©2001 CRC Press LLC (sum rule) (product rules) (chain rule) 14.6 FISST Multisource-Multitarget Statistics Thus far this chapter has described the multisensor-multitarget analogs of measurement and motion models, probability mass functions, and the integral and differential calculus. This section shows how these concepts join together to produce a direct generalization of ordinary statistics to multitarget statistics. Section 14.6.1 illustrates how true multitarget likelihood functions can be constructed from multitarget measurement models using the “turn-the-crank” rules of the FISST calculus. Section 14.6.2 shows how to similarly construct true multitarget Markov densities from multitarget motion models. The concepts of multitarget prior distribution and multitarget posterior distribution are introduced in Sections 14.6.3 and 14.6.4. The failure of the classical Bayes-optimal state estimators in multitarget situations is described in Section 14.6.6. The solution of this problem — the proper definition and verification of Bayes-optimal multitarget state estimators — is described in Section 14.6.7. The remaining two subsections summarize a Cramér-Rao performance bound for vector-valued multitarget state esti- mators and a “multitarget miss distance.” 14.6.1 Constructing True Multitarget Likelihood Functions Let us apply the turn-the-crank formulas of Subsection 5.4 to the belief-mass function β(S|X) = p(S|x 1 ) p(S|x 2 ) corresponding to the measurement model Σ = {Z 1 , Z 2 } of Equation 3.2, where X = {x 1 , x 2 }. We get δ δ ββ δβ δ δβ δZ aSa Sa Z Sa Z S 11 2 2 1 1 2 2 () + () [] = () + () δ δ ββ δβ δ ββ δβ δzz z 12 1 21 2 SS SS S S () () [] = () () + () () δ δ ββ δβ δ δβ δZ SS W S ZW S wz 12 12 () () [] = () − () () ⊆ ∑ δ δ ββ ββ δβ δz fS S f x SSS n i i n n i 1 1 1 () … () () = ∂ ∂ () … () () () = ∑ ,, ,, z δβ δ δ δ β δ δ δ δ δ δ zz z xx z xx x z x zx x x zx 11 1 12 1 12 1 1 2 11 2 1 12 SX SX p S p S p SpS pS p S fpSpSf () = () = ()() [] = ()() + ()() = () () + () () δβ δδ δ δ δβ δ δ δ δ δ 2 21 2 1 11 2 2 2 112 11 2 2 21 12 zz z z zx z x z xzx zx zx zx zx SX SX f pS pS f ff ff () = () = () () + ()( ) = ()( ) + ()() δβ δδδ δ δ δβ δδ 3 321 3 2 21 0 zzz z zz SX SX () = () = III Systems Engineering and Implementation 15 Requirements Derivation for Data Fusion Systems Ed Waltz and David L. Hall Introduction • Requirements Analysis Process • Engineering Flow-Down Approach • Enterprise Architecture Approach • Comparison of Approaches 16 A Systems Engineering Approach for Implementing Data Fusion Systems Christopher L. Bowman and Alan N. Steinberg Scope • Architecture for Data Fusion • Data Fusion System Engineering Process • Fusion System Role Optimization 17 Studies and Analyses with Project Correlation: An In-Depth Assessment of Correlation Problems and Solution Techniques James Llinas, Lori McConnel, Christopher L. Bowman, David L. Hall, and Paul Applegate Introduction • A Description of the Data Correlation (DC) Problem • Hypothesis Generation • Hypothesis Evaluation • Hypothesis Selection • Summary 18 Data Management Support to Tactical Data Fusion Richard Antony Introduction • Database Management Systems • Spatial, Temporal, and Hierarchical Reasoning • Database Design Criteria • Object Representation of Space • Integrated Spatial/Nonspatial Data Representation • Sample Application • Summary and Conclusions 19 Removing the HCI Bottleneck: How the Human-Computer Interface (HCI) Affects the Performance of Data Fusion Systems Mary Jane M. Hall, Sonya A. Hall, and Timothy Tate Introduction • A Multimedia Experiment • Summary of Results • Implications for Data Fusion Systems 20 Assessing the Performance of Multisensor Fusion Processes James Llinas Introduction • Test and Evaluation of the Data Fusion Process • Tools for Evaluation: Testbeds, Simulations, and Standard Data Sets • Relating Fusion Performance to Military Effectiveness — Measures of Merit • Summary 21 Dirty Secrets in Multisensor Data Fusion David L. Hall and Alan N. Steinberg Introduction • The JDL Data Fusion Process Model • Current Practices and Limitations in Data Fusion • Research Needs • Pitfalls in Data Fusion • Summary ©2001 CRC Press LLC ©2001 CRC Press LLC 15 Requirements Derivation for Data Fusion Systems 15.1 Introduction 15.2 Requirements Analysis Process 15.3 Engineering Flow-Down Approach 15.4 Enterprise Architecture Approach The Three Views of the Enterprise Architecture 15.5 Comparison of Approaches