POLITECNICO DI TORINO III Faculty of Information Engineering Master’s Degree in Electronics Engineering Master’s Thesis Design and Simulation of a Star Tracker for the Aramis Small Satellite Advisors: prof. Leonardo Reyneri prof. Alberto Vallan Candidate: Diego Urbina Academic Year 2007-2008 II Summary Star Trackers are devices that provide higher accuracy than other attitude sensors with the added benefits of 3-axis attitude determination. Nevertheless, Star Trackers are frequently heavy, complex and costly systems that can not be adopted by small satellites such as the Aramis from Politecnico di Torino, which needs high-accuracy attitude determination to cover the requirements of certain types of payload. In this thesis, the state of the art in attitude sensing is described, specially that of Star Trackers. Then, a preliminary design of a low-mass, low-cost, low-power and coarse accuracy Star Tracker is proposed to satisfy the requirements of the Aramis spacecraft. Different available algorithms for identifying the presence of single stars on the imager plane are analyzed, as well as those for pattern recognition necessary to ultimately measure the spacecraft attitude. One set of such image processing and pattern recognition algorithms are chosen for use on board Aramis . Subsequently, they are tested with the experimental use of the 3D open source planetarium Ce- lestia, while a parallel test of the image processing algorithms is performed on real star field imagery to confirm their capabilities with real-world data. A scheme is proposed to reduce the amount of false results thanks to the use of attitude approximations coming from other sensors, through the homogeneous segmentation of the celestial sphere. Commonly used methods to produce the desired quaternion output are described, and finally, an assessment of the performance of the tested algorithms is made. III Acknowledgements I thank the following persons who were consulted during the development of this thesis: prof. Leonardo Reyneri, prof. Alberto Vallan, prof. Nikolai Tolyarenko, Dr. Angie Buckley, Dr. Jeff Hoffman, Danilo Roascio, Fabio Maggioni. I also want to thank all my friends that made me feel at home during all these years away from home, Elsa Marie for putting a smile on my face when I most needed it, and my lovely family, specially my mother who has been the Northern Star that helps me not get lost in space. IV Contents Summary III Acknowledgements IV 1 Introduction 1 1.1 Aramis’ predecessor: PicPot . 1 1.2 The Aramis Micro Satellite . 3 1.3 Considerations on the Space Environment . 4 1.4 Attitude Determination and Control . 9 1.5 Attitude Sensors . 10 1.5.1 Horizon Sensors . 10 1.5.2 Radiofrecuency beacons . 11 1.5.3 Solar sensors . 11 1.5.4 Magnetometers . 12 1.6 Star Trackers . 13 2 Architecture 17 2.1 Requirements . 17 2.2 UML Model . 19 2.3 Star Tracker Processing Unit (SPU) . 23 2.3.1 CPU . 23 2.3.2 Flash Memory . 24 2.3.3 RAM Memory . 25 2.4 Camera Unit (SCU) . 25 2.4.1 Imager . 25 2.4.2 Optics assembly . 26 2.5 Components selection and Preliminary Schematics . 29 2.5.1 Star Tracker Processing Unit . 30 2.5.2 Star Tracker Camera Unit . 31 2.6 Comparison with State of the Art . 31 2.7 Star Tracker mounting . 32 V 3 Image Processing 37 3.1 Data Flow . 37 3.2 Simulation Platform . 37 3.3 The Star Signal . 39 3.4 Noise . 40 3.4.1 Signal shot noise . 40 3.4.2 Dark current noise . 40 3.4.3 Background noise . 41 3.4.4 Quantization noise . 41 3.4.5 Readout noise . 42 3.4.6 Total Noise . 42 3.4.7 Signal-to-noise ratio . 42 3.5 Thresholding . 43 3.6 Centroiding . 45 4 Considerations on the Frames of Reference 47 4.1 The celestial Sphere . 47 4.2 Right Ascension and Declination . 