H.B. Mitchell Multi-Sensor Data Fusion An Introduction With 81 Figures and 59 Tables Springer
Contents Part I Basics 1 Introduction 3 1.1 Definition 3 1.2 Synergy 4 1.3 Multi-Sensor Data Fusion Strategies 5 1.3.1 Fusion Type 5 1.3.2 Sensor Configuration 6 1.3.3 Input/Output Characteristics 6 1.4 Formal Framework 7 1.4.1 Multi-Sensor Integration 9 1.5 Catastrophic Fusion 10 1.6 Organization 12 1.7 Further Reading 13 2 Sensors.' 15 2.1 Introduction 15 2.2 Smart Sensor 16 2.3 Logical Sensors 17 2.4 Interface File System (IFS) 17 2.4.1 Interface Types 18 2.4.2 Timing 19 2.5 Sensor Observation 20 2.5.1 Sensor Uncertainty Ay 21 2.6 Sensor Characteristics 23 2.7 Sensor-Sensor Properties 23 2.8 Sensor Model 24 2.9 Further Reading 28
X Contents 3 Architecture 29 3.1 Introduction 29 3.2 Fusion Node 31 3.2.1 Properties 32 3.3 Simple Fusion Networks 33 3.3.1 Single Fusion Cell 33 3.3.2 Parallel Network 33 3.3.3 Serial Network 35 3.3.4 Iterative Network 36 3.4 Network Topology 37 3.4.1 Centralized 38 3.4.2 Decentralized 39 3.4.3 Hierarchical 42 3.5 Software 44 3.6 Further Reading 44 Part II Representation 4 Common Representational Format 47 4.1 Introduction 47 4.2 Spatial-Temporal Transformation 50 4.3 Geographical Information System 51 4.3.1 Spatial Covariance Function 54 4.4 Common Representational Format 55 4.5 Subspace Methods 58 4.5.1 Principal Component Analysis 59 4.5.2 Linear Discriminant Analysis 60 4.6 Multiple Training Sets 64 4.7 Software 67 4.8 Further Reading 67 5 Spatial Alignment 69 5.1 Introduction 69 5.2 Image Registration 69 5.2.1 Mutual Information 70 5.3 Resample/Interpolation 74 5.4 Pairwise Transformation T 76 5.5 Image Fusion 77 5.6 Mosaic Image 80 5.7 Software 81 5.8 Fürther Reading 82
Contents XI 6 Temporal Alignment 83 6.1 Introduction 83 6.2 Dynamic Time Warping 85 6.3 Dynamic Programming 86 6.3.1 Derivative Dynamic Time Warping 88 6.3.2 Continuous Dynamic Time Warping 89 6.4 Video Compression 91 6.5 Software 94 6.6 Further Reading 94 7 Sensor Value Normalization 97 7.1 Introduction 97 7.1.1 Sensor Value Normalization 99 7.2 Binarization 99 7.3 Parametric Normalization Functions 103 7.4 Fuzzy Normalization Functions 104 7.5 Ranking 104 7.6 Conversion to Probabilities 107 7.6.1 Platt Calibration 107 7.6.2 Binning 108 7.6.3 Kernels 108 7.6.4 Isotonic Regression 109 7.6.5 Multi-Class Probability Estimates 110 7.7 Software 111 7.8 Further Reading 111 Part III Data Fusion 8 Bayesian Inference 115 8.1 Introduction 115 8.2 Bayesian Analysis 115 8.3 Probability Model 117 8.4 A Posteriori Distribution 118 8.4.1 Standard Probability Distribution Functions 119 8.4.2 Conjugate Priors 119 8.4.3 Non-Informative Priors 122 8.4.4 Missing Data 123 8.5 Model Selection 126 8.5.1 Laplace Approximation 127 8.5.2 Bayesian Model Averaging 129 8.6 Computation 130 8.6.1 Markov Chain Monte Carlo 130
XII Contents 8.7 Software 131 8.8 Further Reading 131 9 Parameter Estimation 133 9.1 Introduction 133 9.2 Parameter Estimation 133 9.3 Bayesian Curve Fitting 137 9.4 Maximum Likelihood 140 9.5 Least Squares 142 9.6 Linear Gaussian Model 143 9.6.1 Line Fitting 145 9.6.2 Change Point Detection 147 9.6.3 Probabilistic Subspace 149 9.7 Generalized Millman Formula 151 9.8 Software 153 9.9 Further Reading 153 10 Robust Statistics 155 10.1 Introduction 155 10.2 Outliers 157 10.3 Robust Parameter Estimation 158 10.3.1 Student-i Function 159 10.3.2 "Good-and-Bad" Likelihood Function 161 10.3.3 Gaussian Plus Constant 164 10.3.4 Uncertain Error Bars 164 10.4 Classical Robust Estimators 167 10.4.1 Least Median of Squares 167 10.5 Robust Subspace Techniques 168 10.6 Robust Statistics in Computer Vision 168 10.7 Software 170 10.8 Further Reading 171 11 Sequential Bayesian Inference 173 11.1 Introduction 173 11.2 Recursive Filter 175 11.3 Kaiman Filter 178 11.3.1 Parameter Estimation 181 11.3.2 Data Association 182 11.3.3 Model Inaccuracies 186 11.3.4 Multi-Target Tracking 188 11.4 Extensions of the Kaiman Filter 188 11.4.1 Robust Kaiman Filter 189 11.4.2 Extended Kaiman Filter 190
Contents XIII 11.4.3 Unscented Kaiman Filter 191 11.4.4 Switching Kaiman Filter 192 11.4.5 Kriged Kaiman Filter 194 11.5 Particle Filter 195 11.6 Multi-Sensor Multi-Temporal Data Fusion 195 11.6.1 Measurement Fusion 195 11.6.2 Track-to-Track Fusion 197 11.7 Software 200 11.8 Further Reading 200 12 Bayesian Decision Theory 201 12.1 Introduction 201 12.2 Pattern Recognition 201 12.3 Naive Bayes' Classifier 205 12.3.1 Representation 205 12.3.2 Performance 206 12.3.3 Likelihood 207 12.4 Modifications 210 12.4.1 Feature Space 210 12.4.2 Model Assumptions 214 12.4.3 Learning Methods 215 12.4.4 Multiple Classifiers 216 12.5 Error Estimation 217 12.6 Pairwise Classifiers 218 12.7 Software 219 12.8 Further Reading 219 13 Ensemble Learning 221 13.1 Introduction 221 13.2 Bayesian Framework 221 13.3 Empirical Framework 224 13.4 Diversity Techniques 225 13.5 Diversity Measures 227 13.5.1 Ensemble Selection 230 13.6 Classifier Types 230 13.7 Combination Strategies 231 13.7.1 Simple Combiners 231 13.7.2 Meta-Learners 236 13.8 Boosting 238 13.9 Recommendations 240 13.10 Software 240 13.11 Further Reading 240
XIV Contents Part IV Sensor Management 14 Sensor Management 243 14.1 Introduction 243 14.2 Hierarchical Classification 244 14.2.1 Sensor Control 244 14.2.2 Sensor Scheduling 245 14.2.3 Resource Planning 245 14.3 Sensor Management Techniques 246 14.3.1 Information-Theoretic Criteria 246 14.3.2 Bayesian Decision-Making 247 14.4 Further Reading 248 14.5 Postscript 248 Part V Appendices Software Sources 251 Background Material 253 B.l Probability Theory 253 B.2 Linear Algebra 254 B.3 Square Matrices 255 References 257 Index 277