Radar Data Processing With Applications
IEEE Press Series

Radar Data Processing with Applications

He You, Xiu Jianjuan, Guan Xin,Naval Aeronautical and Astronautical University, China

A summary of thirty years? worth of research, this book is a systematic introduction to the theory, development, and latest research results of radar data processing technology. Highlights of the book include sections on data pre-processing technology, track initiation, and data association. Readers are also introduced to maneuvering target tracking, multiple target tracking termination, and track management theory. In order to improve data analysis, the authors have also included group tracking registration algorithms and a performance evaluation of radar data processing.

• Presents both classical theory and development methods of radar data processing
• Provides state-of-the-art research results, including data processing for modern radars and tracking performance evaluation theory
• Includes coverage of performance evaluation, registration algorithm for radar networks, data processing of passive radar, pulse Doppler radar, and phased array radar
• Features applications for those engaged in information engineering, radar engineering, electronic countermeasures, infrared techniques, sonar techniques, and military command

Radar Data Processing with Applications is a handy guide for engineers and industry professionals specializing in the development of radar equipment and data processing. It is also intended as a reference text for electrical engineering graduate students and researchers specializing in signal processing and radars.

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

Dr. Jian-Juan Xiu received her Ph.D in Naval Aeronautical and Astronautical University, China, in 2004. Now she is an associate professor of the university. Her research interests include passive location, multiple target tracking and multi-sensor information fusion.

Dr. Xin Guan received his Ph.D from Naval Aeronautical and Astronautical University in 2006. She is now a professor and master tutor in Department of Electronics and Communication of the same school. She is major in ECM, radar emitter identification and evidence theory. She has published over 70 papers and two academic monographs.