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Spie Press Book

Sensor and Data Fusion: A Tool for Information Assessment and Decision Making
Author(s): Lawrence A. Klein
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Book Description

This book illustrates the benefits of sensor fusion by considering the characteristics of infrared, microwave, and millimeter-wave sensors, including the influence of the atmosphere on their performance.

Applications that benefit from this technology include:

  • vehicular traffic management
  • remote sensing
  • target classification and tracking
  • weather forecasting
  • military and homeland defense

Covering data fusion algorithms in detail, Klein includes a summary of the information required to implement each of the algorithms discussed, and outlines system application scenarios that may limit sensor size but that require high resolution data.


Book Details

Date Published: 7 July 2004
Pages: 362
Volume: PM138

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
List of Figures / xiii
List of Tables / xvii
Preface / xxi
Chapter 1 Introduction / 1
Chapter 2 Multiple Sensor System Applications, Benefits, and Design Considerations / 7
2.1 Data fusion applications to multiple sensor systems / 8
2.2 Selection of sensors / 10
2.3 Benefits of multiple sensor systems / 16
2.4 Influence of wavelength on atmospheric attenuation / 18
2.5 Fog characterization / 21
2.6 Effects of operating frequency on MMW sensor performance / 22
2.7 Absorption of MMW energy in rain and fog / 23
2.8 Backscatter of MMW energy from rain / 25
2.9 Effects of operating wavelength on IR sensor performance / 28
2.10 Visibility metrics / 29
2.10.1 Visibility / 29
2.10.2 Meteorological range / 30
2.11 Attenuation of IR energy by rain / 31
2.12 Extinction coefficient values (typical) / 32
2.13 Summary of attributes of electromagnetic sensors / 32
2.14 Atmospheric and sensor system computer simulation models / 38
2.14.1 LOWTRAN attenuation model / 38
2.14.2 FASCODE and modtran attenuation models / 40
2.14.3 EOSAEL sensor performance model / 41
2.15 Summary / 43
References / 46
Chapter 3 Data Fusion Algorithms andArchitectures / 51
3.1 Definition of data fusion / 51
3.2 Level 1 processing / 54
3.2.1 Detection, classification, and identification algorithms for data fusion / 55
3.2.2 State estimation and tracking algorithms for data fusion / 71
3.3 Level 2, 3, and 4 processing / 78
3.4 Data fusion processor functions / 80
3.5 Definition of an architecture / 82
3.6 Data fusion architectures / 83
3.6.1 Sensor-level fusion / 83
3.6.2 Central-level fusion / 87
3.6.3 Hybrid fusion / 89
3.6.4 Pixel-level fusion / 91
3.6.5 Feature-level fusion / 92
3.6.6 Decision-level fusion / 93
3.7 Sensor footprint registration and size considerations / 93
3.8 Summary / 95
References / 97
Chapter 4 Classical Inference / 101
4.1 Estimating the statistics of a population / 102
4.2 Interpreting the confidence interval / 103
4.3 Confidence interval for a population mean / 105
4.4 Significance tests for hypotheses / 109
4.5 z-test for the population mean / 109
4.6 Tests with fixed significance level / 112
4.7 t-test for a population mean / 114
4.8 Caution in use of significance tests / 117
4.9 Inference as a decision / 118
4.10 Summary / 122
References / 125
Chapter 5 Bayesian Inference / 127
5.1 Bayes' rule / 127
5.2 Bayes' rule in terms of odds probability and likelihood ratio / 129
5.3 Direct application of Bayes' rule to cancer screening test example / 131
5.4 Comparison of Bayesian inference with classical inference / 132
5.5 Application of Bayesian inference to fusing information from multiple sources / 134
5.6 Combining multiple sensor information using the odds probability form of Bayes' rule / 136
5.7 Recursive Bayesian updating / 137
5.8 Posterior calculation using multivalued hypotheses and recursive updating / 138
5.9 Enhancing underground mine detection with data from two noncommensurate sensors / 142
5.10 Summary / 146
References / 147
Chapter 6 Dempster-Shafer Evidential Theory / 149
6.1 Overview of the process / 149
6.2 Implementation of the method / 150
6.3 Support, plausibility, and uncertainty interval / 151
6.4 Dempster's rule for combination of multiple sensor data / 156
6.4.1 Dempster's rule with empty set elements / 158
