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Orbit Calculation and Re-Entry Control of Vorsat Satellite

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Orbit Calculation and Re-Entry Control of Vorsat Satellite FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Orbit Calculation and Re-Entry Control of VORSat Satellite Cristiana Monteiro Silva Ramos PROVISIONAL VERSION Master in Electrical and Computers Engineering Supervisor: Sérgio Reis Cunha (PhD) June 2011 Resumo Desde o lançamento do primeiro satélite artificial para o espaço, Sputnik, mais de 30 000 satélites foram desenvolvidos e foram lançados posteriormente. No entanto, por mais autonomia que o satélite possa alcançar, nenhum satélite construido pelo Homem teria valor se não fosse possível localiza-lo e comunicar com ele. Os olhos humanos foram os primeiros recursos de que os seres humanos dispuseram para observar o Universo. O telescópio surgiu depois e foi durante séculos o único instrumento de exploração do Espaço. Hoje em dia, é possível localizar e seguir o trajecto que o satélite faz no espaço através de programas computacionais que localizam o satélite num dado instante e fazem a previsão do cálculo da órbita. Esta dissertação descreve o desenvolvimento de um sistema de navegação enquadrado no caso de estudo do satélite VORSat. O VORSat é um programa de satélite em desenvolvido na Faculdade de Engenharia da Universidade do Porto (FEUP), Potugal. Este projecto refere-se à construção de um CubeSat, de nome GAMA-Sat, e à reentrada de uma cápsula na Terra (ERC). Os objectivos consistem em determinar os parâmetros que descrevem uma órbita num dado instante (elementos de Kepler) e em calcular as posições futuras do satélite através de observações iterativas, minimizando o erro associado a cada observação. Também se pretende controlar, através de variações do termo de arrastamento, o local de reentrada. Dois métodos estimativos foram abordados: Filtro de Kalman e Mínimos quadrados. Estes foram adaptados ao caso de estudo por forma a avaliar a melhor performance num sistema não-linear tendo em consideração três aspectos: (1) O consumo de bateria no microcontrolador; (2) A capacidade de espaço limitada no microcontrolador; e (3) A precisão das medidas. Apesar deste projecto estar a ser desenvolvido no âmbito do VORSat, utilizou-se dois satélites que se encontram em órbita para validação de resultados. Optou-se pelo PoSAT e o International Space Station (ISS) por ambos se encontrarem em órbita baixa (LEO), terem uma órbita estável e ainda permanecem em órbita passado tantos anos, o que não é usual em satélites de órbita baixa. i ii Abstract Since the first artificial satellite was launched into space, Sputnik, more than 30,000 satellites have been developed and followed him. Regardless of the level of autonomy that the satellites can reach, any man-made spacecraft would have no value if it was unable to locate it and communicate with it. Human eyes were the first resources that humans had to observe the universe. The telescope came later and was used for centuries for space exploration. Nowadays, it is possible to locate and follow satellites in space through computer programs that compute the location of the satellites at any time and predict their orbits. This thesis describes the development of a navigation system that was carried out having in mind a specific case study, VORSat. VORSat is a small satellite program being developed at the Faculty of Engineering of the University of Porto (FEUP), Potugal. This project regards both the development of a CubeSat (named GAMA-Sat) and an Earth Reentry Capsule (ERC). The objective to determine the parameters that describe an orbit at a given moment (Kepler elements) and, through iterative observations to calculate the future positions of the satellite. Er- rors associated with each observation were to be minimized. Another objective was control the location of de-orbiting, through variations of the drag term. Two methods were discussed for the estimator technique: Kalman Filter and Least Squares. They were adapted to the case study in order to evaluate the best performance in a nonlinear system taking into account three aspects: (1) Battery consumption in the microcontroller; (2) limited storage space in the microcontroller; and (3) the accuracy of the measurements. Within the scope of this thesis, it was used two satellites: International Space Station (ISS) and PoSAT, in order to obtain results of the developed algorithm. The choice felt upon these two satellites due the fact that both of them are in LEO orbit, have a stable orbit and remain in orbit for many years. iii iv Acknowledgments To my supervisor, Prof. Sérgio Reis Cunha, for