Multi-Sensor Data Fusion with MATLAB

Multi-Sensor Data Fusion with MATLAB
اسم المؤلف
Jitendra R. Raol
التاريخ
27 أكتوبر 2021
المشاهدات
التقييم
(لا توجد تقييمات)
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Multi-Sensor Data Fusion with MATLAB
Jitendra R. Raol
Contents
Preface . xix
Acknowledgments xxi
Author .xxiii
Contributors . xxv
Introduction .xxvii
Part I: Theory of Data Fusion and Kinematic-Level Fusion
(J. R. Raol, G. Girija, and N. Shanthakumar)

  1. Introduction 3
  2. Concepts and Theory of Data Fusion . 11
    2.1 Models of the Data Fusion Process and Architectures . 11
    2.1.1 Data Fusion Models 13
    2.1.1.1 Joint Directors of Laboratories Model . 13
    2.1.1.2 Modified Waterfall Fusion Model 17
    2.1.1.3 Intelligence Cycle–Based Model 18
    2.1.1.4 Boyd Model . 19
    2.1.1.5 Omnibus Model . 20
    2.1.2 Fusion Architectures 21
    2.1.2.1 Centralized Fusion . 21
    2.1.2.2 Distributed Fusion . 21
    2.1.2.3 Hybrid Fusion . 22
    2.2 Unified Estimation Fusion Models and Other Methods . 23
    2.2.1 Definition of the Estimation Fusion Process . 24
    2.2.2 Unified Fusion Models Methodology 25
    2.2.2.1 Special Cases of the Unified Fusion Models 25
    2.2.2.2 Correlation in the Unified Fusion Models 26
    2.2.3 Unified Optimal Fusion Rules 27
    2.2.3.1 Best Linear Unbiased Estimation Fusion Rules
    with Complete Prior Knowledge . 27
    2.2.3.2 Best Linear Unbiased Estimation Fusion Rules
    without Prior Knowledge . 28
    2.2.3.3 Best Linear Unbiased Estimation Fusion Rules
    with Incomplete Prior Knowledge 28
    2.2.3.4 Optimal-Weighted Least Squares Fusion Rule 28
    2.2.3.5 Optimal Generalized Weighted Least Squares
    Fusion Rule . 29viii Contents
    2.2.4 Kalman Filter Technique as a Data Fuser . 29
    2.2.4.1 Data Update Algorithm . 30
    2.2.4.2 State-Propagation Algorithm . 31
    2.2.5 Inference Methods 32
    2.2.6 Perception, Sensing, and Fusion . 32
    2.3 Bayesian and Dempster–Shafer Fusion Methods 33
    2.3.1 Bayesian Method . 34
    2.3.1.1 Bayesian Method for Fusion of Data from
    Two Sensors 36
    2.3.2 Dempster–Shafer Method . 38
    2.3.3 Comparison of the Bayesian Inference Method and
    the Dempster–Shafer Method . 40
    2.4 Entropy-Based Sensor Data Fusion Approach . 41
    2.4.1 Definition of Information 41
    2.4.2 Mutual Information 43
    2.4.3 Entropy in the Context of an Image . 44
    2.4.4 Image-Noise Index 44
    2.5 Sensor Modeling, Sensor Management, and Information Pooling . 45
    2.5.1 Sensor Types and Classification . 45
    2.5.1.1 Sensor Technology . 46
    2.5.1.2 Other Sensors and their Important Features
    and Usages 48
    2.5.1.3 Features of Sensors 51
    2.5.1.4 Sensor Characteristics . 52
    2.5.2 Sensor Management . 53
    2.5.2.1 Sensor Modeling 55
    2.5.2.2 Bayesian Network Model 58
    2.5.2.3 Situation Assessment Process 58
    2.5.3 Information-Pooling Methods 60
    2.5.3.1 Linear Opinion Pool 60
    2.5.3.2 Independent Opinion Pool . 61
    2.5.3.3 Independent Likelihood Pool . 61
  3. Strategies and Algorithms for Target Tracking and Data
    Fusion . 63
    3.1 State-Vector and Measurement-Level Fusion . 69
    3.1.1 State-Vector Fusion . 70
    3.1.2 Measurement Data–Level Fusion . 71
    3.1.3 Results with Simulated and Real Data Trajectories . 71
    3.1.4 Results for Data from a Remote Sensing Agency with
    Measurement Data–Level Fusion . 72
    3.2 Factorization Kalman Filters for Sensor Data Characterization
    and Fusion 73
    3.2.1 Sensor Bias Errors . 73Contents ix
    3.2.2 Error State-Space Kalman Filter . 75
    3.2.3 Measurement and Process Noise Covariance
    Estimation 76
    3.2.4 Time Stamp and Time Delay Errors . 77
    3.2.5 Multisensor Data Fusion Scheme . 77
    3.2.5.1 UD Filters for Trajectory Estimation . 80
    3.2.5.2 Measurement Fusion . 81
    3.2.5.3 State-Vector Fusion . 82
    3.2.5.4 Fusion Philosophy 82
    3.3 Square-Root Information Filtering and Fusion in
    Decentralized Architecture . 86
    3.3.1 Information Filter 87
    3.3.1.1 Information Filter Concept . 87
    3.3.1.2 Square Root Information Filter Algorithm 88
    3.3.2 Square Root Information Filter Sensor Data Fusion
    Algorithm . 88
    3.3.3 Decentralized Square Root Information Filter . 89
    3.3.4 Numerical Simulation Results 91
    3.4 Nearest Neighbor and Probabilistic Data Association Filter
    Algorithms . 93
    3.4.1 Nearest Neighborhood Kalman Filter . 94
    3.4.2 Probabilistic Data Association Filter 96
    3.4.3 Tracking and Data Association Program for
    Multisensor, Multitarget Sensors . 97
    3.4.3.1 Sensor Attributes 99
    3.4.3.2 Data Set Conversion . 99
    3.4.3.3 Gating in Multisensor, Multitarget 100
    3.4.3.4 Measurement-to-Track Association . 100
    3.4.3.5 Initiation of Track and Extrapolation of Track . 101
    3.4.3.6 Extrapolation of Tracks into Next Sensor Field
    of View . 101
    3.4.3.7 Extrapolation of Tracks into Next Scan . 102
    3.4.3.8 Track Management Process 102
    3.4.4 Numerical Simulation 103
    3.5 Interacting Multiple Model Algorithm for Maneuvering
    Target Tracking . 106
    3.5.1 Interacting Multiple Model Kalman Filter Algorithm 106
    3.5.1.1 Interaction and Mixing . 108
    3.5.1.2 Kalman Filtering 108
    3.5.1.3 Mode Probability Update 109
    3.5.1.4 State Estimate and Covariance Combiner 109
    3.5.2 Target Motion Models .110
    3.5.2.1 Constant Velocity Model 110
    3.5.2.2 Constant Acceleration Model 110x Contents
    3.5.3 Interacting Multiple Model Kalman Filter
    Implementation 111
    3.5.3.1 Validation with Simulated Data . 112
    3.6 Joint Probabilistic Data Association Filter 116
    3.6.1 General Version of a Joint Probabilistic Data
    Association Filter .117
    3.6.2 Particle Filter Sample–Based Joint Probabilistic Data
    Association Filter .119
    3.7 Out-of-Sequence Measurement Processing for Tracking 120
    3.7.1 Bayesian Approach to the Out-of-Sequence
    Measurement Problem . 120
    3.7.2 Out-of-Sequence Measurement with Single Delay and
    No Clutter 121
    3.7.2.1 Y Algorithm 121
    3.7.2.2 Augmented State Kalman Filters . 122
    3.8 Data Sharing and Gain Fusion Algorithm for Fusion . 124
    3.8.1 Kalman Filter–Based Fusion Algorithm 124
    3.8.2 Gain Fusion–Based Algorithm . 125
    3.8.3 Performance Evaluation . 126
    3.9 Global Fusion and H-Infinity Filter–Based Data Fusion . 127
