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A Polarization Approach to Determining Rotational Angles of a Mortar

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A Polarization Approach to Determining Rotational Angles of a Mortar A POLARIZATION APPROACH TO DETERMINING ROTATIONAL ANGLES OF A MORTAR by Muhammad Hassan Chishti A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Computer Engineering Summer 2010 Copyright 2010 Muhammad Chishti All Rights Reserved A POLARIZATION APPROACH TO DETERMINING ROTATIONAL ANGLES OF A MORTAR by Muhammad Hassan Chishti Approved: __________________________________________________________ Daniel S. Weile, Ph.D Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ Kenneth E. Barner, Ph.D Chair of the Department Electrical and Computer Engineering Approved: __________________________________________________________ Michael J. Chajes, Ph.D Dean of the College of Engineering Approved: __________________________________________________________ Debra Hess Norris, M.S Vice Provost for Graduate and Professional Education This thesis is dedicated to, My Sheikh Hazrat Maulana Mufti Muneer Ahmed Akhoon Damat Barakatuhum My Father Muhammad Hussain Chishti My Mother Shahida Chishti ACKNOWLEDGMENTS First and foremost, my all praise and thanks be to the Almighty Allah, The Beneficent, Most Gracious, and Most Merciful. Without His mercy and favor I would have been an unrecognizable speck of dust. I am exceedingly thankful to my advisor Professor Daniel S. Weile. It is through his support, guidance, generous heart, and mentorship that steered me through this Masters Thesis. Definitely one of the smartest people I have ever had the fortune of knowing and working. I am really indebted to him for all that. I would like to thank the Army Research Labs (ARL) in Aberdeen, MD for providing me the funding support to perform the research herein. Especially I would like to mention the name of Dr. Gary Katulka of ARL, whose support and guidance proved invaluable in this project. I would also like to acknowledge Madhu Advani of Cornell University, who was part of our group during the summers of 07’ and 08’, for providing some very useful contribution towards this work. Never to forget my ever hardworking group mates, Xiaobo Wang and Yunqu Lin. Most importantly, I would like to express my utmost and deepest gratitude towards my Sehikh, my parents, my sister Faiza, and my brother Farid. Without them on my side I would not have finished this endeavor successfully. On a closing note, many thanks to my dear friends Syed Fahad Hussain and Dr. Masnoor-Ur-Rehman for their priceless support, and for listening to my whining! iii TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................... vi ABSTRACT ................................................................................................................ viii INTRODUCTION .......................................................................................................... 1 FUNDEMENTALS OF ANTENNAS ........................................................................... 3 2.1 Basic Electromagnetic Theory .................................................................. 3 2.2 Types of Antennas ..................................................................................... 5 POLAR SENSOR NAVIGATION SYSTEM DESCRIPTION ..................................... 7 3.1 General Description ................................................................................... 7 3.2 Overview of Computer Implementation .................................................... 8 3.3 Friis Transmission Equation ...................................................................... 9 3.4 Vector Effective Length .......................................................................... 10 GEOMETRIC COMPLICATIONS ............................................................................. 12 4.1 Introduction ............................................................................................. 12 4.2 Euler Angle Rotations ............................................................................. 13 4.3 Quaternion Rotation ................................................................................ 14 POLARIZATION BASED ATTITUDE SENSOR METHODOLOGY ...................... 16 5.1 Introduction ............................................................................................. 16 5.2 Direction Vectors..................................................................................... 17 5.3 Roll Angle ............................................................................................... 18 MORTAR DESIGN AND SIMULATIONS ................................................................ 20 6.1 Mortar Design 1 ....................................................................................... 20 6.2 Mortar Design 2 ....................................................................................... 22 6.3 Simulation Results ................................................................................... 23 6.3.1 Mortar in Direct Line from the Dipole Transmitter .................... 23 6.3.2 Mortar 10 Degree off Direct Line ............................................... 24 6.3.3 Mortar 20 Degree off Direct Line. .............................................. 25 6.4 Comparison of Mortar Design 1 & 2 ....................................................... 26 6.5 Design Issues ........................................................................................... 28 6.6 Off-beam Problem ................................................................................... 28 6.7 Advantages .............................................................................................. 29 REALISTIC ANTENNA DESIGN .............................................................................. 31 7.1 Introduction ............................................................................................. 31 7.2 Microstrip Patch Antennas ...................................................................... 31 7.3 Advantages and Disadvantages ............................................................... 34 7.4 A Broad-Band Dual Polarized Aperture Coupled Microstrip Patch Antenna .................................................................................................... 35 iv 7.4.1 Introduction ................................................................................. 35 7.4.2 Design Specifications 1: Antenna Layers ................................... 36 7.4.3 Design Specifications 2: Ground Plane, Air Layer, Microstrip Lines .......................................................................... 37 7.4.4 Design Specifications 3: H-Shaped Aperture Coupling .............. 38 7.5 Antenna Parameters ................................................................................. 40 7.6 Results ..................................................................................................... 40 7.6.1 S21 Parameters ............................................................................ 40 7.6.2 Radiation Pattern ......................................................................... 42 SMART ANTENNAS .................................................................................................. 43 8.1 Introduction ............................................................................................. 43 8.2 Angle-of-Arrival Projectile Location ...................................................... 44 8.2.1 AOA Estimation .......................................................................... 45 8.2.2 Projectile Location ...................................................................... 47 SUMMARY AND FUTURE WORK .......................................................................... 50 REFERENCES ............................................................................................................. 51 v LIST OF FIGURES Figure 1. The Three Rotational Angles: Yaw angle , Pitch angle , and Roll angle . ............................................................................................ 8 Figure 2. Determination of the Roll Angle by the Dot-Product of the Receiver and the Polarization of the Transmitted Antenna. .................. 18 Figure 3. Design 1: Mortar Missile in CadFEKO. Antennas are placed on the fins for this design. ........................................................................... 20 Figure 4. Electric Field Radiated by the Hertzian dipole, which acts as the Beacon. ................................................................................................... 21 Figure 5. Design 1: Electric Field Radiated by the Missile as Determined From FEKO Simulation. ........................................................................ 22 Figure 6. Design 2: Mortar Missile in CadFEKO. Antennas are placed farther up the neck. ................................................................................. 22 Figure 7. Far field Produced by Mortar Missile Design 2. .................................... 23 Figure 8. The Calculated and the Actual Roll Angle of the Missile, Given a Constant Angular Velocity, plotted together. ........................................ 24 Figure 9. Actual versus calculated Roll Angle for Missile with a 10-degree rotation around the y-axis. ...................................................................... 25 Figure 10. Actual versus calculated Roll Angle for missile with a 20-degree rotation around the y-axis. .....................................................................
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