Radar Data Processing With Applications

About the Authors xiv Preface xvi 1 Introduction 1 1.1 Aim and Significance of Radar Data Processing 1 1.2 Basic Concepts in Radar Data Processing 2 1.2.1 Measurements 2 1.2.2 Measurement Preprocessing 2 1.2.3 Data Association 4 1.2.4 Wave Gate 4 1.2.5 Track Initiation and Termination 5 1.2.6 Tracking 5 1.2.7 Track 7 1.3 Design Requirements and Main Technical Indexes of Radar Data Processors 9 1.3.1 Basic Tasks of Data Processors 9 1.3.2 The Engineering Design of Data Processors 9 1.3.3 The Main Technical Indexes of Data Processors 11 1.3.4 The Evaluation of Data Processors 11 1.4 History and Present Situation of Research in Radar Data Processing Technology 12 1.5 Scope and Outline of the Book 14 2 Parameter Estimation 20 2.1 Introduction 20 2.2 The Concept of Parameter Estimation 20 2.3 Four Basic Parameter Estimation Techniques 23 2.3.1 Maximum A Posteriori Estimator 23 2.3.2 Maximum Likelihood Estimator 24 2.3.3 Minimum Mean Square Error Estimator 24 2.3.4 Least Squares Estimator 26 2.4 Properties of Estimators 26 2.4.1 Unbiasedness 26 2.4.2 The Variance of an Estimator 26 2.4.3 Consistent Estimators 26 2.4.4 Efficient Estimators 27 2.5 Parameter Estimation of Static Vectors 28 2.5.1 Least Squares Estimator 28 2.5.2 Minimum Mean Square Error Estimator 30 2.5.3 Linear Minimum Mean Square Error Estimator 32 2.6 Summary 33 3 Linear Filtering Approaches 34 3.1 Introduction 34 3.2 Kalman Filter 34 3.2.1 System Model 35 3.2.2 Filtering Model 41 3.2.3 Initialization of Kalman Filters 44 3.3 Steady-State Kalman Filter 48 3.3.1 Mathematical Definition and Judgment Methods for Filter Stability 49 3.3.2 Controllability and Observability of Random Linear System 49 3.3.3 Steady-State Kalman Filter 50 3.4 Summary 52 4 Nonlinear Filtering Approaches 53 4.1 Introduction 53 4.2 Extended Kalman Filter 53 4.2.1 Filter Model 54 4.2.2 Some Problems in the Application of Extended Kalman Filters 58 4.3 Unscented Kalman Filter 58 4.3.1 Unscented Transformation 59 4.3.2 Filtering Model 60 4.3.3 Simulation Analysis 61 4.4 Particle Filter 65 4.4.1 Filtering Model 65 4.4.2 Examples of the Application of EKF, UKF, and PF 67 4.5 Summary 71 5 Measurement Preprocessing Techniques 72 5.1 Introduction 72 5.2 Time Registration 72 5.2.1 Interpolation/Extrapolation Method Using Velocity 73 5.2.2 The Lagrange Interpolation Algorithm 74 5.2.3 Least-Squares Curve-Fitting Algorithm 74 5.3 Space Registration 75 5.3.1 Coordinates 75 5.3.2 Coordinate Transformation 80 5.3.3 Transformation of Several Common Coordinate Systems 83 5.3.4 Selection of Tracking Coordinate Systems and Filtering State Variables 87 5.4 Radar Error Calibration Techniques 88 5.5 Data Compression Techniques 89 5.5.1 Data Compression in Monostatic Radar 89 5.5.2 Data Compression in Multistatic Radar 91 5.6 Summary 93 6 Track Initiation in Multi-target Tracking 95 6.1 Introduction 95 6.2 The Shape and Size of Track Initiation Gates 96 6.2.1 The Annular Gate 96 6.2.2 The Elliptic/Ellipsoidal Gate 97 6.2.3 The Rectangular Gate 99 6.2.4 The Sector Gate 99 6.3 Track Initiation Algorithms 100 6.3.1 Logic-Based Method 101 6.3.2 Modified Logic-Based Method 102 6.3.3 Hough Transform-Based Method 103 6.3.4 Modified Hough Transform-Based Method 106 6.3.5 