    3.9.1 Sensor Data Fusion using H-Infinity Filters . 127
    3.9.2 H-Infinity a Posteriori Filter–Based Fusion
    Algorithm . 130
    3.9.3 H-Infinity Global Fusion Algorithm 131
    3.9.4 Numerical Simulation Results 132
    3.10 Derivative-Free Kalman Filters for Fusion 134
    3.10.1 Derivative-Free Kalman Filters . 136
    3.10.2 Numerical Simulation 137
    3.10.2.1 Initialization of the Data Fusion-Derivative
    Free Kalman Filter Algorithm 140
    3.10.2.2 Computation of the Sigma Points 140
    3.10.2.3 State and Covariance Propagation 141
    3.10.2.4 State and Covariance Update 141
    3.11 Missile Seeker Estimator 143
    3.11.1 Interacting Multiple Model–Augmented Extended
    Kalman Filter Algorithm . 143
    3.11.1.1 State Model 144
    3.11.1.2 Measurement Model 145
    3.11.2 Interceptor–Evader Engagement Simulation 146
    3.11.2.1 Evader Data Simulation . 147
    3.11.3 Performance Evaluation of Interacting
    Multiple Model–Augmented Extended
    Kalman Filter . 147
    3.12 Illustrative Examples 151Contents xi
  4. Performance Evaluation of Data Fusion Systems,
    Software, and Tracking . 157
    4.1 Real-Time Flight Safety Expert System Strategy 160
    4.1.1 Autodecision Criteria 161
    4.1.2 Objective of a Flight Test Range 161
    4.1.3 Scenario of the Test Range 161
    4.1.3.1 Tracking Instruments .162
    4.1.3.2 Data Acquisition . 163
    4.1.3.3 Decision Display System . 163
    4.1.4 Multisensor Data Fusion System 163
    4.1.4.1 Sensor Fusion for Range Safety Computer 164
    4.1.4.2 Algorithms for Fusion . 164
    4.1.4.3 Decision Fusion 165
    4.2 Multisensor Single-Target Tracking . 166
    4.2.1 Hierarchical Multisensor Data Fusion Architecture and
    Fusion Scheme . 166
    4.2.2 Philosophy of Sensor Fusion . 168
    4.2.3 Data Fusion Software Structure . 169
    4.2.3.1 Fusion Module 1 . 169
    4.2.3.2 Fusion Modules 2 and 3 169
    4.2.4 Validation . 170
    4.3 Tracking of a Maneuvering Target—Multiple-Target
    Tracking Using Interacting Multiple Model Probability Data
    Association Filter and Fusion 171
    4.3.1 Interacting Multiple Model Algorithm 171
    4.3.1.1 Automatic Track Formation 171
    4.3.1.2 Gating and Data Association 172
    4.3.1.3 Interaction and Mixing in Interactive Multiple
    Model Probabilistic Data Association Filter . 174
    4.3.1.4 Mode-Conditioned Filtering 174
    4.3.1.5 Probability Computations . 175
    4.3.1.6 Combined State and Covariance Prediction
    and Estimation . 176
    4.3.2 Simulation Validation . 177
    4.3.2.1 Constant Velocity Model . 177
    4.3.2.2 Constant Acceleration Model . 178
    4.3.2.3 Performance Evaluation and Discussions 179
    4.4 Evaluation of Converted Measurement and Modified
    Extended Kalman Filters . 183
    4.4.1 Error Model Converted Measurement Kalman Filter
    and Error Model Modifi ed Extended Kalman Filter
    Algorithms . 184
    4.4.1.1 Error Model Converted Measurement Kalman
    Filter Algorithm 185xii Contents
    4.4.1.2 Error Model Modified Extended Kalman Filter
    Algorithm 186
    4.4.2 Discussion of Results 189
    4.4.2.1 Sensitivity Study on Error Model Modified
    Extended Kalman Filter 191
    4.4.2.2 Comparison of Debiased Converted
    Measurements Kalman Filter, Error Model
    Converted Measurement Kalman Filter, and
    Error Model Modifi ed Extended Kalman Filter
    Algorithms 191
    4.5 Estimation of Attitude Using Low-Cost Inertial Platforms and
    Kalman Filter Fusion 193
    4.5.1 Hardware System 195
    4.5.2 Sensor Modeling . 195
    4.5.2.1 Misalignment Error Model . 196
    4.5.2.2 Temperature Drift Model 196
    4.5.2.3 CG Offset Model 196
    4.5.3 MATLAB®/Simulink Implementation . 196
    4.5.3.1 State Model 197
    4.5.3.2 Measurement Model 198
    4.5.4 Microcontroller Implementation 200
    Epilogue . 203
    Exercises 203
    References 206
    Part II: Fuzzy Logic and Decision Fusion
    (J. R. Raol and S. K. Kashyap)
  5. Introduction 215
  6. Theory of Fuzzy Logic 217
    6.1 Interpretation and Unification of Fuzzy Logic Operations 218
    6.1.1 Fuzzy Sets and Membership Functions 218
    6.1.2 Types of Fuzzy Membership Functions 220
    6.1.2.1 Sigmoid-Shaped Function . 220
    6.1.2.2 Gaussian-Shaped Function . 220
    6.1.2.3 Triangle-Shaped Function 222
    6.1.2.4 Trapezoid-Shaped Function 222
    6.1.2.5 S-Shaped Function . 222
    6.1.2.6 Π-Shaped Function 224
    6.1.2.7 Z-Shaped Function . 224
    6.1.3 Fuzzy Set Operations . 225
    6.1.3.1 Fuzzy Logic Operators 226Contents xiii
    6.1.4 Fuzzy Inference System . 227
    6.1.4.1 Triangular Norm or T-norm . 228
    6.1.4.2 Fuzzy Implication Process Using T-norm 232
    6.1.4.3 Triangular Conorm or S-norm . 239
    6.1.4.4 Fuzzy Inference Process Using S-norm 240
    6.1.5 Relationships between Fuzzy Logic Operators 247
    6.1.6 Sup (max)–Star (T-norm) Composition 248
    6.1.6.1 Maximum–Minimum Composition
    (Mamdani) . 249
    6.1.6.2 Maximum Product Composition (Larsen) . 250
    6.1.7 Interpretation of the Connective “and” 250
    6.1.8 Defuzzification 251
    6.1.8.1 Centroid Method, or Center of Gravity or
    Center of Area . 251
    6.1.8.2 Maximum Decomposition Method . 252
    6.1.8.3 Center of Maxima or Mean of Maximum . 252
    6.1.8.4 Smallest of Maximum . 253
    6.1.8.5 Largest of Maximum . 253
    6.1.8.6 Height Defuzzification 253
    6.1.9 Steps of the Fuzzy Inference Process . 253
    6.2 Fuzzy Implication Functions 255
    6.2.1 Fuzzy Implication Methods 255
    6.2.2 Comparative Evaluation of the Various Fuzzy
    Implication Methods s with Numerical Data . 264
    6.2.3 Properties of Fuzzy If-Then Rule Interpretations 265
    6.3 Forward- and Backward-Chain Logic Criteria 266
    6.3.1 Generalization of Modus Ponens Rule 266
    6.3.2 Generalization of Modus Tollens Rule . 267
    6.4 Tool for the Evaluation of Fuzzy Implication Functions . 268
    6.4.1 Study of Criteria Satisfaction Using MATLAB®
    Graphics . 268
    6.5 Development of New Implication Functions 275
    6.5.1 Study of Criteria Satisfaction by New Implication
    Function Using MATLAB and GUI Tools . 278
    6.6 Fuzzy Logic Algorithms and Final Composition
    Operations 281
    6.7 Fuzzy Logic and Fuzzy Integrals in Multiple Network
    Fusion . 289
  7. Decision Fusion 293
    7.1 Symbol- or Decision-Level Fusion 293
    7.2 Soft Decisions in Kalman Filtering 296
