Space Electronic Reconnaissance
Localization Theories and Methods

Presents the theories and applications of determining the position of an object in space through the use of satellites

As the importance of space reconnaissance technology intensifies, more and more countries are investing money in building their own space reconnaissance satellites. Due to the secrecy and sensitivity of the operations, it is hard to find published papers and journals on the topic outside of military and governmental agencies.  This book aims to fill the gap by presenting the various applications and basic principles of a very modern technology. The space electronic reconnaissance system in mono/multi-satellite platforms is a critical feature which can be used for detection, localization, tracking or identification of the various kinds of signal sources from radar, communication or navigation systems.

Localization technology in space electronic reconnaissance uses single or multiple satellite receivers which receive signals from radar, communication and navigation emitters in the ground, ocean and space to specify the location of emitter.   The methods, principles and technologies of different space electronic reconnaissance localization systems are introduced in this book, as are their performances, and the various methods are explained and analysed.  Digital simulations illustrate the results.

• Presents the theories and applications of determining the position of an object in space through the use of satellites
• Introduces methods, principles and technologies of localization and tracking in the space electronic reconnaissance system, the localization algorithm and error in satellite system and near space platform system, and the tracking algorithm and error in single satellite-to-satellite tracking system
• Provides the fundamentals, the mathematics, the limitations, the measurements, and systems, of localization with emphasis on defence industry applications

Highly relevant for Engineers working in avionics, radar, communication, navigation and electronic warfare.

Chapters include:- the introduction of space electronic reconnaissance localization technology, knowledge about the satellite orbit and basic terminology of passive localization, single satellite geolocation technology based on direction finding, three-satellite geolocation technology based on time difference of arrival (TDOA), two-satellite geolocation technology based on TDOA and frequency difference of arrival (FDOA), the single satellite localization technology based on kinematics theory, localization principles of near-space platform electronic reconnaissance systems, the orbit determination of single satellite-to-satellite tracking using bearings only(BO) information, the orbit determination of single satellite-to-satellite tracking using bearings and frequency information, the orbit determination of single satellite-to-satellite tracking using frequency only(FO) information. Each chapter ends with a problem and solution section, some using Matlab code.

