During the last two centuries many methods have been proposed to solve the angles-only initial orbit determination problem. As this problem continues to be relevant as an initial estimate is needed before high accuracy orbit determination is accomplished, it is important to perform direct comparisons among the popular methods with the aim of determining which methods are the most suitable (accuracy, robustness) for the most important orbit determination scenarios. The methods tested in this analysis were the Laplace method, the Gauss method (suing the Gibbs and Herrick-Gibbs methods to supplement), the Double R method, and the Gooding method. These were tested on a variety of scenarios and popular orbits. A number of methods for quantifying the error have been proposed previously. Unfortunately, many of these methods can overwhelm the analyst with data. A new method is used here that has been shown in previous research by the author. The orbit error is here quantified by two new general orbit error parameters identifying the capability to capture the orbit shape and the orbit orientation. The study concludes that for nearly all but a few cases, the Gooding method best estimates the orbit, except in the case for the polar orbit for which it depends on the observation interval whether one uses the Gooding method or the Double R method. All the methods were found to be robust with respect to noise and the initial guess (if required by the method). All the methods other than the Laplace method suffered no adverse effects when additional observation sites were used and when the observation intervals were unequal. Lastly for the case when the observer is in space, it was found that typically the Gooding method performed the best if a good estimate is known for the range, otherwise the Laplace method is generally best.

This paper is predicated on determining the effectiveness of angles-only initial orbit determination (IOD) methods when limited observational data is available for low-Earth orbit (LEO) rocket body debris. The analysis will be conducted with data obtained from Lockheed Martin Space’s Space Object Tracking (SpOT) facility, focusing on their observational data from 2018 that contains tracking of rocket body debris for less than one minute per overhead pass. After the IOD accuracies are better understood, a feasibility study will follow that investigates the possibility of cataloguing LEO orbital debris from a single optical observation facility with similar observational capabilities as that of the SpOT facility. The IOD accuracy analysis will investigate nine different rocket bodies, with a total of 50 orbital passes of data included in the research. Three main IOD approaches will be tested for each data set to determine the best method in achieving high levels of IOD accuracy: a traditional three-point method, an iterative method, and an assumed-circular orbit method. Application of the iterative approach results in increased accuracy for the resultant initial orbit determination as compared to the three-point IOD method, and an assumed-circular orbit assumption allows for a further increase in accuracy, especially for observed objects in near-circular orbits. The feasibility of cataloguing debris from a singular optical facility shows promise, as subsequent target acquisition after an object’s initial observation is determined to be achievable under the correct circumstances. By choosing a correct telescope pointing angle based on the IOD results from one pass of data, an observed rocket body debris object would pass through the field of view of SpOT’s spotter scope (0.7-degrees) during its next overhead pass for two different test cases. An increase field of view would increase both the likelihood of acquiring the target object and the amount of time the object is visible by the telescope.

A perfect duality exists between the problem of space-based orbit determination from line-of-sight measurements and the problem of designing an interplanetary autonomous navigation system. Mathematically, these two problems are equivalent. Any method solving the first problem can be used to solve the second one and, vice versa. While the first problem estimates the observed unknown object orbit using the known observer orbit, the second problem does exactly the opposite (e.g. the spacecraft observes a known visible planet). However, in an interplanetary navigation problem, in addition to the measurement noise, the following "perturbations" must be considered: 1) light-time effect due to the finite speed of light and large distances between the observer and planets, and 2) light aberration including special relativistic effect. These two effects require corrections of the initial orbit estimation problems. Because of the duality problem of space-based orbit determination, several new techniques of angles-only Initial Orbit Determination (IOD) are here developed which are capable of using multiple observations and provide higher orbit estimation accuracy and also they are not suffering from some of the limitations associated with the classical and some newly developed methods of initial orbit determination. Using multiple observations make these techniques suitable for the coplanar orbit determination problems which are the case for the spacecraft navigation using visible planets as the solar system planets are all almost coplanar. Four new IOD techniques were developed and Laplace method was modified. For the autonomous navigation purpose, Extended Kalman Filter (EKF) is employed. The output of the IOD algorithm is then used as the initial condition to extended Kalman filter. The two "perturbations" caused by light-time effect and stellar aberration including special relativistic effect also need to be taken into consideration and corrections should be implemented into the extended Kalman filter scheme for the autonomous spacecraft navigation problem.