    7.3 Fuzzy Logic–Based Kalman Filter and Fusion Filters . 297
    7.3.1 Fuzzy Logic–Based Process and Design . 298xiv Contents
    7.3.2 Comparison of Kalman Filter and Fuzzy
    Kalman Filter . 299
    7.3.3 Comparison of Kalman Filter and Fuzzy Kalman
    Filter for Maneuvering Target Tracking 301
    7.3.3.1 Training Set and Check-Set Data . 301
    7.3.3.2 Mild and Evasive Maneuver Data . 302
    7.3.4 Fuzzy Logic–Based Sensor Data Fusion 303
    7.3.4.1 Kalman Filter Fuzzification 304
    7.3.4.2 Fuzzy Kalman Filter Fuzzification 306
    7.3.4.3 Numerical Simulation Results . 307
    7.4 Fuzzy Logic in Decision Fusion 308
    7.4.1 Methods Available to Perform Situation
    Assessments 310
    7.4.2 Comparison between Bayesian Network
    and Fuzzy Logic 310
    7.4.2.1 Situation Assessment Using Fuzzy Logic .311
    7.4.3 Level-3 Threat Refinement and Level-4 Process
    Refinement . 312
    7.4.4 Fuzzy Logic–Based Decision Fusion Systems 313
    7.4.4.1 Various Attributes and Aspects of Fuzzy
    Logic–Based Decision Fusion Systems 314
    7.5 Fuzzy Logic Bayesian Network for Situation Assessment 316
    7.5.1 Description of Situation Assessment in Air Combat . 317
    7.5.1.1 Exercise Controller . 317
    7.5.1.2 Integrated Sensor Model 318
    7.5.1.3 Data Processor .318
    7.5.1.4 Pilot Mental Model .318
    7.5.2 Bayesian Mental Model .318
    7.5.2.1 Pair Agent Bayesian Network 319
    7.5.2.2 Along Agent Bayesian Network 320
    7.5.2.3 Attack Agent Bayesian Network 320
    7.5.3 Results and Discussions 320
    7.6 Fuzzy Logic–Based Decision Fusion in a Biometric System 321
    7.6.1 Fusion in Biometric Systems . 322
    7.6.2 Fuzzy Logic Fusion . 322
  8. Performance Evaluation of Fuzzy Logic–Based Decision
    Systems 325
    8.1 Evaluation of Existing Fuzzy Implication Functions 325
    8.2 Decision Fusion System 1—Formation Flight . 328
    8.2.1 Membership Functions 329
    8.2.2 Fuzzy Rules and the Fuzzy Implication Method . 330
    8.2.3 Aggregation and Defuzzification Method 330
    8.2.4 Fuzzy Logic–Based Decision Software Realization 330Contents xv
    8.3 Decision Fusion System 2—Air Lane . 331
    8.3.1 Membership Functions 332
    8.3.2 Fuzzy Rules and Other Methods 333
    8.3.3 Fuzzy Logic–Based Decision Software
    Realization for System 2 . 334
    8.4 Evaluation of Some New Fuzzy Implication Functions 334
    8.5 Illustrative Examples 337
    Epilogue . 347
    Exercises 347
    References 351
    Part III: Pixel- and Feature-Level Image Fusion
    (J. R. Raol and V. P. S. Naidu)
  9. Introduction 357
  10. Pixel- and Feature-Level Image Fusion Concepts and
    Algorithms 361
    10.1 Image Registration 361
    10.1.1 Area-Based Matching . 363
    10.1.1.1 Correlation Method . 364
    10.1.1.2 Fourier Method 364
    10.1.1.3 Mutual Information Method 365
    10.1.2 Feature-Based Methods . 365
    10.1.2.1 Spatial Relation . 366
    10.1.2.2 Invariant Descriptors . 366
    10.1.2.3 Relaxation Technique 367
    10.1.2.4 Pyramids and Wavelets . 367
    10.1.3 Transform Model 368
    10.1.3.1 Global and Local Models 368
    10.1.3.2 Radial Basis Functions 368
    10.1.3.3 Elastic Registration 369
    10.1.4 Resampling and Transformation 369
    10.1.5 Image Registration Accuracy 369
    10.2 Segmentation, Centroid Detection, and Target Tracking with
    Image Data . 370
    10.2.1 Image Noise . 370
    10.2.1.1 Spatial Filter 371
    10.2.1.2 Linear Spatial Filters 372
    10.2.1.3 Nonlinear Spatial Filters . 372
    10.2.2 Metrics for Performance Evaluation 373
    10.2.2.1 Mean Square Error . 373
    10.2.2.2 Root Mean Square Error . 373
    10.2.2.3 Mean Absolute Error . 373xvi Contents
    10.2.2.4 Percentage Fit Error 373
    10.2.2.5 Signal-to-Noise Ratio 374
    10.2.2.6 Peak Signal-to-Noise Ratio 374
    10.2.3 Segmentation and Centroid Detection Techniques 374
    10.2.3.1 Segmentation .374
    10.2.3.2 Centroid Detection . 376
    10.2.4 Data Generation and Results . 377
    10.2.5 Radar and Imaging Sensor Track Fusion 378
    10.3 Pixel-Level Fusion Algorithms . 380
    10.3.1 Principal Component Analysis Method 380
    10.3.1.1 Principal Component Analysis Coefficients 382
    10.3.1.2 Image Fusion . 382
    10.3.2 Spatial Frequency 383
    10.3.2.1 Image Fusion by Spatial Frequency 384
    10.3.2.2 Majority Filter . 384
    10.3.3 Performance Evaluation . 385
    10.3.3.1 Results and Discussion . 387
    10.3.3.2 Performance Metrics When No Reference
    Image Is Available 390
    10.3.4 Wavelet Transform 394
    10.3.4.1 Fusion by Wavelet Transform . 398
    10.3.4.2 Wavelet Transforms for Similar Sensor Data
    Fusion . 398
    10.4 Fusion of Laser and Visual Data . 400
    10.4.1 3D Model Generation . 400
    10.4.2 Model Evaluation 402
    10.5 Feature-Level Fusion Methods . 402
    10.5.1 Fusion of Appearance and Depth Information 403
    10.5.2 Stereo Face Recognition System 404
    10.5.2.1 Detection and Feature Extraction 405
    10.5.2.2 Feature-Level Fusion Using Hand and Face
    Biometrics 406
    10.5.3 Feature-Level Fusion 407
    10.5.3.1 Feature Normalization 407
    10.5.3.2 Feature Selection 407
    10.5.3.3 Match Score Generation 408
    10.6 Illustrative Examples 408
  11. Performance Evaluation of Image-Based Data Fusion Systems . 415
    11.1 Image Registration and Target Tracking . 415
    11.1.1 Image-Registration Algorithms 415
    11.1.1.1 Sum of Absolute Differences 415
    11.1.1.2 Normalized Cross Correlation . 417
    11.1.2 Interpolation 418
    11.1.3 Data Simulation and Results . 420Contents xvii
    11.2 3D Target Tracking with Imaging and Radar Sensors 429
    11.2.1 Passive Optical Sensor Mathematical Model 430
    11.2.2 State-Vector Fusion for Fusing IRST and
    Radar Data . 431
    11.2.2.1 Application of Extended KF . 432
    11.2.2.2 State-Vector Fusion . 433
    11.2.3 Numerical Simulation 435
    11.2.4 Measurement Fusion 437
    11.2.4.1 Measurement Fusion 1 Scheme 437
    11.2.4.2 Measurement Fusion 2 Scheme 439
    11.2.5 Maneuvering Target Tracking 440
    11.2.5.1 Motion Models 441
    11.2.5.2 Measurement Model 442
    11.2.5.3 Numerical Simulation . 442
    11.3 Target Tracking with Acoustic Sensor Arrays and Imaging
    Sensor Data 448
    11.3.1 Tracking with Multiple Acoustic Sensor Arrays 448
    11.3.2 Modeling of Acoustic Sensors . 449
    11.3.3 DoA Estimation . 451
    11.3.4 Target-Tracking Algorithms 453
    11.3.4.1 Digital Filter 455