6.4.2 Dempster's rule when only singleton propositions are reported / 159
6.5 Comparison of dempster-shafer with Bayesian decision theory / 161
6.5.1 Dempster-Shafer - Bayesian equivalence example / 162
6.5.2 Dempster-Shafer - Bayesian computation time comparisons / 163
6.6 Probabilistic models for transformation of Dempster-Shafer belief functions for decision making / 163
6.6.1 Pignistic transferable belief model / 164
6.6.2 Plausibility transformation function / 166
6.6.3 Modified dempster-shafer rule of combination / 171
6.7 Summary / 178
References / 180
Chapter 7 Artificial Neural Networks / 183
7.1 Applications of artificial neural networks / 184
7.2 Adaptive linear combiner / 184
7.3 Linear classifiers / 185
7.4 Capacity of linear classifiers / 187
7.5 Nonlinear classifiers / 188
7.5.1 Madaline / 188
7.5.2 Feedforward network / 190
7.6 Capacity of nonlinear classifiers / 192
7.7 Supervised and unsupervised learning / 193
7.8 Supervised learning rules / 195
7.8.1 LMS steepest descent algorithm / 196
7.8.2 LMS error correction algorithm / 196
7.8.3 Comparison of the LMS algorithms / 197
7.8.4 Madaline I and II error correction rules / 197
7.8.5 Perceptron rule / 198
7.8.6 Backpropagation algorithm / 200
7.8.7 Madaline III steepest descent rule / 202
7.8.8 Dead zone algorithms / 203
7.9 Generalization / 204
7.10 Other artificial neural networks and processing techniques / 205
7.11 Summary / 207
References / 213
Chapter 8 Voting Logic Fusion / 215
8.1 Sensor target reports / 217
8.2 Sensor detection space / 218
8.2.1 Venn diagram representation of detection space / 218
8.2.2 Confidence levels / 218
8.2.3 Detection modes / 219
8.3 System detection probability / 221
8.3.1 Derivation of system detection and false alarm probability for nonnested confidence levels / 221
8.3.2 Relation of confidence levels to detection and false alarm probabilities / 223
8.3.3 Evaluation of conditional probability / 224
8.3.4 Establishing false alarm probability / 225
8.3.5 Calculating system detection probability / 226
8.3.6 Summary of detection probability computation model / 226
8.4 Application example without singleton sensor detection modes / 227
8.4.1 Satisfying the false alarm probability requirement / 228
8.4.2 Satisfying the detection probability requirement / 228
8.4.3 Observations / 230
8.5 Hardware implementation of voting logic sensor fusion / 231
8.6 Application example with singleton sensor detection modes / 231
8.7 Comparison of voting logic fusion with Dempster-Shafer evidential theory / 233
8.8 Summary / 234
References / 235
Chapter 9 Fuzzy Logic and Fuzzy Neural Networks / 237
9.1 Conditions under which fuzzy logic provides an appropriate solution / 237
9.2 Illustration of fuzzy logic in an automobile antilock braking system / 238
9.3 Basic elements of a fuzzy system / 239
9.4 Fuzzy logic processing / 239
9.5 Fuzzy centroid calculation / 241
9.6 Balancing an inverted pendulum with fuzzy logic control / 243
9.6.1 Conventional mathematical solution / 243
9.6.2 Fuzzy logic solution / 245
9.7 Fuzzy logic applied to multitarget tracking / 249
9.7.1 Conventional kalman filter approach / 249
9.7.2 Fuzzy kalman filter approach / 251
9.8 Fuzzy neural networks / 256
9.9 Fusion of fuzzy-valued information from multiple sources / 258
9.10 Summary / 259
References / 261
Chapter 10 Passive Data Association Techniques for Unambiguous Location of Targets / 263
10.1 Data fusion options / 263
10.2 Received-signal fusion / 265
10.2.1 Coherent processing technique / 267
10.2.2 System design issues / 269
10.3 Angle data fusion / 271
10.3.1 Solution space for emitter locations / 272
10.3.2 Zero-one integer programming algorithm development / 275
10.3.3 Relaxation algorithm development / 280
10.4 Decentralized fusion architecture / 282
10.4.1 Local optimization of direction angle track association / 282
10.4.2 Global optimization of direction angle track association / 285
10.5 Passive computation of range using tracks from a single sensor site / 287
10.6 Summary / 288
References / 290
Chapter 11 Retrospective Comments / 293
Appendix A Planck Radiation Law and Radiative Transfer / 299
A.1 Planck radiation law / 299
A.2 Radiative transfer theory /301
References / 305
Appendix B Voting Fusion with Nested Confidence Levels / 307
Index / 309