The following thesis regards the use of small aperture telescopes for space domain awareness efforts. The rapidly populating space domain was motivation for the development of a new operation scheme to conduct space domain awareness feasibility studies using small telescopes. Two 14-inch Schmidt-Cassegrain Telescopes at the California Polytechnic State University and the Air Force Research Lab in Kirtland AFB, NM, in conjunction with a dedicated CCD camera and a commercial DSLR camera, were utilized to conduct optical observations on satellites in Earth orbit. Satellites were imaged during August 2019, and from January 2020 to March 2020, resulting in the collection of 77 valid images of 16 unique satellites. These images were used to obtain celestial spherical coordinates, which were used in Gauss and Double-R angles-only initial orbit determination methods. Initial orbit determination methods successfully produced valid results, reaffirming the feasibility of using small aperture telescopes for such methods. These orbit determinations were used to propagate orbit states forward in time to determine the feasibility of future imaging of the targets with the same apparatus. Propagation results demonstrated that initial orbit determinations rapidly decayed in accuracy over distant times and are most accurate for immediate satellite passes. In addition, an attempt to combine multiple initial orbit determinations using Lambert’s problem solutions was made. Combination of these multiple initial orbit determinations resulted in either no orbit state accuracy improvement compared to individual initial orbit determinations, or a decrease in accuracy compared to these methods. Ultimately, efforts demonstrated that small telescope usage is feasible for orbit determination operations, however there may be a need for hardware and operational revisions to improve the ability of the apparatus.

The expansion of space activities has led to an increase in congestion. With this increase, there has been a growing emphasis on the importance of space situational awareness. Without it, the space environment can become hazardous, with increasing threats of collision and debris generation. As the utilization of space continues to grow, effective methods for tracking objects to maintain situational awareness must also be considered. One approach to tracking objects in space involves a series of steps, including optical observations and orbit estimations using initial orbit determination methods, followed by additional observations and continuous tracking. However, a challenge with this tracking method is the low quality and quantity of observational data, which can impact the accuracy achieved from these methods. This thesis will study two new and two traditional methods of initial orbit determination, analyzing improvements in accuracy with limited data for each method. Additionally, the impact of observation elevation will be analyzed to assess its effects on the quality of data, and how this, along with a limited amount of data, can affect the overall initial orbit determination accuracy.

The probability of satellite collisions and disintegrations cluttering the near-Earth orbital environmentis ever-growing. This is especially true for the congested Low Earth Orbit (LEO) regime; once a critical density of objects is reached, a collisional cascading is projected to generate runaway growth of theorbital population. Comprehensive tracking of Resident Space Objects (RSO) is a requisite precursor to conjunction forecasting and avoidance; a strategy for active debris mitigation. Conducted at Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) Andøya Space, this work presents a means through which a passive optical observation station can be established using only an off-the shelf Canon EOS-1300 camera for uncued detection. A custom processing pipelinewas developed to perform data reduction on the retrieved images and initialisation of the object orbit was accomplished via implementations of the classic Initial Orbit Determination (IOD) algorithms of Laplace and Gauss. RSO identification was performed by reconstruction of the overpass and comparison against objects in a Two Line Elements (TLE) database. The complete script initiates the tracking process, and requires no inputs other than the image, and the geodetic coordinates of the ground station. The processing pipeline was demonstrated to perform robustly on the collected images and the algorithms were tested for different orbital regimes using precision angular data extracted from literature, with the retrieved results corresponding closely to the available reference values for all orbital regimes. Their performance as predictors of satellite position was compared for a variety of test cases, withthe Gauss algorithm producing more consistent results. However, orbits could not be initialised from the images, due to insufficient angular and timing precision. Various adaptations and extensions are suggested in order to achieve the requisite accuracy in the optical data and improve the data collection.