    11.3.4.2 Triangulation 455
    11.3.4.3 Results and Discussion . 455
    11.3.5 Target Tracking . 457
    11.3.5.1 Joint Acoustic-Image Target Tracking . 459
    11.3.5.2 Decentralized KF . 460
    11.3.5.3 3D Target Tracking . 463
    11.3.6 Numerical Simulation 465
    Epilogue . 471
    Exercises 471
    References .474
    Part IV: A Brief on Data Fusion in Other Systems
    (A. Gopal and S. Utete)
  12. Introduction: Overview of Data Fusion in Mobile Intelligent
    Autonomous Systems 479
    12.1 Mobile Intelligent Autonomous Systems 479
    12.2 Need for Data Fusion in MIAS . 481
    12.3 Data Fusion Approaches in MIAS 482
  13. Intelligent Monitoring and Fusion 485
    13.1 The Monitoring Decision Problem . 485
    13.2 Command, Control, Communications, and Configuration 488xviii Contents
    13.3 Proximity- and Condition-Monitoring Systems . 488
    Epilogue . 491
    Exercises 492
    References 492
    Appendix: Numerical, Statistical, and Estimation Methods . 495
    A.1 Some Definitions and Concepts 495
    A.1.1 Autocorrelation Function . 495
    A.1.2 Bias in Estimate . 496
    A.1.3 Bayes’ Theorem . 496
    A.1.4 Chi-Square Test . 496
    A.1.5 Consistency of Estimates Obtained from Data 496
    A.1.6 Correlation Coefficients and Covariance 497
    A.1.7 Mathematical Expectations . 497
    A.1.8 Efficient Estimators . 498
    A.1.9 Mean-Squared Error (MSE) . 498
    A.1.10 Mode and Median . 498
    A.1.11 Monte Carlo Data Simulation 498
    A.1.12 Probability 499
    A.2 Decision Fusion Approaches . 499
    A.3 Classifier Fusion 500
    A.3.1 Classifier Ensemble Combining Methods . 501
    A.3.1.1 Methods for Creating Ensemble Members 501
    A.3.1.2 Methods for Combining Classifiers in Ensembles . 501
    A.4 Wavelet Transforms 502
    A.5 Type-2 Fuzzy Logic . 504
    A.6 Neural Networks 505
    A.6.1 Feed-Forward Neural Networks 506
    A.6.2 Recurrent Neural Networks 508
    A.7 Genetic Algorithm 508
    A.7.1 Chromosomes, Populations, and Fitness 509
    A.7.2 Reproduction, Crossover, Mutation, and Generation 509
    A.8 System Identification and Parameter Estimation . 509
    A.8.1 Least-Squares Method 510
    A.8.2 Maximum Likelihood and Output Error Methods .511
    A.9 Reliability in Information Fusion 516
    A.9.1 Bayesian Method . 518
    A.9.1.1 Weighted Average Methods 518
    A.9.2 Evidential Methods 518
    A.9.3 Fuzzy Logic–Based Possibility Approach . 519
    A.10 Principal Component Analysis . 519
    A.11 Reliability . 520
    References 520
    Index .
    Index
    A
    Absolute errors, 425–427, 429
    Acceleration estimates, 445
    Acceleration profiles, 112–113
    Acoustic target, tracking schemes
    for, 449
    Active sensors, 45
    Adaptive sampling systems, 489
    AEKF algorithm, see Augmented
    extended Kalman filter
    algorithm
    Aggregation process, 289, 330
    Air combat (AC), situation assessment
    in, 316, 317–318
    ALEX system, 193, 194
    Alignment errors, 369
    Along agent BNW (AAN) model, 320
    Angular coordinates, 430, 431
    Area-based matching (ABM), 363–365
    Arithmetic rule of fuzzy implication
    (ARFI), 325
    Artificial intelligence (AI), 15, 217
    Artificial neural networks (ANN), 310,
    505–506
    Attack agent BNW (AtAN) model, 320
    Augmented extended Kalman filter
    (AEKF) algorithm
    IMM, 143–146
    performance evaluation of,
    147–150
    Augmented state Kalman filters, 122
    Autocorrelation function, 495–496
    B
    Backward chain inference rule, 266
    Backward chain logic criteria, 266–268
    Bayes’ classifier, 290, 500
    Bayesian approach to OOSMs
    problem, 120–121
    Bayesian filtering, 118
    Bayesian inference method (BIM), 32,
    40–41
    Bayesian mental model, 318–320
    Bayesian method, 33, 34–36, 518
    for data fusion from two sensors,
    36–38
    vs. DS method, 40–41
    Bayesian network (BNW)
    model, 57, 58, 59, 60
    vs. fuzzy logic, 310
    Bayes’ rule, 32, 34–36
    Bayes’ theorem, 35, 496
    Best linear unbiased estimation
    (BLUE) fusion rules, 27, 28
    Bias errors, 73–75
    Bias in estimate, 496
    BIM, see Bayesian inference method
    Binary neuron, 506
    Biological neural networks
    (BNNs), 505
    Biometrics, feature-level fusion
    methods using, 406–407
    Biometric system, 321–323
    BNW, see Bayesian network
    Boolean rule of fuzzy implication
    (BRFI), 325
    Boyd control cyclic loop (BCL) model,
    19, 20
    C
    Cartesian coordinates, trajectory of
    target in, 457–458, 465
    Cartesian product (CP), 232, 240
    CDT algorithm, see Centroid detection
    and tracking algorithm
    Center of maxima technique, 252
    Centralized fusion, 21, 24, 29
    Centroid detection and tracking
    (CDT) algorithm, 370, 371524 Index
    Centroid detection techniques,
    376–377
    Centroid method, 251–252
    Chi-square test, 496
    Classifier ensemble members,
    methods for creating, 501
    Classifier fusion, 500–502
    Classifiers, combining methods in
    ensembles, 501
    CMKF, see Converted
    measurements Kalman filter
    Cognitive-refinement, 16
    Color transformation (CT)
    method, 358
    Command, control, and
    communication theory, 488
    Competitive sensor network, 12–13
    Complementary sensor network,
    11–12
    Composite operations, 281, 289
    Condition-monitoring, 485, 488–490
    Consistent estimates of data,
    496–497
    Constant acceleration model (CAM),
    110–111, 178–179, 299–300,
    435, 465
    Constant velocity (CV) model, 110,
    177–178, 441–442, 457
    Contact-state sensors (CSSs), 46
    Continuous wavelet transform
    (CWT), differences in
    STFT, 503
    Converted measurements Kalman
    filter (CMKF)
    debiased, 191
    evaluation of, 183
    Cooperative sensor network, 12, 13
    Correlation coefficients, defined, 497
    Correlation method, 364
    Covariance, defined, 497
    Covariance matrices, 73
    computing, 434
    norms of, 152, 154, 155
    Covariance propagation, 141
    Cramer–Rao (CR) lower bound,
    512, 513
    Crisp set, membership functions of,
    218–219
    Cross-entropy, 393
    CWT, see Continuous wavelet
    transform
    D
    Data association (DA), 23, 50, 64, 67
    Data compression, 420
    Data fusion (DF)
    applications in manufacturing,
    8–9
    architectures, 21–22
    conceptual chain of, 12
    methods, 23, 24
    in MIAS, 481–484
    models, 13
