the same direction and target RSOs would appear as a point-source. 10,11 Much research has focused on the detection of streaks in images for RSO detection, using methods from machine learning to polar image transformations. 10,12,13 For certain tracking situations, such as geostationary (GEO) satellites in a constellation, template matching provides an efficient and accurate method of tracking and associating RSOs in a series of images. ...
... 16,17 Images are processed using Gaussian filtering, threshold filtering, and intensity based centroiding. 11,19 First, raw images are imported as astronomical FITS files. Each image is represented as a matrix of intensities where the x, y coordinates give the pixel location, and the matrix value gives the image intensity. ...
Identifying resident space objects (RSOs) in arbitrary space imagery with little a-priori information is a challenging, yet crucial next step in space-domain awareness applications. This work proposes improvements to an existing RSO identification process for unresolved space images. The algorithm has three main phases: image processing, star elimination, and RSO association. Star elimination and RSO association use nearest neighbor association and thresholds on inertial frame-to-frame motion of observations to associate objects. Given a set of unresolved space images contiguous in time, the product of the algorithm presented is a set of measurements for orbit estimation.
... Classically the problem is solved given observations at three times because the measurement consists of two angles at each time which corresponds to the minimum number of observations to find an orbiting objects six orbital states [22]. Gooding's method of IOD will only be summarized here, for further details of the implementation of Gooding's method see references [16,26]. Gooding assumes that measurements are available at three times, and also requires a guess for the range to the satellite at each time. ...
... Plate solving uses the known positions of background stars in an image to find the inertial angular (RA, DEC) pointing of the camera. This research utilized the plate solving capabilities of a local installation of Astrometry.net [25,26]. Converting all associated RSO points to RA, DEC angular observations gives the full set of measurements for orbit determination. ...
View Video Presentation: https://doi.org/10.2514/6.2022-0528.vid This paper proposes a method of autonomous generation of template images for satellite constellation tracking. An initial template image is formed by determining the locations of several resident space objects (RSOs) in an optical image. A template image of a single RSO (i.e. point-source) is matched against the image to determine these RSO locations. The image locations of detected RSOs are then used to form an initial template image. Once an initial template is formed, subsequent frames are matched via normalized cross-correlation to find the generated template in each image. Specific RSOs are then associated across frames by their known position in the template image. In order to handle time-varying configuration of satellites the template image is periodically updated based on a threshold on correlation, or unsuccessful matching. Orbit determination via Gooding's method is then used to provide an initial orbit estimate followed by a precise orbit estimate based on a sequential Unscented Kalman Filter. Experimental results using images obtained from a ground-based telescope system are presented to showcase the algorithm's operation.
... However, robust tracking and identification methods for data obtained from small stations is a prerequisite to their data being deemed useful. 3 Common methods of resident space object (RSO) identification in images involve streak detection, or estimating the gross motion of all objects in the image. 4,5 Image template matching has also been utilized as a method of identifying and tracking RSOs in optical imagery. ...
... An asterisk represents the convolution operation, then the final smoothed image is given by Equation (5). 3 I s (x, y) = G(x, y, σ) * I(x, y) ...
In this paper, an autonomous method of satellite detection and tracking in images is implemented using optical flow. Optical flow is used to estimate the image velocities of detected objects in a series of space images. Given that most objects in an image will be stars, the overall image velocity from star motion is used to estimate the image frame-to-frame motion. Objects seen to be moving with velocity profiles distinct from the overall image velocity are then classified as potential resident space objects. The detection algorithm is exercised using both simulated star images and ground-based imagery of satellites. Finally, this algorithm will be tested and compared using a commercial and an open-source software approach to provide the reader two different options based on their need.
... However, robust tracking and identification methods for data obtained from small stations is a prerequisite to their data being deemed useful. 3 Common methods of resident space object (RSO) identification in images involve streak detection, or estimating the gross motion of all objects in the image. 4,5 Image template matching has also been utilized as a method of identifying and tracking RSOs in optical imagery. ...
... An asterisk represents the convolution operation, then the final smoothed image is given by Equation (5). 3 I s (x, y) = G(x, y, σ) * I(x, y) ...
... Regardless, if one examines the images in the inertial (RA/Dec) frame, it should be possible to distinguish RSOs from stars no matter which of these scenarios is the case. There are multiple image processing techniques that can be applied to space images to achieve the above goal [3], but in a very broad sense, the steps involved in processing each image are: 1) Initial Processing, including calibration, filtering, and noise reduction. 2) Centroiding, by which each illuminated object in an image above a noise threshold is localized in the camera frame. ...
... At their most basic level, images can be represented by a matrix of intensity counts expressed as I(x, y), where x, y are the image plane coordinates, and the value of I at the coordinates x, y gives the intensity detected at that pixel location. Fig. 2 provides an overview of the image processing algorithm outlined by the authors [3]. The first step is image calibration using Dark, Bias, and Flat frames to remove hot pixels, random thermal noise, and non-symmetric field illumination. ...
... Let " * " denote the convolution operation, and I(x, y) the original image, then the final smoothed image I s (x, y) is given by (2) [3]. ...
This work is a discussion about the application of angles only preliminary orbit determination methods for multi-observers. The methods discussed in this work are the Gauss and Gooding's methods. The application of Gauss method is easier, but it needs adjustments for the elevation and the angle between observations. On the other hand, using Gooding's method is a bit involved; however, this method works with various conditions and gives high accuracy results. Revealing these points and making a discussion about the results of these methods are the main targets of this paper. The study presents a nice perspective for angles only methods for multi-observer case.
