Basic Radar Tracking

Detailed closed-loop bandwidth and transient response approach is a subject rarely found in current literature. This innovative resource offers practical explanations of closed-loop radar tracking techniques in range, Doppler and angle tracking. To address analog closed loop trackers, a review of basic control theory and modeling is included. In addition, control theory, radar receivers, signal processors, and circuitry and algorithms necessary to form the signals needed in a tracker are presented. Digital trackers and multiple target tracking are also covered, focusing on g-h and g-h-k filters. Readers learn techniques for modeling digital, closed-loop trackers. The radar circuitry/block diagrams necessary for range, Doppler and angle tracking are presented and described, with examples and simulations included. Factors such as noise and Swerling type fluctuations are taken into account. In addition to numerous worked examples, this approachable reference includes MATLAB® code associated with analysis, simulations and figures. The book contains solutions to practical problems, making it useful for both novice and advanced radar practitioners. Software will be available for download on this page. Artech House Radar Series Basic Radar Tracking 1 Contents 6 Preface 10 Acknowledgments 12 Chapter 1 Tracking Basics 14 1.1 Introduction 14 1.2 Tracker Types 14 1.3 Book Outline 16 References 17 Chapter 2 Control Theory Review 20 2.1 Introduction 20 2.2 Continuous Time Systems 22 2.2.1 System Type and Steady State Error 22 2.2.2 Root Locus and Transient Behavior 26 2.2.2.1 Example 1 28 2.2.2.2 Example 2 29 2.2.2.3 Example 3 31 2.2.2.4 Example 4 33 2.3 Discrete Time Servos 33 2.3.1 System Type and Steady State Error 34 2.3.2 Root Locus and Transient Behavior 36 2.4 Modeling Closed Loop Servos 38 2.4.1 Analog Servo Modeling 38 2.4.1.1 State Variable Method 38 2.4.1.2 z-Transform Method 41 2.4.1.3 Simulation Examples 41 2.4.1.3.1 State Variable Approach 42 2.4.1.3.2 z-Transform Approach 43 2.4.1.3.3 Determining the Open Loop Parameters 44 2.4.1.3.3.1 A Specific Case 47 2.4.1.3.3.2 Example Plots 48 2.4.2 Digital Servo Modeling 49 2.4.2.1 Deriving the z-Transfer Function from a State Variable Representation 49 2.5 Exercises 50 References 52 Chapter 3 Track Filters 55 3.1 Introduction 55 3.2 Kalman, α-(, and α-(-( Track Filters 55 3.2.1 Background 55 3.3 The Prediction Equation 58 3.3.1 Closed Loop Tracker Structure 61 3.3.2 Filter Stability and Variance Reduction 63 3.3.2.1 Stability Triangle 63 3.3.2.2 Variance Ratio 66 3.3.2.3 Noise Bandwidth and Variance Ratio 66 3.4 Benedict-Bordner Method for α-( Filter Design 68 3.5 Polge-Bhagavan Method for α-(-( Filter Design 71 3.6 CALCULATION OF α FOR THE BENEDICT-BORDNER AND POLGE-BHAGAVAN FILTERS 71 3.7 Responses of the Optimal α-b and α-b-y Filters 73 3.8 Control Theory Approach 74 3.8.1 Type 1 Servo 74 3.8.2 α-( Tracker 76 3.8.3 α-(-( Tracker 80 3.8.3.1 Critically Damped Case 81 3.8.3.2 Type 3 Servo with Equal Open Loop Zeros 83 3.9 Linear Kalman Filter 85 3.10 Example 87 3.11 Exercises 91 APPENDIX 3A: Stability Triangle and Variance Ratio 94 3A.1 Stability Triangle 94 3A.2 Stability Triangle—(-( Tracker 94 3A.3 Stability Triangle—(-(-( Tracker 96 3A.4 Variance Ratio 97 APPENDIX 3B: Derivation of (3.60)—Benedict and Bordner α-( Relation 99 Chapter 4 Closed Loop Range Tracking 106 4.1 Introduction 106 4.2 Sampling Gate Range Discriminator 107 4.2.1 LFM Pulse 113 4.2.2 Other Waveforms 117 4.3 Summing Gate Range