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Over-The-H Orizon Radar Array Calibration q'q" Over-the-H orizon Radar Array Calibration by IsHnN Savrrsvn DRNrpr SorovroN B.ENc.(HoNs), B.Sc. Thesis submitted for the degree of Doctor of Philosophy Department of Electrical and Electronic Engineering Faculty of Engineering The University of Adelaide Adelaide, South Australia April 1998 Contents Abstract vl Declaration viii Acknowledgments ix List of Figures x List of Tâbles xvi Glossary xvii Publications xxt 1 Introduction 1 1.1 ProblemDescription I 1.2 Outline of Thesis and Main Contributions 4 2 Background Array Processing and Array Calibration 6 2.1 Array Processing Background . 6 2.1.1 MaximumLikelihoodMethod 10 2.1.2 Beamformers l1 2.1.3 Subspace Methods l3 2.2 Array Calibration Application Areas 15 2.2.1 Telescope Images l5 2.2.2 General Antenna Arrays t6 2.2.3 Airborne Radar l6 2.2.4 Synthetic Aperture Radar l7 2.2.5 Passive Sonar Towed Arrays I7 CONTENTS ll 2.2.6 Sonar Imaging Systems l8 2.2.7 Synthetic Aperture Sonar Imaging Systems l8 2.2.8 Computer Vision l8 2.2.9 UltrasoundArrays l9 2.2.10 Microphone Arrays l9 2.3 Previous Array Calibration Methods 19 2.3.1 Methods for Estimating Sensor Positions 20 2.3.2 Methods forEstimating Mutual Coupling 24 2.3.3 Methods for Estimating Sensor Positions and Mutual Coupling 25 2.3.4 Other Methods 26 2.4 Discussion 27 3 Effect of Model Errors on Radar Array Processing 28 3.1 Literature 29 3.2 Description 31 3.3 Performance Measures 32 3.3.1 Signal-to-Noise Ratio and Array Gain JJ 3.3.2 BeampointingError JJ 3.3.3 Sidelobe Levels 34 3.4 Non-stationary Interferer Environment . 36 3.4.I Fluctuating Interferer Wavefront Model 38 3.4.2 Fluctuating Interferer DOA Model 38 3.4.3 Sea Clutter Model 40 3.4.4 Results 40 3.5 Conclusion 43 4 Array Calibration using Disjoint Sources 45 4.1 Mutual Coupling Models 46 4.2 Generalised Weiss-Friedlander Method 48 4.3 Performance of Generalised Method 52 4.4 Modified Algorithm for OTH radars 55 4.5 Simulation Example 59 4.6 Monte Carlo Analysis 6l 4.7 Alternative Sensor Position Estimator 65 CONTENTS lll 4.8 Performance Criteria 67 4.9 Mutual Coupling Estimation Investigation 70 4.10 Error Surface 72 4.ll Conclusion 79 5 Array Calibration using Disparate Sources 83 5.1 Signal Model 84 5.2 Time-varying DOA Sources 85 5.3 Time-invariant DOA Sources 86 5.4 Overall Cost Function 87 5.5 An Example 87 5.6 Algorithm 88 5.6.1 Initialisation 89 5.6.2 Sensor Position Estimation 91 5.6.3 Coupling Matrix Estimation 93 5.6.4 DOA Estimation 93 5.6.5 Estimation of Complex s's . 95 5.6.6 Assumptions 95 5.7 Simulation Example 96 5.8 Monte Carlo Analysis 99 5.9 Special Case 100 5.9.1 SimulationExample . 103 5.9.2 Monte Carlo Analysis 104 5.10 Error Surface 109 5.10.1 4-element Array 110 5.10.2 Theoretical Analysis of 2-element Array ll3 5.11 Perforrnance with Larger Model Errors 118 5.12 Conclusion 119 6 Cramer-Rao Lower Bounds 122 6.1 CRLB for Disjoint Sources 122 6.1.1 DOA - DOA Terms 124 6.1.2 Sensor Position - Sensor Position Terms 124 6.I.3 Coupling - Coupling Terms t25 CONTENTS IV 6.I.4 Cross Terms 125 6.1.5 CRLB Analysis 126 6.I.6 Algorithm Comparison with CRLB t32 6.1.7 Mutual Coupling Estimation using a Single Source 133 6.2 CRLB for Disparate Sources 142 6.2.1 DOA - DOA Terms r42 6.2.2 Sensor Position - Sensor Position Terms t44 6.2.3 Coupling - Coupling Terms r44 6.2.4 Cross Terms r45 6.2.5 Algorithm Comparison with CRLB 145 6.2.6 CRLB Analysis t46 6.3 Conclusion t47 7 Sources for HF Array Calibration 150 7.I Jindalee Radar Overview . 150 7.2 Meteors . 154 7.2.I VisualObservations . 155 7.2.2 Radar Observations . 155 7.2.3 Underdense versus Overdense Echoes .156 7.2.4 Shower Meteors and Sporadic Meteors . 157 7.2.5 Radio Frequency Dependence . t57 7.2.6 DiurnalVariation . 160 7.2.7 Range and Altitude Dependence . 160 7.2.8 Numerous Disjoint Sources of Opportunity . 161 7.2.9 Spatial Stationarity Analysis of Head and Trail Echoes . 169 7.2.10 Multimode Echoes . t72 1.3 External Noise . t73 7.3.I Suitable Noise Sources . t74 7.3.2 HF Noise Statistics . It5 1.4 Other Sources . 176 7.5 Jindalee Array Calibration . 176 7.5.1 Calibration over Receivers . t77 7.5.2 PerformanceDetermination .180 1.6 Conclusion . 180 CONTENTS I Conclusion 185 8.1 Overview and Contributions 185 I 8.2 Future Work 187 A Sidelobes for 2-D Array with Mutual Coupling 188 B Mutual Coupling Estimation using a Single Source 190 8.1 Passive Array Calibration 195 8.2 Active Array Calibration 198 8.3 Interpretation for Non-Identifiable Conditions 200 C Analytic Expressions for Error Surfaces 201 C.l Source DOA 202 C.2 Sensor Position Error 203 C.3 Coupling Amplitude 204 C.4 Coupling Phase 205 C.5 Complex Scalar sn . 