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 random set 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 and relational 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.

Inhalt
1 Introduction.- 1.1 What is Data Fusion?.- 1.2 Random Set Theory.- 1.3 Conditional and Relational Event Algebra.- I Introduction to Data Fusion.- 2 Data Fusion and Standard Techniques.- II The Random Set Approach to Data Fusion.- 3 Foundations of Random Sets.- 4 Finite Random Sets.- 5 Finite-Set Statistics.- 6 Fusion of Unambiguous Observations.- 7 Fusion of Ambiguous Observations.- 8 Output Measurement.- III Use of Conditional and Relational Events in Data Fusion.- 9 Introduction to the Conditional and Relational Event Algebra Aspects of Data Fusion.- 10 Potential Application of Conditional Event Algebra to Combining Conditional Information.- 11 Three Particular Conditional Event Algebras.- 12 Further Development of Product Space Conditional Event Algebra.- 13 Product Space Conditional Event Algebra as a Tool for Further Analysis of Conditional Event Algebra Issues.- 14 Testing of Hypotheses for Distinctness of Events and Event Similarity Issues.- 15 Testing Hypotheses And Estimation Relative To Natural Language Descriptions.- 16 Development of Relational Event Algebra Proper to Address Data Fusion Problems.