References 15.1 Introduction The design of practical systems requires the translation of data fusion theoretic principles, practical constraints, and operational requirements into a physical, functional, and operational architecture that can be implemented, operated, and maintained. This translation of principles to practice demands a discipline that enables the system engineer or architect to perform the following basic functions: •Define user requirements in terms of functionality (qualitative description) and performance (quantitative description), •Synthesize alternative design models and analyze/compare the alternatives in terms of require- ments and risk, •Select optimum design against some optimization criteria, •Allocate requirements to functional system subelements for selected design candidates, •Monitor the as-designed system to measure projected technical performance, risk, and other factors (e.g., projected life cycle cost) throughout the design and test cycle, •Verify performance of the implemented system against top- and intermediate-level requirements to ensure that requirements are met and to validate the system performance model. The discipline of system engineering, pioneered by the aerospace community to implement complex systems over the last four decades, has been successfully used to implement both research and develop- ment and large-scale data fusion systems. This approach is characterized by formal methods of require- ment definition at a high level of abstraction, followed by decomposition to custom components, that can then be implemented. More recently, as information technology has matured, the discipline of enterprise architecture design has also developed formal methods for designing large-scale enterprises using commercially available and custom software and hardware components. Both of these disciplines contribute sound methodologies for implementing data fusion systems. Ed Waltz Veridian Systems David L. Hall The Pennsylvania State University ©2001 CRC Press LLC 16 A Systems Engineering Approach for Implementing Data Fusion Systems 16.1 Scope 16.2 Architecture for Data Fusion Role of Data Fusion in Information Processing Systems • Open System Environment • Layered Design • Paradigm-Based Architecture 16.3 Data Fusion Systems Engineering Process Data Fusion Engineering Methodology • The Process of Systems Engineering 16.4 Fusion System Role Optimization Fusion System Requirements Analysis • Fusion System Tree Optimization • Fusion Tree Node Optimization • Detailed Design and Development References 16.1 Scope This chapter defines a systematic process for developing data fusion systems and intends to provide a common, effective foundation for the design and development of such systems. It also provides guidelines for selecting among design alternatives for specific applications. This systems engineering approach has been developed to provide •A standard model for representing the requirements, design, and performance of data fusion systems, and •A methodology for developing multisource data fusion systems and for selecting system architecture and technique alternatives for cost-effective satisfaction of system requirements. This systems engineering approach builds on a set of data fusion engineering guidelines that were developed in 1995–96 as part of the U.S. Air Force Space Command’s Project Correlation. 1,2 * The present work extends these guidelines by proposing a formal model for systems engineering, thereby establishing the basis for rigorous problem decomposition, system design, and technique application. *A closely related set of guidelines 3 for selecting among data correlation and association techniques, developed as part of the same project, is discussed in Chapter 17. Christopher L. Bowman Consultant Alan N. Steinberg Utah State University . Implementing Data Fusion Systems Christopher L. Bowman and Alan N. Steinberg Scope • Architecture for Data Fusion • Data Fusion System Engineering Process • Fusion System Role Optimization 17 Studies. Performance of Multisensor Fusion Processes James Llinas Introduction • Test and Evaluation of the Data Fusion Process • Tools for Evaluation: Testbeds, Simulations, and Standard Data Sets • Relating Fusion. 16.2 Architecture for Data Fusion Role of Data Fusion in Information Processing Systems • Open System Environment • Layered Design • Paradigm-Based Architecture 16.3 Data Fusion Systems Engineering