Preface xiii

Acknowledgments xv

Acronyms xvii

1 Introduction to Space Electronic Reconnaissance Geolocation 1

1.1 Introduction 1

1.2 An Overview of Space Electronic Reconnaissance Geolocation Technology 3

1.2.1 Geolocation of an Emitter on the Earth 3

1.2.2 Tracking of an Emitter on a Satellite 8

1.2.3 Geolocation by Near-Space Platforms 9

1.3 Structure of a Typical SER System 9

References 11

2 Fundamentals of Satellite Orbit and Geolocation 13

2.1 An Introduction to the Satellite and Its Orbit 13

2.1.1 Kepler’s Three Laws 13

2.1.2 Classification of Satellite Orbits 15

2.2 Orbit Parameters and State of Satellite 18

2.2.1 Orbit Elements of a Satellite 18

2.2.2 Definition of Several Arguments of Perigee and Their Correlations 20

2.3 Definition of Coordinate Systems and Their Transformations 21

2.3.1 Definition of Coordinate Systems 21

2.3.2 Transformation between Coordinate Systems 25

2.4 Spherical Model of the Earth for Geolocation 27

2.4.1 Regular Spherical Model for Geolocation 27

2.4.2 Ellipsoid Model of the Earth 27

2.5 Coverage Area of a Satellite 30

2.5.1 Approximate Calculation Method for the Coverage Area 30

2.5.2 Examples of Calculation of the Coverage Area 31

2.5.3 Side Reconnaissance Coverage Area 33

2.6 Fundamentals of Geolocation 33

2.6.1 Spatial Geolocation Plane 34

2.6.2 Spatial Line of Position (LOP) 34

2.7 Measurement Index of Geolocation Errors 38

2.7.1 General Definition of Error 38

2.7.2 Geometrical Dilution of Precision (GDOP) 40

2.7.3 Graphical Representation of the Geolocation Error 40

2.7.4 Spherical Error Probability (SEP) and Circular Error Probability (cep) 41

2.8 Observability Analysis of Geolocation 44

References 45

3 Single-Satellite Geolocation System Based on Direction Finding 47

3.1 Direction Finding Techniques 47

3.1.1 Amplitude Comparison DF Technique 48

3.1.2 Interferometer DF Technique 49

3.1.3 Array-Based DF Technique 55

3.1.4 Other DF Techniques 57

3.2 Single-Satellite LOS Geolocation Method and Analysis 57

3.2.1 Model of LOS Geolocation 57

3.2.2 Solution of LOS Geolocation 59

3.2.3 CRLB of the LOS Geolocation Error 60

3.2.4 Simulation and Analysis of the LOS Geolocation Error 62

3.2.5 Geometric Distribution of the LOS Geolocation Error 63

3.3 Multitimes Statistic LOS Geolocation 64

3.3.1 Single-Satellite Multitimes Triangulation 65

3.3.2 Average for Single-Satellite Multitimes Geolocation 66

3.3.3 Weighted Average for Single-Satellite Multitimes Geolocation 67

3.3.4 Simulation of Single-Satellite LOS Geolocation 67

3.4 Single HEO Satellite LOS Geolocation 73

3.4.1 Analysis of Single GEO Satellite LOS Geolocation 73

3.4.2 Geosynchronous Satellite Multitimes LOS Geolocation 74

References 77

4 Multiple Satellites Geolocation Based on TDOA Measurement 79

4.1 Three-Satellite Geolocation Based on a Regular Sphere 80

4.1.1 Three-Satellite Geolocation Solution Method 80

4.1.2 Multisatellite TDOA Geolocation Method 82

4.1.3 CRLB of a Multisatellite TDOA Geolocation Error 85

4.1.4 Osculation Error of the Spherical Earth Model 86

4.2 Three-Satellite Geolocation Based on the WGS-84 Earth Surface Model 88

4.2.1 Analytical Method 89

4.2.2 Spherical Iteration Method 92

4.2.3 Newton Iteration Method 94

4.2.4 Performance Comparison among the Three Solution Methods 96

4.2.5 Altitude Input Location Algorithm 100

4.3 Ambiguity and No-Solution Problems of Geolocation 102

4.3.1 Ambiguity Problem of Geolocation 102

4.3.2 No-Solution Problem of Geolocation 106

4.4 Error Analysis of Three-Satellite Geolocation 109

4.4.1 Analysis of the Random Geolocation Error 109

4.4.2 Analysis of Bias Caused by Altitude Assumption 112

4.4.3 Influence of Change of the Constellation Geometric Configuration on GDOP 114

4.5 Calibration Method of the Three-Satellite TDOA Geolocation System 117

4.5.1 Four-Station Calibration Method and Analysis 117

4.5.2 Three-Station Calibration Method 125

References 130

5 Dual-Satellite Geolocation Based on TDOA and FDOA 133

5.1 Introduction of TDOA–FDOA Geolocation by a Dual-Satellite 133

5.1.1 Explanation of Dual-Satellite Geolocation Theory 133

5.1.2 Structure of Dual-Satellite TDOA–FDOA Geolocation System 134

5.2 Dual LEO Satellite TDOA–FDOA Geolocation Method 136

5.2.1 Geolocation Model 136

5.2.2 Solution Method of Algebraic Analysis 138

5.2.3 Approximate Analytical Method for Same-Orbit Satellites 141

5.2.4 Method for Eliminating an Ambiguous Geolocation Point 143

5.3 Error Analysis for TDOA–FDOA Geolocation 144

5.3.1 Analytic Method for the Geolocation Error 144

5.3.2 GDOP of the Dual LEO Satellite Geolocation Error 146

5.3.3 Analysis of Various Factors Influencing GDOP 151

5.4 Dual HEO Satellite TDOA–FDOA Geolocation 152

5.4.1 Dual Geosynchronous Orbit Satellites TDOA–FDOA Geolocation 152

5.4.2 Calibration Method Based on Reference Sources 155

5.4.3 Calibration Method Using Multiple Reference Sources 159

5.4.4 Flow of Calibration and Geolocation 164

5.5 Method of Measuring TDOA and FDOA 165

