Ebook: Mathematics of Data Fusion

Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of randomset theory and conditional and relational event algebra.
This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional andrelational event algebra.
Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.

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Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of randomset theory and conditional and relational event algebra.
This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional andrelational event algebra.
Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.

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Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of randomset theory and conditional and relational event algebra.
This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional andrelational event algebra.
Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-14
Front Matter....Pages 15-16
Data Fusion and Standard Techniques....Pages 17-89
Front Matter....Pages 91-91
Foundations of Random Sets....Pages 93-129
Finite Random Sets....Pages 131-173
Finite-Set Statistics....Pages 175-218
Fusion of Unambiguous Observations....Pages 219-262
Fusion of Ambiguous Observations....Pages 263-293
Output Measurement....Pages 295-338
Front Matter....Pages 339-344
Introduction to the Conditional and Relational Event Algebra Aspects of Data Fusion....Pages 345-358
Potential Application of Conditional Event Algebra to Combining Conditional Information....Pages 359-367
Three Particular Conditional Event Algebras....Pages 369-382
Further Development of Product Space Conditional Event Algebra....Pages 383-403
Product Space Conditional Event Algebra as a Tool for Further Analysis of Conditional Event Algebra Issues....Pages 405-423
Testing of Hypotheses for Distinctness of Events and Event Similarity Issues....Pages 425-454
Testing Hypotheses And Estimation Relative To Natural Language Descriptions....Pages 455-480
Development of Relational Event Algebra Proper to Address Data Fusion Problems....Pages 481-501
Back Matter....Pages 503-508

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Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of randomset theory and conditional and relational event algebra.
This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional andrelational event algebra.
Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-14
Front Matter....Pages 15-16
Data Fusion and Standard Techniques....Pages 17-89
Front Matter....Pages 91-91
Foundations of Random Sets....Pages 93-129
Finite Random Sets....Pages 131-173
Finite-Set Statistics....Pages 175-218
Fusion of Unambiguous Observations....Pages 219-262
Fusion of Ambiguous Observations....Pages 263-293
Output Measurement....Pages 295-338
Front Matter....Pages 339-344
Introduction to the Conditional and Relational Event Algebra Aspects of Data Fusion....Pages 345-358
Potential Application of Conditional Event Algebra to Combining Conditional Information....Pages 359-367
Three Particular Conditional Event Algebras....Pages 369-382
Further Development of Product Space Conditional Event Algebra....Pages 383-403
Product Space Conditional Event Algebra as a Tool for Further Analysis of Conditional Event Algebra Issues....Pages 405-423
Testing of Hypotheses for Distinctness of Events and Event Similarity Issues....Pages 425-454
Testing Hypotheses And Estimation Relative To Natural Language Descriptions....Pages 455-480
Development of Relational Event Algebra Proper to Address Data Fusion Problems....Pages 481-501
Back Matter....Pages 503-508
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