Hough Transform and Logic-Based Method 107 6.3.6 Formation Target Method Based on Clustering and Hough Transform 108 6.4 Comparison and Analysis of Track Initiation Algorithms 109 6.5 Discussion of Some Issues in Track Initiation 116 6.5.1 Main Indicators of Track Initiation Performance 116 6.5.2 Demonstration of Track Initiation Scan Times 116 6.6 Summary 117 7 Maximum Likelihood Class Multi-target Data Association Methods 118 7.1 Introduction 118 7.2 Track-Splitting Algorithm 118 7.2.1 Calculation of Likelihood Functions 119 7.2.2 Threshold Setting 120 7.2.3 Modified Likelihood Function 121 7.2.4 Characteristics of Track-Splitting Algorithm 122 7.3 Joint Maximum Likelihood Algorithm 123 7.3.1 Establishment of Feasible Partitions 123 7.3.2 Recursive Joint Maximum Likelihood Algorithm 125 7.4 0–1 Integer Programming Algorithm 126 7.4.1 Calculation of the Logarithm Likelihood Ratio 126 7.4.2 0–1 Linear Integer Programming Algorithm 128 7.4.3 Recursive 0–1 Integer Programming Algorithm 129 7.4.4 Application of 0–1 Integer Programming Algorithm 130 7.5 Generalized Correlation Algorithm 130 7.5.1 Establishing the Score Function 130 7.5.2 Application of the Generalized Correlation Algorithm 133 7.6 Summary 137 8 Bayesian Multi-target Data Association Approach 138 8.1 Introduction 138 8.2 Nearest-Neighbor Algorithm 138 8.2.1 Nearest-Neighbor Standard Filter 138 8.2.2 Probabilistic Nearest-Neighbor Filter Algorithm 139 8.3 Probabilistic Data Association Algorithm 141 8.3.1 State Update and Covariance Update 141 8.3.2 Calculation of the Association Probability 144 8.3.3 Modified PDAF Algorithm 146 8.3.4 Performance Analysis 147 8.4 Integrated Probabilistic Data Association Algorithm 152 8.4.1 Judgment of Track Existence 152 8.4.2 Data Association 154 8.5 Joint Probabilistic Data Association Algorithm 154 8.5.1 Basic Models of JPDA 155 8.5.2 Calculation of the Probability of Joint Events 160 8.5.3 Calculation of the State Estimation Covariance 162 8.5.4 Simplified JPDA Model 164 8.5.5 Performance Analysis 165 8.6 Summary 167 9 Tracking Maneuvering Targets 169 9.1 Introduction 169 9.2 Tracking Algorithm with Maneuver Detection 170 9.2.1 White Noise Model with Adjustable Level 171 9.2.2 Variable-Dimension Filtering Approach 172 9.3 Adaptive Tracking Algorithm 174 9.3.1 Modified-Input Estimation Algorithm 174 9.3.2 Singer Model Tracking Algorithm 176 9.3.3 Current Statistical Model Algorithm 180 9.3.4 Jerk Model Tracking Algorithm 182 9.3.5 Multiple Model Algorithm 184 9.3.6 Interacting Multiple Model Algorithm 186 9.4 Performance Comparison of Maneuvering Target Tracking Algorithms 189 9.4.1 Simulation Environment and Parameter Setting 189 9.4.2 Simulation Results and Analysis 191 9.5 Summary 201 10 Group Target Tracking 203 10.1 Introduction 203 10.2 Basic Methods for Track Initiation of the Group Target 204 10.2.1 Group Definition 204 10.2.2 Group Segmentation 205 10.2.3 Group Correlation 208 10.2.4 Group Velocity Estimation 209 10.3 The Gray Fine Track Initiation Algorithm for Group Targets 214 10.3.1 Gray Fine Association of Targets within the Group Based on the Relative Position Vector of the Measurement 215 10.3.2 Confirmation of the Tracks within a Group 220 10.3.3 Establishment of State Matrixes for Group Targets 221 10.3.4 