Preface

Data and Sensor Fusion: A Tool for Information Assessment and Decision Making is the latest version of Data and Sensor Fusion Concepts and Applications, which last appeared as Tutorial Text 35 from SPIE. The information in this edition has been substantially expanded and updated to incorporate recent approaches to data and sensor fusion.

The book serves as a companion text to courses taught by the author on multisensor, multitarget data fusion techniques for tracking and identification of potential targets. Material regarding the benefits of multisensor systems and data fusion originally developed for courses on advanced sensor design for defense applications was utilized in preparing the original edition. Those topics that deal with applications of multiple sensor systems; target, background, and atmospheric signature-generation phenomena and modeling; and methods of combining multiple sensor data in target identity and tracking data fusion architectures were expanded for this book. Most signature phenomena and data fusion techniques are explained with a minimum of mathematics or use relatively simple mathematical operations to convey the underlying principles. Understanding of concepts is aided by the nonmathematical explanations provided in each chapter.

Multisensor systems are frequently designed to overcome space limitations associated with smart weapons applications or to combine and assess information from noncollated or dissimilar sources. Packaging volume restrictions associated with the construction of fire-and-forget missile systems often constrain sensor selection to those operating at infrared and millimeter-wave frequencies. In addition to having relatively short wavelengths and hence occupying small volumes, these sensors provide high resolution and complementary information as they respond to different signature-generation phenomena. The result is a large degree of immunity to inclement weather, clutter, and signature masking produced by countermeasures. Sensor and data fusion architectures are utilized in these multisensor systems to combine information from the individual sensors and other sources in an efficient and effective manner.

Chapters 2 - 11 discuss the benefits of infrared and millimeter-wave sensor operation including atmospheric effects; multiple sensor system applications; definitions and examples of data fusion architectures and algorithms; classical inference, which forms a foundation for the more general Bayesian inference and Dempster-Shafer evidential theory that follow in succeeding chapters; artificial neural networks; voting logic as derived from Boolean algebra expressions; fuzzy logic; detecting and tracking objects using only passively acquired data; and a summary of the information required to implement each of the data fusion methods discussed.

Weather forecasting, Earth resource surveys that use remote sensing, vehicular traffic management, target classification and tracking, and battlefield assessment are some of the applications that will benefit from the discussions provided of signature-generation phenomena, sensor fusion architectures, and data fusion algorithms. There continues to be high interest in military and homeland defense usage of data fusion to assist in the identification of missile threats, suicide bombers, strategic and tactical targets, assessment of information, evaluation of potential responses to a threat, and allocation of resources. The signature- generation phenomena and fusion architectures and algorithms presented in this book continue to be applicable to these areas as well as the growing number of nondefense applications.

Several people have made valuable suggestions that were incorporated into this work. Henry Heidary, in addition to his major contributions to Chapter 10, reviewed other sections of the original manuscript. Sam Blackman reviewed the original text and provided several references for new material that was subsequently incorporated. Pat Williams reviewed sections on tracking and provided data concerning tracking algorithm execution times. Martin Dana, with whom I teach the multisensor, multitarget data fusion course, reviewed several of the newer sections. His insightful suggestions have improved upon the text. Merry Schnell, Sharon Streams, Eric Pepper, and the rest of the SPIE staff provided, as usual, technical and editorial assistance that improved the quality of the material in the text. That the book has many strengths, I am indebted to these and so many other colleagues; its faults are, of course, mine.

Lawrence A. Klein
June 2004


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