Mahler R.P.S. Statistical Multisource-Multitarget Information Fusion

Artech House, 2007. — 883 p.The purpose of this book is not to reprise what has already been adequately addressed. Rather, it is a textbook style introduction to a fundamentally new, seamlessly unified, and fully statistical approach to information fusion.
The emergence of unconventional defense and security challenges has greatly increased the need for fusing and exploiting unconventional and highly disparate forms of information. Conventional data is supplied by sensors and can often be modeled and characterized statistically. Nontraditional information tends to involve target identity and often requires human mediation. Typical examples include attributes extracted from images by human operators; features extracted from signatures by digital signal processors or by human analysts; textual or verbal natural language statements; and inference rules drawn from knowledge bases.
Numerous expert systems approaches have been proposed to address such problems. The great majority of these approaches bear no obvious relationship with the most mature subdiscipline of information fusion: single-target and multitarget detection and tracking theory. As a consequence it has often been unclear how to develop systematic and integrated solutions to many real-world challenges.
This book is the result of a decade long effort on the author's part to address such challenges. The fundamental methodology I propose is conceptually parsimonious. It consists of a systematic and novel utilization of formal Bayes modeling and the recursive Bayes filter. It provides techniques for modeling uncertainties due to randomness or ignorance, propagating these uncertainties through time, and extracting estimates of desired quantities (as well as measures of reliability of those estimates) that optimally reflect the influence of inherent system uncertainties.
The process just described is well known. What makes my version of it unique is my systematic application of it to multitarget information, and to unconventional information in both single-target and multitarget problems. One of its consequences is a seamlessly unified statistical approach to multitarget-multisource integration.
This seamless uni_cation includes the following:
A unified theory of measurements, both single-target and multitarget;
Unified mathematical representation of uncertainty, including randomness, imprecision, vagueness, ambiguity, and contingency;
A unified single-target and multitarget modeling methodology based on generalized likelihood functions;
A unification of much of expert systems theory, including fuzzy, Bayes, Dempster-Shafer, and rule-based techniques;
Unified and optimal single-target and multitarget detection and estimation;
Unified and optimal fusion of disparate information;
A systematic multitarget calculus for devising new approximations.
The subject of this book is finite set statistics (FISST), a recently developed theory that unifies much of information fusion under a single probabilistic - in fact, Bayesian - paradigm. It does so by directly generalizing the 'statistics 101' formalism that most signal processing practitioners learn as undergraduates. Since its introduction in 1994, FISST has addressed an increasingly comprehensive expanse of information fusion, including multitarget-multisource integration (MSI), also known as level 1 fusion; expert systems theory; sensor management for level 1 fusion, including management of dispersed mobile sensors; group target detection, tracking, and classification; robust automatic target recognition; and scientific performance evaluation.Introduction to the Book
Unified Single-Target Multisource Integration
Single-Target Filtering
General Data Modeling
Random Set Uncertainty Representations
UGA Measurements
AGA Measurements
AGU Measurements
Generalized State-Estimates
Finite-Set Measurements
Unified Multitarget-Multisource Integration
Conventional Multitarget Filtering
Multitarget Calculus
Multitarget Likelihood Functions
Multitarget Markov Densities
The Multitarget Bayes Filter
Approximate Multitarget Filtering
Multitarget Particle Approximation
Multitarget-Moment Approximation
Multi-Bernoulli Approximation
Appendices
A Glossary of Notation
B Dirac Delta Functions
C Gradient Derivatives
D Fundamental Gaussian Identity
E Finite Point Processes
F FISST and Probability Theory
G Mathematical Proofs