5.5.1 The Cross-Ambiguity Function 165

5.5.2 Theoretical Analysis on the TDOA–FDOA Measurement Performance 166

5.5.3 Segment Correlation Accumulation Method for CAF Computation 168

5.5.4 Resolution of Multiple Signals of the Same Time and Same Frequency 172

References 174

6 Single-Satellite Geolocation System Based on the Kinematic Principle 177

6.1 Single-Satellite Geolocation Model 177

6.2 Single-Satellite Single-Antenna Frequency-Only Based Geolocation 179

6.2.1 Frequency-Only Based Geolocation Method 179

6.2.2 Analysis of the Geolocation Error 180

6.2.3 Analysis of the Frequency-Only Based Geolocation Error 181

6.3 Single-Satellite Geolocation by the Frequency Changing Rate Only 183

6.3.1 Model of Geolocation by the Frequency Changing Rate Only 183

6.3.2 CRLB of the Geolocation Error 185

6.3.3 Geolocation Simulation 186

6.4 Single-Satellite Single-Antenna TOA-Only Geolocation 186

6.4.1 Model and Method of TOA-Only Geolocation 186

6.4.2 Analysis of the Geolocation Error 189

6.4.3 Geolocation Simulation 192

6.5 Single-Satellite Interferometer Phase Rate of Changing-Only Geolocation 192

6.5.1 Geolocation Model 192

6.5.2 Geolocation Algorithm 195

6.5.3 CRLB of the Geolocation Error 196

6.5.4 Calculation Analysis of the Geolocation Error 197

References 201

7 Geolocation by Near-Space Platforms 203

7.1 An Overview of Geolocation by Near-Space Platforms 203

7.1.1 Near-Space Platform Overview 203

7.1.2 Geolocation by the Near-Space Platform 204

7.2 Multiplatform Triangulation 204

7.2.1 Theory of 2D Triangulation 204

7.2.2 Error Analysis for Dual-Station Triangulation 205

7.2.3 Optimal Geometric Configuration of Observers 207

7.3 Multiplatform TDOA Geolocation 211

7.3.1 Theory of Multiplatform TDOA Geolocation 211

7.3.2 2D TDOA Geolocation Algorithm 212

7.3.3 TDOA Geolocation Using the Altitude Assumption 215

7.3.4 3D TDOA Geolocation Algorithm 215

7.4 Localization Theory by a Single Platform 217

7.4.1 Measurement Model of Localization 218

7.4.2 A 2D Approximate Localization Method 219

7.4.3 MGEKF (Modified Gain Extended Kalman Filter) Localization Method 221

7.4.4 Simulation 223

References 225

8 Satellite-to-Satellite Passive Orbit Determination by Bearings Only 227

8.1 Introduction 227

8.2 Model and Method of Bearings-Only Passive Tracking 227

8.2.1 Mathematic Model in the Case of the Two-Body Problem 228

8.2.2 Tracking Method in the Case of the Two-Body Model 229

8.2.3 Mathematical Model Considering J₂ Perturbation of Earth Oblateness 232

8.2.4 Tracking Method Considering J₂ Perturbation of Earth Oblateness 233

8.3 System Observability Analysis 235

8.3.1 Description Method for System Observability 235

8.3.2 Influence of Factors on the State Equation 236

8.3.3 Influence of Factors on the Measurement Equation 237

8.4 Tracking Simulation and Analysis 239

8.4.1 Simulation in the Case of the Two-Body Model 241

8.4.2 Simulation Considering J₂ Perturbation of Earth Oblateness 251

8.5 Summary 258

References 259

9 Satellite-to-Satellite Passive Tracking Based on Angle and Frequency Information 261

9.1 Introduction of Passive Tracking 261

9.2 Tracking Model and Method 262

9.2.1 Mathematic Model in the Case of the Two-Body Model 262

9.2.2 Tracking Method in the Case of the Two-Body Model 263

9.2.3 Mathematical Models Considering J₂ Perturbation of Earth Oblateness 266

9.2.4 Tracking Method Considering J₂ Perturbation of Earth Oblateness 267

9.3 System Observability Analysis 268

9.3.1 Influence of Factors of the State Equation 269

9.3.2 Influence of Factors of the Measurement Equation 269

9.4 Simulation and Its Analysis 277

9.4.1 Simulation in the Case of the Two-Body Model 278

9.4.2 Simulation Considering J₂ Perturbation of Earth Oblateness 296

9.5 Summary 308

References 309

10 Satellite-to-Satellite Passive Orbit Determination Based on Frequency Only 311

10.1 The Theory and Mathematical Model of Passive Orbit Determination Based on Frequency Only 313

10.1.1 The Theory of Orbit Determination Based on Frequency Only 313

10.1.2 The System Model in the Case of the Two-Body Model 313

10.1.3 The System Model for J₂ Perturbation of Earth Oblateness 315

10.2 Satellite-to-Satellite Passive Orbit Determination Based on PSO and Frequency 317

10.2.1 Introduction of Particle Swarm Optimization (PSO) 317

10.2.2 Orbit Determination Method Based on the PSO Algorithm 319

10.3 System Observability Analysis 320

10.3.1 Simulation Scenario 1 322

10.3.2 Simulation Scenario 2 323

10.3.3 Simulation Scenario 3 325

10.4 CRLB of the Orbit Parameter Estimation Error 329

10.5 Orbit Determination and Tracking Simulation and Its Analysis 333

10.5.1 Simulation in the Case of the Two-Body Model 334

10.5.2 Simulation in the Case of Considering the Perturbation 347

References 348

11 A Prospect of Space Electronic Reconnaissance Technology 349

Appendix Transformation of Orbit Elements, State and Coordinates of Satellites in Two-Body Motion 351

Index 355