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Resource Constrained Adaptive Sensing RESOURCE CONSTRAINED ADAPTIVE SENSING by Raghuram Rangarajan A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering: Systems) in The University of Michigan 2007 Doctoral Committee: Professor Alfred O. Hero III, Chair Professor Jeffrey A. Fessler Professor Susan A. Murphy Professor Demosthenis Teneketzis Assistant Professor Clayton Scott c Raghuram Rangarajan 2007 All Rights Reserved To my mom, my dad, and my brother ii ACKNOWLEDGEMENTS I would like to extend my sincere thanks and deepest gratitude to Professor Alfred Hero for his invaluable guidance, encouragement, and patience during the course of my research. Through the years, I have come to admire Professor Hero’s vast knowledge and deep insight on any scientific field, creativity in problem solving, and his exceptional time management skills. I consider myself extremely lucky to have found an advisor in Professor Alfred Hero and his attributes will definitely exert a great influence in all my future endeavors. My sincere thanks and gratitude also goes to Raviv Raich, with whom I have collaborated on many of my research topics. His invaluable inputs on my research and his ability to breakdown problems have helped me find solutions much quicker and more efficiently. It has also been an absolute pleasure interacting with him on a day-to-day basis for the last 3 years on many other topics of research and life in general. I am grateful to my committee members Professor Jeffrey Fessler, Professor Susan Murphy, Professor Demosthenis Teneketzis, and Professor Clayton Scott for their valuable input on my work and their helpful comments on my dissertation. I would like to extend my sincere thanks to all the faculty members at the EECS department for giving me a solid foundation on different topics in electrical engineering. Many thanks to my lab mates Michael Ting, Arvind Rao, Xing Zhou, Mark Kliger, Neal Patwari, Doron Blatt, and Dongxiao Zhu for creating a great work atmosphere and iii the nice interactions over coffee. This section would not be complete without acknowledging the support of my friends who have always be there for me and who have made my life in Ann Arbor so much more fun and memorable. In particular, my deep thanks to Ambalavanan Jayaraman, Somesh Srivastava, Deepak Sivaraman, Chandrasekaran Sethu, Arun Ramamurthy, Arun Kumar Panneerselvam, Satish Kumar, Nandakumar Vasudevan, and Harsha Chavali. Thanks also to the entire cricketing community and my friends at Indian Students Association for giving me exciting times. Last but not the least, I would like to extend my love to my entire family - my mom, my dad, my brother, my sister-in-law, and my grandparents for their constant source of encouragement, unconditional support, sacrifices, and prayers throughout my life. They have been my pillars of strength and my source of energy. The credit to all my academic achievements and to every positive quality I possess goes to my parents. Special thanks to my fianc`ee Sujatha for her love, support, and encouragement during my last year of research. iv TABLE OF CONTENTS DEDICATION .......................................... ii ACKNOWLEDGEMENTS .................................. iii LIST OF FIGURES ...................................... viii LIST OF TABLES ....................................... xii CHAPTER I. Introduction ....................................... 1 1.1 Overview...................................... 1 1.2 Motivation..................................... 2 1.2.1 Radarimaging ............................. 2 1.2.2 Target and sensor localization in sensor networks . ....... 4 1.3 Contributions ................................... 7 1.3.1 Personalperspective . .. .. .. .. .. .. .. .. .. .. .. 8 1.4 Detailedoutlineofthesis . .... 9 1.5 Connections .................................... 12 1.6 Publications .................................... 13 II. Energy allocation for estimation in linear models ............... 15 2.1 Introduction .................................... 15 2.1.1 Relatedwork-waveformdesign . 16 2.1.2 Related work - sequential design for estimation . ...... 17 2.2 Problemstatement ................................ 22 2.2.1 Non-adaptivestrategy . 24 2.3 Omniscient optimal two-step sequential strategy . ........... 25 2.4 Omniscient suboptimal two-step strategy . ........ 30 2.5 Strictenergyconstraintsolution . ....... 33 2.6 Parameter independent two-step design strategy . .......... 38 2.6.1 Problemstatement .. .. .. .. .. .. .. .. .. .. .. .. 38 2.6.2 Solution ................................. 38 2.7 Design of N-stepprocedure............................ 42 2.8 Sequentialdesignfor vectorparameters . ........ 46 2.8.1 Worstcaseerrorcriterion . 46 2.8.2 Tracecriterion ............................. 