206 Abstract Modern over-the-horizon radars are currently being developed which have arrays than can be erected quickly, with minimal site preparation. Due to the rapid deployment of these affays, antenna/sensor position effors may be present. Further since the antennas have a simple and cost-effective design, mutual coupling may be present. These imperfections, which can degrade radar perfonnance, form the basis for the work conducted in this thesis. The effect of these model effors on radar performance is first analysed. The degradation in signal-to-noise ratio, anay gain, bearing estimation and array sidelobe levels, are determined. The major degradation is observed in the array sidelobe levels, which in turn results in the clutter-to-noise ratio (and hence target detectability) being worsened in the presence of non- stationary interferences. For these reasons, array calibration is required to improve the array sidelobe levels. New array calibration algorithms are then developed to correct for sensor position errors and mutual coupling, using sources in the radar environment. These algorithms are analysed using simulations, and are found to perform well. The Cramer-Rao lower bound is derived, for the problem scenarios considered, and the algorithms are shown to achieve the bound. Further the Cramer-Rao lower bound is analysed, to obtain useful insight into the array calibration problem and identifi ability. Scattered echoes from meteor trails are shown to be excellent sources of opportunity for over-the-horizon radar array calibration. These echoes are found in general to : have planar wavefronts, be present in large numbers, be sufficiently strong, and be of adequate duration for sufficient snapshots to be obtained for array calibration. It also is shown that meteor head echoes are good sources of opportunity, and their properties along with that of other sources, are determined. Finally, the receivingarray of the Jindalee over-the-horizonradar (located in central Aus- tralia) is calibrated using echoes from meteor trails. The results obtained are compared with vl ABSTRACT vll standard calibration (for this radar), which involves the use of special calibration sources. Array calibration using meteor trail echoes is found to perform as well as the standard array t calibration, indicating that echoes from meteor trails can perform good array calibration. Acknowledgments I would like to first thank Professor Douglas Gray, my principal supervisor. His expertise in anay processing, together with his general signal processing knowledge, enabled him to provide extremely useful criticism, analysis, and suggestions on my work. He also taught me a lot about presentations, both oral and written. Dr. Stuart Anderson, my co-supervisor, suggested this problem and provided me with advice on matters relating to radars, both of skywave and surface-\ryave types. He also helped me significantly with the final phase of publications. Professor Yuri Abramovich, while not officially a supervisor, was instrumental, from the formulation of the problem, to its conclusion. He provided me with several suggestions and criticism, on many wide ranging aspects of radar signal processing. I would like to thank the Defence Science and Technology Organisation, for supporting me during the course of this research; I am especially grateful to Dr. Bruce Ward, Dr. Chris Coleman, Dr. Dan Meehan, Dr. Dick Thomas and Mrs. Elizabeth Ashforth. I also would like to thank the Cooperative Research Centre for Sensor Signal and Information Processing, for providing me with good facilities for conducting research. I am also grateful to Professor Benjamin Friedlander, who provided me with good feed- back when I contacted him in California, and Professor Kok Teo who provided some useful suggestions on my work. I would like to thank the Lord for all things, and finally I would like to thank my parents for their support and sacrifices, over the years, and to them I dedicate this thesis. IX List of Figures 1.1 The surface-wave radar environment. 2 1.2 Example of surface-wave radar data. J 2.1 Planewave signal impinging ararray of sensors l 3.1 Variation of signal-to-noise ratio with signal-interference separation, for the specifiedmodel error- (a) gaineffors i oa^ = 0 (-), 0.2 (--),0.4 (-.-), 0.5 (...); (b)phase effors 1 o,þ^ = 0o (-), 12'(--),24' (-.-),36" (...); (c) sensorposition effors I or- os^= 0 (-),0.1d (--),0.2d (-.-),0.3d (...); (d) mutual coupling : element height (h) = 0.25¡ (-), 0.4À (-.-), 0.5À (--) .
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