allowing me to enter into the VORSat world with which I strongly identified myself. To Prof. for his guidance, endless support, contagious enthusiasm and for always trusting in me and my capabilities. I also want to thank all VORSat team for helping me integrating into the project, the long conversations we had on this work possibilities and for their patience while explaining me every detail of VORSat project. To the European Space Agency for sponsoring my participation in the first Conference in the IAA University CubeSat Satellites and Missions of the Winter Workshop Session in Rome. Conference in which I learned a lot, that allowed me to learn about various projects increasing my motivation to develop this thesis. They were classmates, but in these last six months have become more than colleagues. For the games and the support, thank you, Alexandre Gomes, Mariana Magalhaes and Paulo Pereira. To all my dear Friends for their support and assistance over the years. Throughout the univer- sity time I acquired knowledge, soft skills but nothing compares to the friendships that I acquired during my stay at FEUP. A very special thanks to my closest ones, Sónia, Hugo, Tiago, Filipe, Pedro and Miguel. Although I have already been grateful to my closest friends, I want to show my special thanks to one of the people who was always there when I needed throughout this years. To you, Teresa, for your patience with me during all this years and while reviewing and advising me about this thesis. This thesis would not be a thesis if it had not been for your love and support, I can not thank you enough! Lastly, however more important, I wish to thank my parents, my sister and Luís, for instill the values and principles that have been guiding my life and have made me the person I am today. It all starts and ends at family and it is impossible to thank properly for everything they represent and do for me. Thank you one and all. v vi "It is difficult to say what is impossible, for the dream of yesterday is the hope of today and reality of tomorrow." Robert Goddard vii viii Contents 1 Introduction 1 1.1 Motivation . 1 1.2 Objectives and Work Organization . 3 1.3 Structure . 3 2 Case Study Presentation 5 2.1 CubeSat . 5 2.1.1 QB50 . 6 2.2 Project . 7 2.2.1 Project’ Vision and Objectives . 7 2.2.2 GAMA-Sat . 7 2.2.3 VORSat . 10 2.3 Summary . 12 3 Literature Review 13 3.1 Satellites . 13 3.1.1 Satellites Features . 14 3.1.2 Satellites Classification by Altitude . 15 3.2 Navigation System . 18 3.2.1 Principles of Orbital Motion . 18 3.2.2 Orbital Motion as a Two-Body Problem . 19 3.2.3 Orbit Determination Methods . 26 3.3 Perturbed Orbits . 29 3.3.1 Atmospheric models . 31 3.4 Interaction Station - Satellite . 33 3.4.1 Measuring from the Earth . 33 3.4.2 Measuring from Space . 34 3.4.3 Communication . 37 3.5 Summary . 38 4 Orbit and Location of De-orbiting Parameters Determination 39 4.1 Problem Description . 39 4.1.1 Case study Parameters . 40 4.1.2 Kalman Filter Algorithm . 42 4.1.3 Least-Squares Estimation Algorithm . 44 4.1.4 Methods Assessment . 46 4.2 Prediction of the Decay . 47 4.3 Summary . 49 ix x CONTENTS 5 Implementation and Results 51 5.1 Orbit Prediction . 51 5.1.1 Position and Velocity . 52 5.1.2 Kalman Filter . 54 5.2 Test Cases . 60 5.2.1 Unkown Inputs Parameters Values . 60 5.2.2 Accuracy of Kalman filter . 62 5.2.3 Observations only with positions . 64 5.3 De-orbiting Location Prediction . 64 5.4 Summary . 65 6 Conclusion and Future Work 67 6.1 Main Results . 67 6.2 Work’s Assessment . 67 6.3 Future Work . 68 A Time and Coordinate Systems 69 A.1 Time . 69 A.1.1 Sidereal Time . 69 A.1.2 Universal Time . 69 A.2 Coordinates . 71 A.2.1 Geographic Coordinates . 71 A.2.2 Cartesian Coordinates . 71 A.2.3 Datum . 73 B Futher Analysis of the Results 75 B.1 TLE file used in the simulations . 75 B.2 Kalman Filter Performance . 75 B.3 Unkown Inputs Parameters Values . 76 C Futher Analysis of the Results - Continue 91 C.1 Accuracy of Kalman Filter . 91 C.2 Observations only with positions . 91 References 97 List of Figures 1.1 Work Plan . 3 2.1 First draft of VORSat/GAMA-Sat architecture [1] . 8 2.2 GAMA-Sat Structure [1] . 9 2.3 Capsule phases. Courtesy of João Gomes . 10 2.4 Capsule Structure. Courtesy of João Gomes . 11 2.5 Interior of the Capsule. Adapted from [2] . 11 2.6 Batery Charge [1] . 11 3.1 Evolution of satellites over the years . 14 3.2 The two-boy motion [3] . 20 3.3 Motion of an orbiting body [4] . 23 3.4 Keplerian Elements . 24 3.5 Procedure of the Kalman Filter . 28 3.6 Ground Station. [5] . 34 3.7 Equipment ON/OFF state depending on battery charge. [5] . 35 5.1 Loop to perform the propagation .
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