Simulation Verification and Analysis of the Algorithm 221 10.3.5 Discussion 231 10.4 Centroid Group Tracking 233 10.4.1 Initiation, Confirmation, and Cancellation of Group Tracks 234 10.4.2 Track Updating 234 10.4.3 Other Questions 237 10.5 Formation Group Tracking 238 10.5.1 Overview of Formation Group Tracking 238 10.5.2 Logic Description of Formation Group Tracking 238 10.6 Performance Analysis of Tracking Algorithms for Group Targets 240 10.6.1 Simulation Environment 240 10.6.2 Simulation Results 240 10.6.3 Simulation Analysis 240 10.7 Summary 246 11 Multi-target Track Termination Theory and Track Management 250 11.1 Introduction 250 11.2 Multi-target Track Termination Theory 250 11.2.1 Sequential Probability Ratio Test Algorithm 250 11.2.2 Tracking Gate Method 252 11.2.3 Cost Function Method 253 11.2.4 Bayesian Algorithm 254 11.2.5 All-Neighbor Bayesian Algorithm 255 11.2.6 Performance Analysis of Several Algorithms 256 11.3 Track Management 258 11.3.1 Track Batch Management 258 11.3.2 Track Quality Management 266 11.3.3 Track File Management in the Information Fusion System 273 11.4 Summary 275 12 Passive Radar Data Processing 276 12.1 Introduction 276 12.2 Advantages of Passive Radars 276 12.3 Passive Radar Spatial Data Association 278 12.3.1 Phase Changing Rate Method 278 12.3.2 Doppler Changing Rate and Azimuth Joint Location 283 12.3.3 Doppler Changing Rate and Azimuth, Elevation Joint Location 285 12.3.4 Multiple-Model Method 286 12.4 Optimal Deployment of Direction-Finding Location 289 12.4.1 Area of the Position Concentration Ellipse 289 12.4.2 Derivation of the Conditional Extremum Based on the Lagrange Multiplier Method 292 12.4.3 Optimal Deployment by the Criterion that the Position Concentration Ellipse Area is Minimum 297 12.5 Passive Location Based on TDOA Measurements 299 12.5.1 Location Model 299 12.5.2 Two-Dimensional Condition 299 12.5.3 Three-Dimensional Condition 301 12.6 Summary 303 13 Pulse Doppler Radar Data Processing 304 13.1 Introduction 304 13.2 Overview of PD Radar Systems 304 13.2.1 Characteristics of PD Radar 304 13.2.2 PD Radar Tracking System 305 13.3 Typical Algorithms of PD Radar Tracking 307 13.3.1 Optimal Range–Velocity Mutual Coupling Tracking 309 13.3.2 Multi-target Tracking 312 13.3.3 Target Tracking with Doppler Measurements 312 13.4 Performance Analysis on PD Radar Tracking Algorithms 321 13.4.1 Simulation Environments and Parameter Settings 321 13.4.2 Simulation Results and Analysis 322 13.5 Summary 331 14 Phased Array Radar Data Processing 332 14.1 Introduction 332 14.2 Characteristics and Major Indexes 333 14.2.1 Characteristics 333 14.2.2 Major Indexes 334 14.3 Structure and Working Procedure 334 14.3.1 Structure 334 14.3.2 Working Procedure 335 14.4 Data Processing 336 14.4.1 Single-Target-in-Clutter Tracking Algorithms 337 14.4.2 Multi-target-in-Clutter Tracking Algorithm 343 14.4.3 Adaptive Sampling Period Algorithm 345 14.4.4 Real-Time Task Scheduling Strategy 349 14.5 Performance Analysis of the Adaptive Sampling Period Algorithm 355 14.5.1 Simulation Environment and Parameter Settings 355 14.5.2 Simulation Results and Analysis 356 14.5.3 Comparison and Discussion 360 14.6 Summary 361 15 Radar Network Error Registration Algorithm 362 15.1 Introduction 362 15.2 