This thesis investigates the use of the Swedish Allsky Meteor Network (SAMN) for observing, identifying, and determining the orbits of satellites. The overall goal of this project is to determine the feasibility of using such a network for Space Situational Awareness (SSA) purposes, which requires identification and monitoring of objects in orbit. This thesis is a collaboration with the Swedish Defense Research Agency (FOI) to support their efforts in SSA. Within the frame of this project, the author developed software that can take data of observations of an object collected from the all-sky cameras of SAMN and do an Initial Orbit Determination (IOD) of the object. An algorithm that improves the results of the IOD was developed and integrated into the software. The software can also identify the object if it is in a database that the program has access to or, if it could not be identified, make an approximate prediction of when and where the object will be visible again the next time it flies over. A program that analyses the stability of the results of the IOD was also developed. This measures the spread in results of the IOD when a small amount of artificial noise is added to one or more of the observed coordinates in the sky. It was found that using multiple cameras at different locations greatly improves the stability of the solutions. Gauss' method was used for doing the IODs. The advantages and disadvantages of using this method are discussed, and ultimately other methods, such as the Gooding method or Double R iteration, are recommended for future works. This is mostly because Gauss' method has a singularity when all three lines of sight from observer to object lie in the same plane, which makes the results unreliable. The software was tested on a number of observations, both synthetic and real, and the results were compared against known data from public databases. It was found that these techniques can, with some changes, be used for doing IOD and satellite identification, but that doing very accurate position determination required for full orbit determination is not feasible. / Detta examensarbete undersöker möjligheterna att använda ett svenskt nätverk av allskykameror kallat SAMN (Swedish Allsky Meteor Network) för att observera, identifiera och banbestämma satelliter. Det övergripande målet med detta projekt är att bestämma hur användbart ett sådant nätverk skulle vara för att skapa en rymdlägesbild, vilken i sin tur kräver bevakning och identifikation av objekt som ligger i omloppsbana. Detta examensarbete är ett samarbete mellan Uppsala Universitet och FOI (Totalförsvarets Forskningsinstitut). Inom ramen för detta projekt har författaren utvecklat mjukvara som kan ta data från observationer av objekt utförda av SAMN och göra initiala banbestämningar av objekten. En algoritm som förbättrar resultaten av den initiala banbestämningen utvecklades och integrerades i programmen. Programmen kan också identifiera satelliter om de finns med i en databas som programmet har tillgång till eller förutsäga objektets nästa passage över observatören om det inte kunde identifieras. Ett annat program som analyserar känsligheten av resultaten av den initiala banbestämningen utvecklades också. Detta program mäter spridningen i resultat som orsakas av små störningar i de observerade koordinaterna på himlen. Det framkom att stabiliteten av resultaten kan förbättras avsevärt genom att använda flera observatörer på olika orter. I detta projekt användes Gauss metod för att göra banbestämningarna. Metodens för- och nackdelar diskuteras och i slutänden rekommenderas istället andra metoder, som Goodings metod eller Dubbel R-iteration, för framtida arbeten. Detta beror mest på att Gauss metod innehåller en singularitet när alla siktlinjer från observatören till objektet ligger i samma plan som varandra vilket gör resultaten opålitliga i de fallen. Programmen testkördes på ett antal olika observationer, både artificiella och verkliga, och resultaten jämfördes med kända positioner. Slutsatsen av arbetet är att de undersökta teknikerna kan, med vissa modifikationer, användas för att göra initiala banbestämningar och satellitidentifikationer, men att göra de väldigt precisa positionsbestämningarna som krävs för fullständig banbestämning är inte genomförbart.

In this report I present a feasibility study of using open astronomical data to make Initial Orbit Determination (IOD) for Resident Space Objects (RSO) appearing as streaks in telescope images. The purpose is to contribute to Space Surveillance and Tracking (SST) for maintaining Space Situation Awareness (SSA). Data from different wide-field survey telescopes were considered but due to availability constraints only mask images from Zwicky Transient Facility (ZTF) survey were chosen for the analysis. An algorithm was developed to detect streaks in the mask images and match them to RSO known to be within the Field of View (FoV) at the observation time. Further, the IOD was made with angles-only Laplace’s method and the state vectors calculated for the streaks from the IOD were compared to those from the TLE for the matching RSO. The algorithm was tested with 6 different image fields acquired between the 14th to the 16th December 2019, of which 4 are characterised as non-crowded and 2 as crowded. The streak finding algorithm has a better precision and sensitivity for the non-crowded field, with an F1-score of 0.65, but is worse for the crowded fields with an F1-score of 0.035. In the non-crowded fields 95% of all streak and object matches are true matches to unique RSO, while for the crowded field only 10% are true matches. It was found that the 1''/pixel resolution in the images is too low for doing an IOD with Laplace’s method, despite how well the streak finding algorithm performs. However, with some improvements, the method is suitable as a cost effective way to verify known RSO in catalogues. / I den här rapporten presenterar jag en studie om att använda öppen astronomiska data för att göra initial banbestämning för artificiella rymdobjekt avbildade som streck i teleskopbilder. Syftet är att tillhandahålla information för att upprätthålla en god rymdlägesbild. Data från olika kartläggnings teleskop övervägdes men på grund av begränsningar i tillgänglighet valdes endast mask-bilderna från Zwicky Transient Facility för analysen. En algoritm utvecklades för att upptäcka streck i mask-bilderna och matcha dem med kända objekt i bildens synfält vid observationstillfället. Vidare gjordes den initiala banbestämningen med Laplaces metod, som använder vinkelkoordinaterna för streckens position vid observationen. Tillståndsvektorerna för strecken och de matchade objekten jämfördes, de beräknades från den initiala banbestämningen respektive objektets TLE. Algoritmen testades med 6 olika bildfält från observationsdatum mellan den 14:e till den 16:e december 2019, av dessa karakteriseras 4 som glesa och 2 som fyllda. Algoritmen för streck detektering har bättre precision och känslighet för de glesa fälten, med ett F1-värde på 0.65, men sämre för de fulla fälten med ett F1-värde på 0.035. I de glesa fälten är 95% av alla streck- och objektmatchningar korrekta matchningar med unika objekt, medan för det fulla fälten är endast 10% korrekta matchningar. Det visar sig att upplösningen på 1''/pixel i bilderna är för låg för att göra en initial banbestämning med Laplaces metod, oavsett hur bra algoritmen för streck detektering presterar. Genom att göra vissa förbättringar i algoritmen är metoden lämplig för att, på ett kostnadseffektivt sätt, verifiera kända objekt i kataloger.