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.

An increasing number of GPS applications require a high level of accuracy. To reduce the error contributed by the GPS ephemerides, an accurate modeling of the forces acting on GPS satellites is necessary. These forces can be categorized into gravitational and non-gravitational forces. The non-gravitational forces are a significant contribution to the total force on a GPS satellite but they are still not fully understood whereas the gravitational forces are well modeled. This study focuses on two non-gravitational forces: Solar Radiation Pressure (SRP) and the y-bias force. Different SRP models are available in the University of Texas Multi-Satellite Orbit Determination Program (MSODP). The recently developed University College London model was implemented for the purpose of this study. Several techniques to compute parameters associated with SRP models and the y-bias force during an orbit prediction were examined. Using the International GNSS Service (IGS) precise ephemerides as a reference, five different models were compared in the study. Satellite Laser Ranging (SLR) residuals were also studied to validate the approach. Results showed that the analytical UCL model performed as well as a purely empirical model such as the Extended CODE model. This is important since analytical models attempt to represent the physical phenomena and thus might be better suited to separate SRP from other forces. The y-bias force was then shown to have a once per revolution effect. The time evolution of the y-bias was found to be dependent on the SRP model used, the satellite Block type, the orbital plane, and the attitude of the satellite which suggests that estimates of y-bias contain errors from other sources, particularly the SRP models. The dependency of the y-bias evolution on the orbital plane suggests that the orientation of the plane towards the Sun is important. / text

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2001Bitstream added on 2014-06-13T19:06:44Z : No. of bitstreams: 1 silva_aa_me_guara.pdf: 449677 bytes, checksum: 4be6e3535fba004c9b44ce9da9bf8c3a (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O Sistema de Posicionamento Global oferece um poderoso e relativamente barato processo para se determinar órbitas de satélites artificiais da Terra. Este trabalho apresenta um método de determinação de órbita para satélites com um receptor GPS a bordo. Medidas de pseudo-distância são usadas para estimar o vetor de estado. O estimador considerado é o método dos mínimos quadrados recursivo, através de rotações ortogonais de Givens, com a finalidade de evitar problemas numéricos e de inversão de matrizes. É considerado a modelagem das forças devido ao geopotencial de alto grau e ordem. Resultados indicam que a precisão em posição melhor que 10 m foi obtido usando dados reais do satélite Topex (com um mínimo de duas horas de dados - aproximadamente um período orbital). O resíduo de pseudo-distância teve um desvio padrão cerca de 5 m. / The Global Positioning System is a powerful and low cost process to compute orbits for some artificial Earth satellites. This work presents a method of orbit determination for satellites with an onboard GPS receiver. Pseudo-ranges are used in the measurements equations for the orbit estimator. The estimator considered is the recursive least squares method, numerically improved with orthogonal Givens rotations and thus avoiding problems concerning inversion of matrices. Up to high order geopotential perturbations are taken into account. Results indicate that precision better than 10 m is easily obtained using batches of one orbital period for the TOPEX satellite (two hours of orbital period). Standard deviation of about 5 m resulted for the residuals.

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.

<p dir="ltr">The future of the global economy lies in space. As the economic and scientific benefits from space become more accessible and apparent to the public, the demand for more spacecrafts will only increase. However, simply using the current space architecture to sustain any major activities past low Earth orbit is infeasible. The limiting factor of relying on ground operators via the Deep Space Network will blunt future growth in cislunar space traffic as the bandwidth is insufficient to satisfy the needs of every spacecraft in this domain. For this reason, spacecrafts must begin to operate autonomously or semi-autonomously for operators to be able to manage more missions at a given time. This thesis focuses on the guidance and navigation policies that could help vehicles such as logistical or resupply spacecrafts perform their rendezvous autonomously. It is found that using GNSS signals and Moon-based optical navigation has the potential to help spacecrafts perform autonomous orbit determination in near-Moon trajectories. The estimations are high enough quality such that a stochastic controller can use this navigation solution to confidently guide the spacecraft to a target within a tolerance before proximity operations commence. As the reliance on the ground is shifted away, spacecrafts would be able to operate in greater numbers outside of Earth's lower orbits, greatly assisting humanity's presence in space. </p>