The Composition and Influence of Systematic Errors 362 15.2.1 The Composition of Systematic Errors 362 15.2.2 The Influence of Systematic Errors 363 15.3 Fixed Radar Registration Algorithm 366 15.3.1 Radar Registration Algorithm Based on Cooperative Targets 366 15.3.2 RTQC Algorithm 368 15.3.3 LS Algorithm 370 15.3.4 GLS Algorithm 371 15.3.5 GLS Algorithm in ECEF Coordinate System 373 15.3.6 Simulation Analysis 377 15.4 Mobile Radar Registration Algorithm 380 15.4.1 Modeling Method of Mobile Radar Systems 380 15.4.2 Mobile Radar Registration Algorithm Based on Cooperative Targets 386 15.4.3 Mobile Radar Maximum Likelihood Registration Algorithm 390 15.4.4 ASR Algorithm 397 15.4.5 Simulation Analysis 398 15.5 Summary 402 16 Radar Network Data Processing 405 16.1 Introduction 405 16.2 Performance Evaluation Indexes of Radar Networks 406 16.2.1 Coverage Performance Indexes 406 16.2.2 Target Capacity 407 16.2.3 Anti-jamming Ability 407 16.3 Data Processing of Monostatic Radar Networks 408 16.3.1 The Process of Data Processing of the Monostatic Radar Network 408 16.3.2 State Estimation of Monostatic Radar Networks 410 16.4 Data Processing of Bistatic Radar Networks 413 16.4.1 Basic Location Relation 413 16.4.2 Combined Estimation 416 16.4.3 An Analysis of the Feasibility of Combinational Estimation 417 16.5 Data Processing of Multistatic Radar Networks 420 16.5.1 Tracking Principle of Multistatic Radar Systems 421 16.5.2 Observation Equation of Multistatic Radar Network Systems 422 16.5.3 The Generic Data Processing Process of Multistatic Tracking Systems 422 16.6 Track Association 423 16.7 Summary 426 17 Evaluation of Radar Data Processing Performance 427 17.1 Introduction 427 17.2 Basic Terms 428 17.3 Data Association Performance Evaluation 429 17.3.1 Average Track Initiation Time 429 17.3.2 Accumulative Number of Track Interruptions 430 17.3.3 Track Ambiguity 431 17.3.4 Accumulative Number of Track Switches 432 17.4 Performance Evaluation of Tracking 432 17.4.1 Track Accuracy 433 17.4.2 Maneuvering Target Tracking Capability 434 17.4.3 False Track Ratio 434 17.4.4 Divergence 435 17.5 Evaluation of the Data Fusion Performance of Radar Networks 436 17.5.1 Track Capacity 436 17.5.2 Detection Probability of Radar Networks 436 17.5.3 Response Time 437 17.6 Methods of Evaluating Radar Data Processing Algorithms 438 17.6.1 Monte Carlo Method 438 17.6.2 Analytic Method 438 17.6.3 Semi-physical Simulation Method 439 17.6.4 Test Validation Method 440 17.7 Summary 440 18 Radar Data Processing Simulation Technology 441 18.1 Introduction 441 18.2 Basis of System Simulation Technology 442 18.2.1 Basic Concept of System Simulation Technology 442 18.2.2 Digital Simulation of Stochastic Noise 444 18.3 Simulation of Radar Data Processing Algorithms 449 18.3.1 Simulation of Target Motion Models 449 18.3.2 Simulation of the Observation Process 452 18.3.3 Tracking Filtering and Track Management 453 18.4 Simulation Examples of Algorithms 457 18.5 Summary 463 19 Practical Application of Radar Data Processing 464 19.1 Introduction 464 19.2 Application in ATC Systems 464 19.2.1 Application, Components, and Requirement 464 19.2.2 Radar Data Processing Structure 466 19.2.3 ATC Application 467 19.3 Application in Shipboard Navigation Radar 474 19.4 