48 2.9 Applications .................................... 61 2.9.1 MIMOchannelestimation . 61 2.9.2 Inversescatteringproblem . 63 2.10Conclusions .................................... 65 2.11 Appendix: proofofequivalence. ...... 66 v 2.12 Appendix: solutiontoproblem2.6.1. ....... 67 2.12.1 The N two-stepprocedure. 68 2.13 Appendix: derivation× of the N-stepprocedure . 72 2.14 Appendix: derivation of two-step minmax criteria . ........... 74 2.15 Appendix: distribution of Gaussian mixture . ......... 75 2.16 Appendix: proof of theorem 2.7.1 ........................ 76 III. Energy allocation for estimation in a nonlinear model ............ 81 3.1 Introduction .................................... 81 3.2 Modelandmathematicaldescription . ..... 83 3.3 Meansquarederrorcalculation. ..... 87 3.3.1 One-stepestimator .. .. .. .. .. .. .. .. .. .. .. .. 87 3.3.2 Two-stepnonsequentialdesign . 88 3.3.3 Two-stepsequentialdesign. 94 3.4 Conclusions ....................................101 3.5 Appendix: timereversalimaging. .. .. 103 3.5.1 CRBforscatteringcoefficients. 107 3.6 Appendix: two-step sequential strategy, constrained case ...........111 3.7 Appendix: resultsfrommatrixtheory . ...... 113 3.8 Appendix: resultfromintegralcalculus . ........114 IV. Energy allocation for detection in linear models ................115 4.1 Introduction .................................... 115 4.2 Problemformulation .............................. 119 4.3 Frequentistapproach . .. .. .. .. .. .. .. .. .. .. .. .. 119 4.3.1 Singlestepsolution.. .. .. .. .. .. .. .. .. .. .. .. 120 4.3.2 Two-stepdesign. .. .. .. .. .. .. .. .. .. .. .. .. 120 4.4 Bayesianapproach................................ 127 4.4.1 One-stepsolution . .. .. .. .. .. .. .. .. .. .. .. .. 128 4.4.2 Two-stepsolution. .. .. .. .. .. .. .. .. .. .. .. .. 129 4.5 Conclusions ....................................135 V. Adaptive waveform selection for state estimation ...............136 5.1 Introduction .................................... 136 5.2 Problemformulation .............................. 139 5.3 Proposedsolution ................................ 140 5.4 Comparisontopreviousstrategies . ...... 141 5.5 Numericalstudy.................................. 142 5.6 Computationalcomplexity . 145 5.7 Simulationresults ............................... 146 5.8 Conclusions ....................................148 VI. Sparsity penalized MDS for blind tracking in sensor networks .......150 6.1 Introduction .................................... 151 6.2 Problemformulation .............................. 158 6.3 ClassicalMDSandvariations. 160 6.4 SparsitypenalizedMDS. 163 6.4.1 Minimizing cost function by optimization transfer . ........167 6.4.2 Implementation . .. .. .. .. .. .. .. .. .. .. .. .. 170 6.5 TrackingusingsparseMDS. 173 vi 6.5.1 NumericalStudy ............................ 177 6.6 Realworldapplications . 183 6.6.1 ZebraNetdatabase . 183 6.6.2 UCSDwirelesstracedata . 188 6.7 Conclusions ....................................201 6.8 Appendix: derivation of sparsity penalized dwMDS . .........202 6.9 Appendix: experimentalsetup . 206 6.10 Appendix: optimal likelihood ratio test . .........208 VII. Conclusion and future directions ..........................210 BIBLIOGRAPHY ........................................ 214 vii LIST OF FIGURES Figure 2.1 Reduction in MSE for varying values of α1. ...................... 29 2.2 Plot of the optimal and suboptimal solution to the normalized energy transmitted at the second stage as functions of received signal at first stage............ 29 2.3 Theoretical versus simulation results for suboptimal strategy. Reduction in MSE for varying values of ρ at optimal α1∗ =0.7319. .................... 32 2.4 Theoretical versus simulation results for suboptimal strategy. Reduction in MSE for varying values of α1 at optimal ρ∗ =0.675...................... 33 2.5 Typical plots of the MSE as a function of f....................... 34 2.6 MSE(2) SNR(2) vs. ρ. ................................. 36 × 2.7 Re(Bias) vs. ρ. ...................................... 37 2.8 Plot of reduction in MSE versus percentage error in guess of parameter of θ1 for variousSNR. ....................................... 39 2.9 Description of the N two-stepprocedure.. 41 × 2.10 Illustration of the N two-step procedure: the omniscient optimal two-step proce- × dure, where energy E1 is allocated to the first step and E2 is chosen optimally at the second step based on the past measurements, is shown in Fig. (a). Figure (b) illustrates the N 2-step procedure, where N independent two-step experiments are performed with× the energy design as the optimal two-step energy allocation strategy scaled through 1/N but with θg replacing θ1. By averaging the estimates of the N two-step estimators, we asymptotically
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