<p dir="ltr">The Global Navigation Satellite System (GNSS) is heavily relied on for the navigation of Earth satellites. For satellites in cislunar space and beyond, GNSS is not readily available. As a result, other sources such as NASA's Deep Space Network (DSN) must be relied on for navigation. However, DSN is overburdened and can only support a small number of satellites at a time. Furthermore, communication with external sources can become interrupted or deprived in these environments. Given NASA's current efforts towards cislunar space operations and the expected increase in cislunar satellite traffic, there will be a need for more autonomous navigation options in cislunar space and beyond.</p><p dir="ltr">In this thesis, a navigation system capable of accurate and computationally efficient orbit determination in these communication-deprived environments is proposed and investigated. The emphasis on computational efficiency is in support of cubesats which are constrained in size, cost, and mass; this makes navigation even more challenging when resources such as GNSS signals or ground station tracking become unavailable.</p><p dir="ltr">The proposed navigation system, which is called GRAVNAV in this thesis, involves a two-satellite formation orbiting a planet. The primary satellite hosts an Extended Kalman Filter (EKF) and is capable of measuring the relative position of the secondary satellite; accurate attitude estimates are also available to the primary satellite. The relative position measurements allow the EKF to estimate the absolute position and velocity of both satellites. In this thesis, the proposed navigation system is investigated in the two-body and three-body problems.</p><p dir="ltr">The two-body analysis illuminates the effect of the gravity model error on orbit determination performance. High-fidelity gravity models can be computationally expensive for cubesats; however, celestial bodies such as the Earth and Moon have non-uniform and highly-irregular gravity fields that require complex models to describe the motion of satellites orbiting in their gravity field. Initial results show that when a second-order zonal harmonic gravity model is used, the orbit determination accuracy is poor at low altitudes due to large gravity model errors while high-altitude orbits yield good accuracy due to small gravity model errors. To remedy the poor performance for low-altitude orbits, a Gravity Model Error Compensation (GMEC) technique is proposed and investigated. Along with a special tuning model developed specifically for GRAVNAV, this technique is demonstrated to work well for various geocentric and lunar orbits.</p><p><br></p><p dir="ltr">In addition to the gravity model error, other variables affecting the state estimation accuracy are also explored in the two-body analysis. These variables include the six Keplerian orbital elements, measurement accuracy, intersatellite range, and satellite formation shape. The GRAVNAV analysis shows that a smaller intersatellite range results in increased state estimation error. Despite the intersatellite range bounds, semimajor axis, measurement model, and measurement errors being identical for both orbits, the satellite formation shape also has a strong influence on orbit determination accuracy. Formations that place both satellites in different orbits significantly outperform those that place both satellites in the same orbit.</p><p dir="ltr">The three-body analysis primarily focuses on characterizing the unique behavior of GRAVNAV in Near Rectilinear Halo Orbits (NRHOs). Like the two-body analysis, the effect of the satellite formation shape is also characterized and shown to have a similar impact on the orbit determination performance. Unlike the two-body problem, however, different orbits possess different stability properties which are shown to significantly affect orbit determination performance. The more stable NRHOs yield better GRAVNAV performance and are also less sensitive to factors that negatively impact performance such as measurement error, process noise, and decreased intersatellite range.</p><p dir="ltr">Overall, the analyses in this thesis show that GRAVNAV yields accurate and computationally efficient orbit determination when GMEC is used. This, along with the independence of GRAVNAV from GNSS signals and ground-station tracking, shows that GRAVNAV has good potential for navigation in cislunar space and beyond.</p>