Application in Shipboard Radar Clutter Suppression 476 19.4.1 Principle of Clutter Suppression in Data Processing 476 19.4.2 Clutter Suppression Method through Shipboard Radar Data Processing 477 19.5 Application in Ground-Based Radar 480 19.5.1 Principle of Data Acquisition 480 19.5.2 Data Processing Procedure 481 19.6 Applications in Shipboard Monitoring System 482 19.6.1 Application, Components, and Requirement 482 19.6.2 Structure of the Marine Control System 483 19.7 Application in the Fleet Air Defense System 484 19.7.1 Components and Function of the Aegis Fleet Air Defense System 484 19.7.2 Main Performance Indexes 485 19.8 Applications in AEW Radar 486 19.8.1 Features, Components, and Tasks 486 19.8.2 Data Processing Technology 487 19.8.3 Typical Working Mode 489 19.9 Application in Air Warning Radar Network 492 19.9.1 Structure of Radar Network Data Processing 492 19.9.2 Key Technologies of Radar Network Data Processing 493 19.10 Application in Phased Array Radar 495 19.10.1 Functional Features 495 19.10.2 Data Processing Procedure 495 19.10.3 Test Examples 496 19.11 Summary 498 20 Review, Suggestions, and Outlook 499 20.1 Introduction 499 20.2 Review of Research Achievements 499 20.2.1 The Basis of State Estimation 499 20.2.2 Measurement Preprocessing Technology 500 20.2.3 Track Initiation in Multi-target Tracking 500 20.2.4 Multi-target Data Association Method 500 20.2.5 Maneuvering Target and Group Tracking 500 20.2.6 Multi-target Tracking Termination Theory and Track Management 501 20.2.7 System Error Registration Issue 501 20.2.8 Performance Evaluation of Radar Data Processors 501 20.2.9 Simulation Technology of Radar Data Processing 501 20.2.10 Applications of Radar Data Processing Techniques 502 20.3 Issues and Suggestions 502 20.3.1 The Application of Data Processing Technology in Other Sensors 502 20.3.2 Track Initiation in Passive Sensor Tracking 502 20.3.3 Non-Gaussian Noise 503 20.3.4 Data Processing in Non-standard and Nonlinear Systems 503 20.3.5 Data Processing in Multi-radar Networks 503 20.3.6 Joint Optimization of Multi-target Tracking and Track Association 503 20.3.7 Comprehensive Utilization of Target Features and Attributes in Multi-radar Tracking 504 20.3.8 Comprehensive Optimization of Multi-radar Information Fusion Systems 504 20.3.9 Tracking Multi-targets in Complex Electromagnetic Waves and Dense Clutter 504 20.4 Outlook for Research Direction 505 20.4.1 Information Fusion and Control Integration Technology of Multi-radar Networks 505 20.4.2 Joint Optimization of Target Tracking and Identification 505 20.4.3 Integration Technology of Search, Tracking, Guidance, and Command 505 20.4.4 Multi-radar Resource Allocation and Management Technology 505 20.4.5 Database and Knowledge Base Technology in Radar Data Processing 506 20.4.6 Engineering Realization of Advanced Radar Data Processing Algorithms 506 20.4.7 High-Speed Calculation and Parallel Processing Technology 506 20.4.8 Establishment of System Performance Evaluation Methods and Test Platforms 506 20.4.9 Common Theoretical Models for Variable Structure State Estimation 506 20.4.10 Automatic Tracking of Targets in Complex Environments 507 20.4.11 Tracking and Invulnerability of Multi-radar Network Systems 507 References 508 Index 523