    process and taxonomy, 23
    sensor networks, 11–13
    wavelet transform for sensor,
    398–400
    Data processor (DP), 318
    Data set conversion, 99
    Data sharing, 126–127
    Data simulation (DS), 301–302
    for maneuvering target, 112–114
    using PC-MATLAB®, 420
    Data update algorithm, 30–31
    Dead-reckoning errors, 481
    Debiased converted measurements
    Kalman filter (CMKF-D), 191,
    192, 193
    Decentralized fusion networks,
    merits of, 86
    Decentralized square root
    information filter (SRIF),
    89–91
    Decision accuracy (DA), 41
    Decision fusion, 293–296
    algorithm, 358
    in biometric systems, 321–323
    fuzzy logic in, 308
    method, 499–500
    rule, 519
    Decision fusion systems (DFS),
    313–316
    air lane, 331–334
    formation flight, 328–331
    Decision making, 486, 487Index 525
    Decision problem, 485–487
    Decision process, 293
    Defuzzification, 251–253, 306, 331
    Delta-4 aircraft, specifications
    for, 341
    Dempster–Shafer (DS) method, 34, 38,
    518–519
    fusion rule, 39
    vs. BIM, 40–41
    Derivative-free Kalman filters
    (DFKF), 134–137, 140
    DFS, see Decision fusion systems
    Differential GPS (DGPS), 48
    Direction of arrival (DoA) estimation,
    449, 451–453
    Distributed fusion, 21, 22, 24
    DoA, see Direction of arrival
    Doppler effect, 49
    DS, see Data simulation
    DS method, see Dempster–Shafer
    method
    Dynamic world modeling (DWM), 33
    E
    Earth-centered, earth-fixed (ECEF)
    frame, 74–75
    East-North-Vertical (ENV) frame,
    74–75
    ECMKF algorithm, see Error model
    converted measurement KF
    algorithm
    Efficient estimator, 498
    EKF, see Extended Kalman filters
    Elastic registration method, 369
    Electronically scanned antennae
    (ESA) radars, 67
    Electro-optical tracking systems
    (EOTs), 52, 83
    Embedded MATLAB–based fuzzy
    implication method
    (EMFIM), 335
    EMEKF algorithm, see Error model
    modified extended KF
    algorithm
    EM-induction (EMI) sensor, 50
    ENSS, see External navigational state
    sensors
    Entropy, 392
    Entropy-based sensor data fusion
    approach, 41
    image information, 44
    image-noise index, 44–45
    information, 41–43
    mutual information, 43–44
    Error covariance time
    propagation, 80
    Error model converted measurement
    Kalman filter (ECMKF)
    algorithm, 184–186, 193
    features of, 192
    performance of, 190–191
    Error model Kalman filter (EMKF),
    185–186
    Error model modified extended
    Kalman filter (EMEKF)
    algorithm, 186–189, 193
    features of, 192
    performance of, 190–191
    sensitivity study on, 191
    Error-state Kalman filter (ESKF)
    formulation for estimating
    bias errors, 73
    Error state-space Kalman filter,
    75–76
    Estimate error, 149
    Estimation fusion (EF), 21; see also
    Unified fusion models
    process, definition of, 24–25
    rules, 27–29
    Estimator filter, 143
    Evader data simulation, 147
    Evasive maneuver (EM) data,
    302–303
    Event detector (ED), 314
    Exercise controller (EC), 317–318
    Exponential mixture density (EMD)
    models, 483
    Extended Kalman filters (EKF),
    183–184, 194, 296
    application of, 432–433
    limitations, 134–135
    Exterioceptive sensors, 481
    External navigational state sensors
    (ENSS), 47–48
    Extrapolation of track, 101–102526 Index
    F
    Face detection, 405
    Feature-based methods, 365–367
    Feature detection, 363, 365
    Feature extraction, 405–406
    Feature-level fusion
    methods, 358, 402–403
    using hand and face biometrics,
    406–407
    Feature matching, 363, 365, 366, 367
    Feature normalization, 407
    Feature selection, 407
    Feed-forward neural networks
    (FFNNs), 506–508
    FIE, see Fuzzy inference engine
    Field of view (FOV) sensor,
    extrapolation of tracks into,
    101–102
    Filter initialization parameters, 147
    FIM, see Fuzzy implication methods
    FIP, see Fuzzy implication process
    Fitness value, 509
    FL, see Fuzzy logic
    FLDS, see Fuzzy logic–based decision
    software
    Flight safety expert system strategy,
    real-time, 160
    autodecision criteria, 161
    decision fusion, 165–166
    flight test range, see Flight test range
    multisensor data fusion system,
    163–165
    Flight test range, 160
    data acquisition, 163
    decision display system, 163
    hierarchical MSDF fusion scheme,
    166–168
    objective of, 161
    tracking instruments, 161, 162
    Flight vehicle
    computation of trajectories of, 160
    decision for termination of, 160, 163
    Forward chain-inference rule, 265
    Forward chain logic criteria, 266–268
    Forward-looking IR (FLIR)
    sensors, 48, 49
    data generation from, 377
    Fourier method, 364
    FOV sensor, see Field of view sensor
    Frequency-domain filtering
    (FDF), 371
    Function approximation (FA), 288–289
    Fusion
    of appearance and depth
    information, 403–404
    of laser and visual data, 400–402
    by wavelet transform, 398
    Fusion covariance matrix, computing,
    434–435
    Fusion equations, 89
    Fusion filters, 297
    H-Infinity norm, 133
    performance evaluation, 126–127
    Fusion processes
    applications, 8–9
    levels of modes, 7
    Fusion quality index (FQI), 393–394
    Fusion similarity metric (FSM), 394
    Fusion state vector, computing,
    434–435
    Fuzzification, 228, 305; see also
    Defuzzification
    Fuzzy complement, 245–246
    Fuzzy composition, 248–250
    Fuzzy disjunction (FD), 240
    Fuzzy engineering, 281, 288
    Fuzzy if-then rule, 265, 288
    Fuzzy implication functions
    and aggregation process, 289
    development of, 275–278
    evaluation of, 325–328, 334–337
    evaluation tool for, 268–274
    rule of, 275–277
    for satisfying GMP and GMT
    criteria, 268, 278–281
    Fuzzy implication methods (FIM),
    215, 216, 255–258, 325
    development of, 275–278
    evaluation using numerical
    data, 264
    menu panel ideas for, 269
    Fuzzy implication process
    (FIP), 228
    standard methods, 256–257
    using T-norm, 232–238Index 527
    Fuzzy inference engine (FIE), 225, 330,
    331, 336
    Fuzzy inference process
    steps, 253–255
    using S-norm, 240–246
    Fuzzy inference system (FIS),
    228, 299
    Fuzzy integrals (FI), 289–291