The pursuit of precision and flexibility in satellite missions has led to an increased number of formation flying missions being developed. These systems consist of multiple satellites flying at close distances (from a few kilometres to a few meters) to achieve common objectives. This master thesis delves into the domain of the Guidance, Navigation and Control (GNC) for formation flying satellite systems, aiming to propose a novel architecture of different sets of sensors capable of determining absolute and relative positioning of the formation, ensuring mission success. This research begins by providing an overall status of existing and tested in-space systems. It will be complemented with novel and other systems already tested and promising new technologies in development. The thesis then delves into the design of an absolute and a relative Extended Kalman Filter (EKF) for distributed Synthetic Aperture Radar (SAR) systems implemented as part of an in-house simulator. Concluding with the results when using simulated Global Navigation Satellite Systems (GNSS) data as the filter input. Finally, the thesis will be completed with a trade-off analysis of the sensor systems, which could be used in formation-flying satellite systems in the near future. The outcome of this thesis is a novel proposal of a set of sensors to be brought to space navigation, with a corresponding detailed trade-off analysis. Additionally, to validate some of the sensor systems, an EKF is proposed, implemented and tested with the results from an in-house formation flying simulator. This master thesis report is the outcome of the work done during an internship at the Microwave and Radar Institute of the Deutsche Zentrum für Luft- und Raumfahrt e.V. (DLR) – German Aerospace Center – in Oberpfaffenhofen, Bavaria, Germany.

This paper investigates the feasibility of a rendezvous with an uncooperative space object using only optical sensors and takes a closer look at the performance of different algorithms used to estimate an object’s orbit. The ability to perform a rendezvous with an uncooperative target is critical for a wide variety of future missions, such as space debris removal. The main satellite, referred to as chaser, has to determine precisely the orbit of the space object of interest, referred to as target. After some elements of mission analysis, this report dives into the angles-only method of Initial Orbit Determination developed by Gooding, which is a method well suited for space-based observations. It gives access to the osculating orbit at the time of measurements. Then, the estimated orbit is refined using a Batch Least Squares algorithm. The accuracy of the orbit determination depends on the number and precision of the measurements. An optimal strategy for the distribution of the measurements on orbit is to take measurements regularly throughout the whole orbit. The constraints of eclipses and ground stations contacts are taken into account. Finally, the Rendezvous and Proximity Operations are explored in a mission scenario. / Detta examensarbete undersöker möjligheten av ett rendezvous med ett icke-samarbetsvilligt rymdobjekt som endast använder optiska sensorer och tar en närmare titt på prestandan hos olika algoritmer som används för att uppskatta ett objekts omloppsbana. Förmågan att utföra ett möte med ett icke samarbetsvilligt mål är avgörande för en mängd olika framtida uppdrag, till exempel borttagning av rymdskrot. Den viktigaste satelliten, kallad chaser, måste exakt bestämma omloppsbanan för rymdföremål av intresse, kallad target. Efter några element av uppdragsanalys, dyker denna rapport in i den vinkelbaserade metoden för initial omloppsbestämning som utvecklats av Gooding, som är en metod som är väl lämpad för rymdbaserade observationer. Den ger tillgång till den osulerande banan vid tidpunkten för mätningarna. Därefter förfinas den beräknade omloppsbanan med hjälp av minstakvadratmetoden. Noggrannheten i omloppsbestämningen beror på antalet mätningar och deras precision. En optimal strategi för fördelningen av mätningarna i omloppsbana är att göra mätningar regelbundet över hela omloppsbanan. Begränsningarna i förmörkelser och markstationernas kontakter beaktas. Slutligen utforskas mötes- och närhetsoperationer i ett uppdragsscenario.

The main objective of this work is to demonstrate some new computational methods for estimation, optimization and modeling of dynamical systems that use automatic differentiation. Particular focus will be upon dynamical systems arising in Aerospace Engineering. Automatic differentiation is a recursive computational algorithm, which enables computation of analytically rigorous partial derivatives of any user-specified function. All associated computations occur, in the background without user intervention, as the name implies. The computational methods of this dissertation are enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate Embedding Method). OCEA has been recently developed and makes possible efficient computation and evaluation of partial derivatives with minimal user coding. The key results in this dissertation details the use of OCEA through a number of computational studies in estimation and dynamical modeling. Several prototype problems are studied in order to evaluate judicious ways to use OCEA. Additionally, new solution methods are introduced in order to ascertain the extended capability of this new computational tool. Computational tradeoffs are studied in detail by looking at a number of different applications in the areas of estimation, dynamical system modeling, and validation of solution accuracy for complex dynamical systems. The results of these computational studies provide new insights and indicate the future potential of OCEA in its further development.

