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 |  موضوع: كتاب Multi-Sensor Data Fusion with MATLAB الأربعاء 27 أكتوبر 2021, 11:02 pm | |
| 
أخواني في الله
أحضرت لكم كتاب
Multi-Sensor Data Fusion with MATLAB
Jitendra R. Raol
و المحتوى كما يلي :
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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