    Fuzzy Kalman filter (FKF), 297
    fuzzification, 306
    vs. Kalman filter, 299–303
    Fuzzy logic (FL)
    algorithms, 281
    applications, 215
    based on Kalman filters and fusion
    filters, 297
    based on sensor data fusion,
    303–308
    Bayesian network and, 310–312,
    316–321
    controller, 217
    in decision fusion, 308
    and fuzzy integrals, 289–291
    and Kalman filter, 216
    operators, 218, 226–227, 247
    system, 217, 218
    Fuzzy logic–based decision fusion
    systems, 313–316
    Fuzzy logic–based decision software
    (FLDS)
    for air lane, 334, 335
    performance of, 328
    realization, 330–331, 334
    Fuzzy logic–based process (FLP),
    298–299, 301
    Fuzzy logic–based process variable
    (FLPV) vector, 298
    Fuzzy logic possibility method, 519
    Fuzzy measure, 290–291
    Fuzzy membership function (FMF),
    218, 220–225
    Fuzzy rules for aircraft, 330, 333
    Fuzzy sets
    Cartesian product (CP) of, 232
    membership functions of, 218–220,
    329, 332–333
    operations, 225–227
    Fuzzy variable, 219, 288, 322–323
    G
    Gain fusion algorithm, 126–127
    Gating
    in MSMT, 93, 100
    use of, 64
    validation/confirmation
    region, 65
    Gaussian distribution, 421
    Gaussian lease square (GLS)
    method, 512
    Gaussian noise, 147, 371, 375
    Gaussian-shaped function, 220–222
    Gauss Newton method, see Modified
    Newton–Raphson method
    Generalized modus ponens (GMP),
    216, 325, 326
    comparison of, 282–284
    criteria, 265, 268, 278–281
    Generalized modus tollens (GMT),
    126, 265, 325, 327
    comparison of, 285–287
    criteria, 266, 268, 278–281
    Genetic algorithms (GAs), 508–509
    GKF, see Global Kalman filter
    Global fused estimate, 92
    Global Kalman filter (GKF), 460, 461,
    463, 465
    Global positioning systems (GPS), 47,
    73, 184, 193
    Goguen’s rule of fuzzy implication
    (GRFI), 325
    GPS, see Global positioning systems
    Gram–Schmidt orthogonalization
    process, 80
    Graphic user interface (GUI) tools,
    278–281
    Ground-penetrating radars (GPRs), 50
    H
    Height defuzzification, 253
    H-Infinity a posteriori filter-based
    fusion algorithm, 130–131
    H-Infinity filters, sensor data fusion
    using, 127–130
    H-Infinity global fusion algorithm,
    131–132528 Index
    Human-computer interface (HCI),
    15, 17
    Hybrid fusion, 22, 25
    I
    Identity fusion, 16
    IF, see Information fusion
    Image decomposition, 2D, 395–396
    Image fusion
    algorithms, performance
    evaluation of, 385–387,
    390–394
    approaches for, 357
    levels of, 358
    PCA based, 382–383
    by spatial frequency, 384–385
    wavelet transform, 398
    Image noise, 370–372
    Image-noise index (INI), 44–45
    Image registration
    accuracy, 369
    algorithms, 415
    applications, 362
    area-based matching, 363–365
    feature-based methods, 365–367
    methods of, 363
    process, 361
    resampling, 369
    transformation, 369
    transform model, 368–369
    Image restoration, 2D, 397
    Imaging sensor, track fusion, 378
    IMMKF, see Interacting multiple
    model Kalman filter
    IMMPDAF, see Interacting multiple
    model probability data
    association filters
    Independent likelihood pool
    (ILP), 61
    Independent opinion pool, 61
    Inertial measurement units
    (IMUs), 193
    Inference methods (IM), 32, 33
    Information filter (IF), 87–91
    Information fusion (IF), 4, 516–519
    Information-pooling methods,
    60–61
    Information process cycle, 294
    Infrared (IR) sensors, 50, 57
    Infrared search-and-track (IRST)
    sensor
    azimuth and elevation data of,
    442, 443
    simulated measurement, 436, 444
    state-vector fusion for, 431–435
    Innovation sequence, 158–159
    Integrated sensor model, 318
    Intelligence cycle–based (IC) model,
    18–19
    Intelligent monitoring, 485, 489–490
    Intensity spikes, 370
    Interacting multiple model Kalman
    filter (IMMKF)
    algorithm, 106–109
    implementation in MATLAB,
    111–116
    Interacting multiple model
    probability data association
    filters (IMMPDAF), 171
    algorithm
    automatic track formation, 171
    gating and data association,
    172–174
    interaction and mixing, 174
    mode-conditioned filtering,
    174–175
    probability computations,
    175–176
    state estimate and covariance
    prediction, 176–177
    for multiple sensor data fusion,
    180–183
    performance evaluation of,
    179–183
    simulation validation, 177–179
    Interceptor-evader engagement
    simulation, 146–147
    Internal state sensors (ISSs), 46
    Interpolation, 418–419
    Inverse 2D wavelet transform (IWT)
    process, 397
    IRST sensor, see Infrared search-andtrack sensor
    Iterative-end-point-fit (IEPF)
    algorithm, 400Index 529
    J
    JDL fusion model, see Joint
    Directors of Laboratories
    fusion model
    Joint acoustic-image target tracking,
    459–460
    Joint Directors of Laboratories (JDL)
    fusion model, 13–17
    Joint Gaussian random variable, 121
    Joint probabilistic data association
    filter, 116–120
    K
    Kalman filter (KF)
    augmented state, 122
    as Bayesian fusion algorithm, 33
    covariance of, 109
    decentralized, 460–463, 464
    error state-space, 75–76
    fusion algorithm, 124
    and fusion filters, 297
    and fuzzy logic, 216
    as MATLAB S-function, 197
    soft decisions in, 296–297
    state estimate, 64, 109
    technique, 29–32
    vs. fuzzy Kalman filter, 299–303
    Kalman filter fuzzification (KFF),
    304–306
    Kalman gain, 296
    KF, see Kalman filter
    Kinematic fusion, 7, 16, 29, 92
    Kinematic model, 328
    L
    Laplacian pyramids, 359
    Largest of maximum method, 253
    Laser data fusion, 400, 401
    Laser ranging systems, 49
    Least-squares method, 364, 510–511
    Linear measurement models, 461
    Linear opinion pool, 60–61, 500, 518
    Linear spatial filters, 372
    Line-of-sight (LOS) rates, 147
    LKF, see Local Kalman filter
    Localization errors, 369
    Local Kalman filter (LKF), 460, 461, 465
    Logarithmic opinion pools, 518
    M
    MAE, see Mean absolute error
    Maneuver data, 302–303
    Maneuver mode probabilities, 114
    Maneuvering target tracking, 106,
    171, 179
    comparison of KF and FKF for,
    301–303
    models for, 440–442