When developing products for space, including nanosatellites, the verification and validation process is a mandatory part of any project conducted within the European space industry. Within such a process, testing is a method for verification and validation. In this degree project, the appropriate tests for verification and validation of a nanosatellite were investigated. The project was conducted at the Royal Institute of Technology and the Polytechnic of Milan, as part of a larger research project under the name HERMES-SP. The research project was, at the time at which the degree project was taking place, in its first phase of the verification process. Therefore, tests for verification and validation of the Orbit Determination System (ODS) had not yet been defined. HERMES-SP is developing a nanosatellite platform with a very precise and reliable ODS, combining both Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS). This degree project was thus conducted with HERMES-SP as an applicative case to investigate tests for a ’nanosatellites onboard ODS focusing on the GNSS. The ODS developed for the nanosatellite platform was studied, along with the underlying theory for ODS and GNSS. The plan for verification defined within HERMES-SP was also examined, and the presented methodology for test development was followed. To fully answer the project’s research question, the appropriate tests had to be identified and defined. This was done by first determining the requirements related to the ODS, and then identifying the tests that were needed to verify the requirements. Lastly, the tests were defined in test specifications and procedures. It was found that the relevant tests in the verification process were a handful of tests on the Equipment Test (ET), Software Test (SWT), and Subsystem Integration Test (SSIT) test levels. The tests were needed for verification of individual components in the system, as well as integrated components and their interfaces. The defined tests were considered appropriate for verification and validation for the first phase of the verification process. The project contributed to the identification and definition of tests for a restricted part of the verification process, related to the specified system of the HERMES-SP nanosatellite. The findings could be used in other nanosatellite projects with similar ODS by following the process and the methodology for test development documented in this report. / Vid utvecklandet av produkter ämnade för rymden, såsom satelliter, är processen för verifiering och validering en obligatorisk del av projekt utförda inom den Europeiska rymdindustrin. Under en sådan process är testning en metod för verfiering och validering. I detta examensarbete undersöktes de lämpliga testerna för verifiering och validering av en nanosatellit. Arbetet utfördes på Kungliga Tekniska Högskolan (KTH) och Politecnico di Milano, som en del av ett större foskningsprojekt under namnet HERMES-SP. När detta examensarbete tog plats var forskningsprojektet i sin första verifieringsfas. Därför hade inte tester för verifiering och validering av systemet för ombord banbestämning ännu definerats. Inom HERMES-SP utvecklas en platform för nanosatelliter med ett precist och tillförlitligt banbestämmnings system. Systemet kombinerar därför både tröghetsnavigeringssystem och satellitnavigering (GNSS). Systemet för ombord banbestäming utvecklat för nanosatelliten studerades, tillsammans med underliggande teori för banbestäming och GNSS. HERMES-SPs plan för verifiering och validering studerades, och den presenterade metodiken för testning adapterades. För att besvara arbetets forskningsfråga behövdes de lämpliga testerna identifieras och sedan defineras. Detta gjorder genom att först bestämma krav på systemet för banbestämning, och därefter identifiera de tester som behövdes för att verifiera kraven. Sist definerades testen i form av test specifikationer och test procedurer. Arbetet resulterade i att en handfull at tester relevanta för verifieringsprocessen identifierades. Dessa tester tillhörde olika nivåer av testing, nämligen testning av komponenter, mjukvara, och integrering av delsystem. Dessa tester var nödvändiga för att utvärdera individuella komponenter i systemet, samt integrerade komponenter och deras gränssnitt. De tester som definerades i arbetet ansågs nödvändiga för verifiering och validering under den första fasen av processen för verifiering. Examensarbetet bidrog till identifiering och definering av tester tillhörande en begränsad fas av verifieringsprocessen, relaterade till det specifiecerade systemet av HERMES-SPs nanosatellit. Upptäckterna skulle kunna användas i andra projekt för nanosatelliter med liknande system för banbestämning, genom att följa metodiken för utveckling av tester dokumenterade i denna rapport.