Discriminator 117 4.3.1 Unmodulated Pulse 118 4.3.2 LFM Pulse 122 4.3.3 Barker Coded Pulse 123 4.3.4 Digital Matched Filter Implications 123 4.4 Direct Range Measurement 125 4.5 Range Tracker Modeling 127 4.5.1 Signal Model 128 4.5.2 Noise Model 131 4.5.2.1 Generating Correlated Noise Samples 133 4.5.3 Scaling the Signal and Noise 136 4.5.4 Signal and Noise Generation Algorithm 136 4.6 Signal Processor Considerations 137 4.7 Examples 137 4.7.1 Example 1: Sampling Gate Discriminator and - Filter 138 4.7.2 Example 2: Summing Gate Discriminator and - Filter 144 4.7.3 Example 3: Direct Range Measurement and -- Filter 145 4.8 Functional Level Error Model 149 4.9 Exercises 150 References 151 Appendix 4A: Derivation of ve when q < 1⁄2 and q(p < |((| < (1(q)(p 153 Chapter 5 Closed Loop Angle Tracking 155 5.1 Introduction 155 5.1.1 Chapter Outline 158 5.2 Types of Monopulse Sensing 158 5.3 Phase Comparison Monopulse 162 5.4 Amplitude Comparison Monopulse 171 5.5 Monopulse Combiners 177 5.5.1 Magic Tee 177 5.5.2 Rat Race 179 5.5.3 3-dB Coupler 180 5.6 Monopulse Receivers 185 5.6.1 Three-Channel Monopulse Receiver 185 5.6.2 Two-Channel Monopulse Receiver 187 5.6.2.1 Continuous Multiplexing 187 5.6.3 Simultaneous Multiple Beams/Digital Beam Forming 193 5.7 Conical Scan 194 5.8 Monopulse Processors 199 5.8.1 Exact Processor 200 5.8.1.1 Constrained Feed Array 202 5.8.1.2 Space-Fed Array 203 5.8.2 Modified Exact Processor 205 5.8.3 Log-Based Processor 208 5.9 Example 1: Angle Tracker with Different Monopulse Processors 211 5.10 Example 2: Combined Angle and Range Tracker 217 5.11 Functional Level Error Model 220 5.12 Exercises 222 References 223 Chapter 6 Closed Loop Doppler Tracking 226 6.1 Introduction 226 6.2 CW Doppler Discriminator 227 6.3 Pulsed Doppler Discriminator 233 6.4 Direct Doppler Measurement 236 6.5 Doppler Tracking in Low PRF Pulsed Radars 238 6.6 Example 1: CW Doppler Tracker 246 6.7 Example 2: Low PRF tracker 252 6.8 Functional Level Error Model 260 6.9 Exercises 261 References 261 APPENDIX 6A: Derivation of the Correlation Coefficient of the BPF Outputs 262 Chapter 7 Simulation Examples 266 7.1 Introduction 266 7.2 RCS Fluctuation 266 7.2.1 Example 1 268 7.3 Dual Target Tracking 272 7.3.1 Background 272 7.3.2 Example 2: Ideal Angle Tracker—Demonstration of Dichotomous Tracking 274 7.3.3 Example 3: A Variation on Example 2 277 7.3.4 Example 4: Example 3 with a Realistic Antenna 278 7.4 Crossing Target Examples 280 7.4.1 Example 5: Equal Doppler Frequencies and Target Sizes 282 7.4.2 Example 6: Different Doppler Frequencies and Target Sizes 284 7.4.3 Example 7: A Different Geometry—Collinear Target Trajectories 286 7.5 Crossing Target Examples—Fluctuating Target RCS 289 7.5.1 Example 8: Same Set Up as Example 5 with Fluctuating RCSs 289 7.5.2 Example 9: Same Set Up as Example 7 with Fluctuating RCSs 291 7.6 Multipath Examples 292 7.6.1 Specular Multipath Modeling 294 7.6.2 Target Model for Multipath 294 7.6.3 Example 10: Tracking in the Presence of Specular Multipath 296 7.7 Exercises 301 References 303 Chapter 8 Acquisition and Track Initiation 308 8.1 Introduction 308 8.2 Background 309 8.2.1 Acquisition Volume Design 309 8.2.2 Acquisition and Track Initiation Process 310 8.2.2.1 Search Acquisition Volume 311 8.2.2.2 Process Detection Table 313 8.2.2.3 Verify and Track Initiation 315 References 316 Acronyms and Abbreviations 318 Variables 320 About the Authors 331 Index 333 Radar;,Tracking;,Artech,House;,978-1-63081-335-2 Radar,Tracking,Artech House,978-1-63081-335-2