    Markov chain transition matrix, 111,
    112, 443
    MASAs, see Multiple acoustic sensor
    arrays
    Matching errors, 369
    Mathematical expectation,
    defined, 497
    MATLAB®, 216, 325, 328, 334
    FLDS in, 330
    to satisfy GMP and GMT criteria,
    268, 278–281
    Maximum decomposition method for
    defuzzification, 252
    Maximum likelihood estimation
    (MLE), 511–516
    Maximum product composition, 250
    Max-min composition, 249
    Max-min rule of fuzzy implication
    (MRFI), 325, 328
    Mean absolute error (MAE), 373, 386,
    423, 437, 448
    Mean filter, see Spatial filter
    Mean square error (MSE), 373, 498
    Measurement errors, 149, 511
    Measurement fusion, 81–82,
    437–439
    Measurement level fusion, 69, 71, 72
    Measurement model, 145–146, 442
    Measurement noise covariance,
    estimation of, 76–77
    Measurement-noise variances, 443
    Measurement-to-track association,
    100–101
    Median, 498530 Index
    Median filter, state error
    reduction, 429
    MEKF algorithm, see Modified
    extended Kalman filter
    (MEKF) algorithm
    Membership functions
    for FLP, 298
    of fuzzy sets, 218–220, 329, 332–333
    MIAS, see Mobile intelligent
    autonomous systems
    Microelectrical mechanical sensors
    (MEMS)–based IMU, 193
    Microwave radars, 49, 51
    Mild maneuver (MM) data, 302–303
    Millimeter wave radar (MMWR)
    sensor, 51–52
    Miniaturized inertial platform (MIP)
    attitude estimation using,
    193, 194
    hardware system, 195
    MATLAB/Simulink
    implementation, 196–200
    microcontroller implementation,
    200–202
    sensor modeling, 195–196
    Min-operation rule of fuzzy
    implication (MORFI), 235,
    257, 270–274, 325
    MIP, see Miniaturized inertial
    platform
    Missile seeker estimator, 143
    Mobile intelligent autonomous
    systems (MIAS), data fusion
    in, 479, 481–484
    Mobile robots, 481, 482
    Mode probabilities, 109, 148, 150, 445
    Mode switching process, 108
    Modified extended Kalman filter
    (MEKF) algorithm
    error model, 186–189
    evaluation of, 183–184
    Modified Newton–Raphson
    method, 513
    Modular robotics, 7–8
    Modus ponens rule, 266–267
    Modus tollens rule, 267–268
    Monte Carlo simulation, 142, 437,
    498–499
    Movie parameters, 420
    MSMT sensors, see Multisensor,
    multitarget sensors
    MSST tracking, see Multisensor
    single-target tracking
    Multibiometric systems, levels of,
    406–407
    Multilayer perceptrons
    (MLPNs), 506
    Multiple acoustic sensor arrays
    (MASAs), 448–451
    Multiple network fusion, 289–291
    Multiple-server monitoring, 485
    Multiresolution method (MRM), 359
    Multisensor, multitarget (MSMT)
    sensors, 93–94, 173
    Multisensor imaging fusion
    (MSIF), 380
    Multisensor single-target (MSST)
    tracking, 166
    multisensor data fusion (MSDF)
    architecture, 166–168
    fusion scheme, 166–168
    range limit of sensors, 168
    software structure, 169
    validation of, 170–171
    Multitarget (MTT) system, 67
    Multitarget tracking, 97
    Multivariate polynomial (MP)
    technique, 402, 403
    MUSIC algorithm, 451–453
    Mutual information (MI) method,
    365, 386
    N
    NASA Mars Pathfinder Mission’s
    Sojourner Rover, 8
    Nearest neighborhood Kalman filter
    (NNKF), 68, 94–95
    features of, 99
    numerical simulation,
    103–106
    Network fusion, multiple, 289–291
    Network-monitoring sensor systems,
    489
    NNKF, see Nearest neighborhood
    Kalman filterIndex 531
    Noise
    image, 370–372
    parameters, 420
    variances, 111
    Noise attenuation factors (NAF), 148,
    150
    Non-contact state sensors (NCSSs), 46
    Nondestructive testing (NDT), 8, 9
    Nonlinear spatial filters, 372
    Nonstandard distributed fusion, 27
    Nonvision-based ENSS, 47
    Normalized cross correlation (NCC),
    364, 417–418, 428–429
    Normalized estimation error
    square, 159
    Normalized innovation
    square, 159
    Normalized random noise, 132
    O
    Object refinement (OR), 15–16, 309
    Offline monitoring, 486
    Omnibus (OB) model, 20–21
    Online monitoring, 486
    Optimal generalized weighted least
    squares fusion rule, 29
    Optimal-weighted least squares
    fusion rule, 28
    Order filters (OF), 372
    Out-of-sequence measurements
    (OOSMs) for tracking,
    120–123
    Output error method (OEM),
    511–516
    P
    Pair agent Bayesian network
    (PAN), 319
    Parameter estimation, 509–510
    Parametric sensors, see Active sensors
    Particle filters, 116, 119
    Passive optical sensor, mathematical
    model, 430–431
    Passive sensors, 46
    PCA, see Principal component
    analysis
    PCBSAP, 275, 278–281, 335
    PC MATLAB®
    for data generation, 132,
    151–153, 420
    IMMKF implementation in,
    111–112
    PDAF, see Probabilistic data
    association filter
    Peak signal-to-noise ratio (PSNR), 374,
    386, 391, 392
    Percentage fit errors (PFEs), 133, 373,
    378–380, 385, 423
    calculation, 92
    metrics, 105, 437, 448
    in position, 157
    residual, 126
    for track positions, 105
    of trajectory, 71
    Percentage state errors, 133–135
    Perceptual fusion, 32–33
    PFEs, see Percentage fit errors
    Pilot mental model (PMM), 318
    Pixel coordinates, 430, 431
    Pixel-level fusion, 358, 361, 380
    Point mass models, 328
    Poisson clutter model, 97
    PORFI, see Product-operation rule of
    fuzzy implication
    Principal component analysis (PCA),
    519–520
    based image fusion, 382–383
    of blurred images, 390
    coefficients, 382
    error images by, 388, 389, 392, 393
    fused images by, 388, 389, 392, 393
    PSNR of, 391
    RMSE of, 390
    method, 380–381
    Probabilistic data association filter
    (PDAF), 68, 96–99
    computational steps, 98
    numerical simulation, 103–106
    Probability, defined, 499
    Process noise coefficient matrix, 79
    Process noise covariance, estimation
    of, 76–77
    Process noise gain matrix, 102
    Process noise variance, 443532 Index
    Process refinement (PR), 16, 312–313
    Product-operation rule of fuzzy
    implication (PORFI), 325,
    333, 334
    Propositional calculus standard
    union algebraic product
    (PCSUAP), 337
    Proprioceptive sensors, 49, 481
    Proximity-monitoring systems,
    488–490
    ∏-shaped function, 224