48 4.3 Precession, nutation and polar motion . 49 4.4 Epochs . 49 4.5 Catalogue . 50 4.5.1 The Yale Bright Star Catalogue . 50 4.5.2 Catalogue Optimization . 50 5 Pattern Recognition 55 5.1 Single Star Matching . 55 5.2 Grid Pattern Matching . 56 5.3 Angle Method Pattern Matching . 57 5.4 Spherical Triangle Method Pattern Matching . 58 5.5 Planar Triangle Method Pattern Matching . 59 5.6 K-vector search algorithm . 64 5.7 Pivoting . 65 5.8 Star Selection and Matching . 66 5.9 Aided Mode . 68 6 Attitude Determination 71 6.1 Attitude Representation . 71 6.1.1 Direction Cosine Matrix . 71 6.1.2 Euler Angles . 72 6.1.3 Quaternions . 73 6.2 QUEST Algorithm . 74 VI 7 Code Usage and Description 77 7.1 Ground Software . 77 7.1.1 Star Compilation . 77 7.1.2 K-vectors generation . 79 7.1.3 Buckminster Fuller polyhedron tags generation . 79 7.2 Simulation scripts for Celestia . 79 7.2.1 Celestia initialization . 80 7.2.2 Image captures and attitude reference files . 80 7.3 In-flight Software . 80 8 Algorithm Performance 83 8.1 Dynamic Image Thresholding and Centroiding . 83 8.2 Results with pivoting (LIS) . 83 8.3 Results with pivoting (aided mode) . 85 9 Conclusions and Future Work 89 A SPU Miscellaneous Parts 91 A.1 SDRAM Memory . 91 A.2 Flash Memory . 91 A.3 Alternative embedded option . 92 B Schematics 95 B.1 Star Tracker Camera Unit . 95 B.2 Star Tracker Processing Unit . 97 C Ground Code 99 C.1 Catalogue reader. 99 C.2 Star reading and filtering . 100 C.3 k-vector tags generation . 107 C.4 Buckingham Fuller Polyhedron tags compilation . 111 D Simulator scripts 115 D.1 Celestia Initializer . 115 D.2 Image reader/attitude reference obtainer . 116 E In-flight Code 121 Bibliography 137 VII List of Tables 1.1 Galileo Avionica A-Star Tracker Specifications . 14 1.2 Current sensor types comparison . 15 5.1 Star identification matrix . 66 5.2 Star identification matrix . 67 5.3 An example of star matching . 67 VIII List of Figures 1.1 PicPot, Politecnico di Torino CUBESAT . 2 1.2 Dnepr launch. Source: Christian Hessmann . 3 1.3 Aramis satellite in a 2x2x1 configuration . 4 1.4 GENSO educational network coverage . 5 1.5 South Atlantic Anomaly and Van Allen Belts. Source: NASA. 5 1.6 STARDUST: GOES-8 graph describing the solar wind event. Source: NASA. 6 1.7 STARDUST: Last acquired image under the effect of a solar flare. Source: NASA. 8 1.8 STARDUST: Image from the Star Tracker some days after, showing stars and a planet. Source: NASA. 8 1.9 Planet Earth as seen in the infrared spectrum by the GOES-N Geo- stationary Satellites. Source: NASA. 11 1.10 A sun sensor for microsatellites from Jet Propulsion Lab, Caltech . 12 1.11 The Oersted satellite magnetometer (right) mounted on the same platform with a Star Tracker (left). Source: Danish Meteorological Institute. 12 1.12 A-Star Tracker from Galileo Avionica . 14 2.1 Oersted µASC .............................. 18 2.2 Star Tracker block diagram . 19 2.3 Use cases of the Star Tracker with 1B232 and Stars/Sky as actors . 20 2.4 Use cases of the Star Tracker with 1B1 Power Management Subsystem as an actor . 21 2.5 Use cases of the Star Tracker with Integrator and Configurer as actors 21 2.6 Star Tracker Hardware Class Diagram . 24 2.7 Field Curvature. Source: University of British Columbia . 28 2.8 Field Curvature effect on a Star Field. Side images: wide Field of View, center image: Detail of a distorted star. 28 2.9 Double Gauss lens. Source: Zemax software . 29 2.10 Aramis Star Tracker HW Block Scheme . 30 2.11 ADSPBF533 Functional Diagram. Analog Devices. 32 IX 2.12 Aptina sensor-dsp interface. On the left, imager video source. On the right, PPI of Blackfin. Source: Analog Devices [1] . 32 2.13 TECHSPEC Double Gauss Focusable Lens. [1] . ..