    PSNR, see Peak signal-to-noise ratio
    Pyramids, 359, 367
    R
    Radar, 49, 51
    data, 74
    state-vector fusion for,
    431–435
    measurements, 436, 444
    track fusion, 378–379
    Radar cross section (RCS)
    fluctuation, 147
    Radial basis function (RBF), 368
    Range safety officer (RSO), 160, 167
    Real flight test data, 72
    Recurrent neural networks
    (RNNs), 508
    Reduced multivariate polynomial
    model (RMPM), 403, 404
    Relational matrices, 249, 264
    Relaxation technique, 367
    Reliability
    coefficients, 517, 519
    defined, 520
    in information fusion, 516–519
    Remote sensing agency (RSA) data
    using measurement level
    fusion, 72–73
    RMSE, see Root mean square error
    RMSPE, see Root mean square
    percentage error
    RMSVE, see Root mean square vector
    error
    Robotic system, 479
    Root mean square error (RMSE),
    157–158, 373, 385, 390, 391
    Root mean square error in
    acceleration (RMSAE), 437
    Root mean square percentage error
    (RMSPE), 103, 378, 379, 380
    for data loss in track 1, 105
    performance metrics, 423, 437
    Root mean square vector error
    (RMSVE), 378, 379, 380, 437
    Root-sum-square (RSS) errors, 158
    in acceleration, 438, 445, 446
    in position, 85, 445, 446
    variances, 115, 445, 447
    in velocity, 445, 446
    S
    Salt-and-pepper (SP) noise, 370, 375
    Segmentation, 370, 374–376
    Sensor
    attributes, 99
    characteristics, 52–53
    data fusion, 303–308
    using H-Infinity filters,
    127–130
    wavelet transform for,
    398–400
    features, 48–52
    fusion networks, 11–13, 45
    management, 53–55
    measurement system
    advantages, 5
    problems in, 4–5
    modeling, 55–57
    nodes, 86
    technology, 46–48
    types, 45–46
    usages, 48–50
    Sensor-targets-environment data
    fusion (STEDF), 54
    SF, see Spatial frequency
    Short time Fourier transform (STFT),
    502, 503
    Sigma points, 135, 136, 140–141
    Sigmoid neuron, 506
    Sigmoid-shaped function, 220, 221
    Signal-to-noise ratio (SNR),
    374, 386
    Simulink®, 216, 330, 334Index 533
    Singer–Kanyuck association
    metrics, 105
    Singular value decomposition
    (SVD), 452
    Situation assessment (SA), 315
    in air combat, 316, 317–318
    fuzzy logic Bayesian network for,
    316–321
    methods for, 310
    process, 58–60
    stages of, 308
    using fuzzy logic, 311–312
    Situation refinement, 16
    Smallest of maximum method, 253
    S-norm
    defined, 239
    fuzzy inference process using,
    240–246
    SNR, see Signal-to-noise ratio
    Soft decisions in Kalman filtering,
    296–297
    Software, MSDF, 169
    Spatial-domain filtering (SDF), 371
    Spatial filter, 371–372, 428, 429
    Spatial frequency (SF), 383–384
    error images by, 388, 389, 392, 393
    fused images by, 388, 389, 391,
    392, 393
    image fusion process, 384–385
    Split-and-merge algorithm
    (SAMA), 401
    Square root information filter data
    fusion (SRIFDF) algorithm
    advantage of, 87
    nodes of, 92
    S-shaped function, 222–224
    Standard deviation (STD), 391
    Standard distributed fusion, 25
    Standard fuzzy complement (SFC),
    245–246
    State error, 158
    State-estimate time propagation, 80
    State estimation, 109
    error, 148, 152–155, 424
    using Kalman filter, 151
    State model, 144
    State propagation, 31–32, 141
    State transition matrix, 79
    State-vector fusion (SVF), 7, 69–70,
    82, 297
    for IRST and radar data, 431–435
    simulated data for, 72
    Statistical and numerical (SN)
    approach for pixel-level
    fusion, 358
    Stereo face recognition system,
    404–405
    Sum of absolute differences (SAD),
    415–417, 428–429
    Sup-star composition, 248–250
    Surveillance-system model (SSM), 54,
    56–57
    Switching probabilities, 111
    Symbol-level fusion, see Decision
    fusion
    System identification, 509–510
    T
    Target motion
    models, 69, 79, 110–111
    numerical simulation in position
    of, 91–92
    Target tracking, 63–68, 457–459; see
    also Maneuvering target
    tracking
    3D, 463–464
    joint acoustic-image, 459–460
    with MASAs, 448–449
    motion model for, 432
    performance evaluation for,
    421–422
    using image data, 370
    Target trajectory, simulation of,
    71–72, 442
    Threat assessment (TA), 316
    Threat refinement (TR), 16, 312–313
    3-degrees-of-freedom (DOF)
    kinematic model, see
    Constant acceleration
    model (CAM)
    3D image capture, techniques for, 403
    3D model, 400–402
    3D target tracking, 463–464
    Time delay errors, 77
    Time stamp, 77534 Index
    Time synchronization, 77
    T-norm, 228
    composition, 248–250
    fuzzy implication process using,
    232–238
    Tool failure detection system, 8
    Track
    extrapolation of, 101–102
    initiation, 101
    loss simulation, 105
    management process, 102–103
    Tracking filters, performance of,
    83–84
    Tracking sensors
    classification of, 82
    flight test range, 161, 162
    Track-to-measurement correlation
    matrix (TMCR), 100
    Track-to-track correlation, 69
    Transform domain (TD)
    algorithms, 358
    Trapezoid-shaped function, 222
    Triangle-shaped function, 222
    Triangular conorm, 239
    Triangular norm, see T-norm
    Triangulation, 460, 463
    2-degrees-of-freedom (DOF)
    kinematic model, see
    Constant velocity (CV) model
    Type-2 fuzzy logic, 504
    U
    UD filter
    factorization, 75
    for sensor characterization, 74
    for trajectory estimation, 80–81
    Unified fusion models (UM), 23–27
    Unified optimal fusion rules, 27–29
    Universal quality index, 386–387
    V
    Value of information (VOI), 41, 44
    Velocity estimates, 445
    Vision-based ENSS, 48
    Visual data fusion, 400, 401
    W
    Waterfall fusion process (WFFP)
    model, 17–18
    Wavelet package (WP) method, 359
    Wavelets, 359, 367, 395
    Wavelet transforms (WT), 394–397,
    502–503
    analysis, 395
    image fusion, 398
    package fusion method,
    359, 360
    for sensor data fusion, 398–400
    Weighted average methods, 518
    Weighted least squares (WLS) fusion
    rule, 28, 29
    White noise processes, 130
    WT, see Wavelet transforms
    Y
    Y algorithm, 121–122
    Z
    Z-shaped function, 224–225

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