©2001 CRC Press LLC Within this metaphor, sensor data relates to the short-term knowledge, while long-term knowledge relates to relatively static factual and procedural knowledge. Because the goal of both biological and artificial situation awareness systems is the development and maintenance of the current relevant percep- tion of the environment, the dynamic situation description represents medium-term memory. In both biological and tactical data fusion systems, current emphasizes the character of the dynamically changing scene under observation, as well as the potentially time-evolving analysis process that could involve interactions among a network of distributed fusion processes. Memory limitations and the critical role medium-term memory plays in both biological and artificial situation awareness systems enables only relevant states to be maintained. Because sensor measurements are inherently information-limited, real- world events are often nondeterministic, and uncertainties often exist in the reasoning process, a disparity between perception and reality must be expected. As illustrated in Figure 6.7, sensor observables represent short-term declarative knowledge and the situation description represents medium-term declarative knowledge. Templates, filters, and the like are static declarative knowledge; domain knowledge includes both static (long-term) and dynamic (medium- and short-term) declarative context knowledge; and F represents the fusion process reasoning (long-term procedural) knowledge. Thus, as in biological situation awareness development, machine-based approaches require the interaction among short-, medium-, and long-term declarative knowledge, as well as long-term procedural knowledge. Medium-term knowledge tends to be highly perishable, while long-term declarative and procedural knowledge is both learned and forgotten much more slowly. With the exception of the difference in the time constants, learning of long-term knowledge and update of the situation description are fully analogous operations. In general, short-, medium-, and long-term knowledge can be either context-sensitive or context- insensitive . In this chapter, context is treated as a conditional dependency among objects, attributes, or functions (e.g., f(x 1 ,x 2 |x 3 = a)). Thus, context represents both explicit and implicit dependencies or conditioning that exist as a result of the state of the current situation representation or constraints imposed by the domain and/or the environment. Short-term knowledge is dynamic, perishable, and highly context sensitive. Medium-term knowledge is less perishable and is learned and forgotten at a slower rate than short-term knowledge. Medium-term knowledge maintains the context-sensitive situation description at all levels of abstraction. The inherent context-sensitivity of short- and medium-term knowledge indicates that effective interpretation can be achieved only through consideration of the broadest possible context. Long-term knowledge is relatively nonperishable information that may or may not be context- sensitive. Context-insensitive long-term knowledge is either generic knowledge, such as terrain/elevation, soil type, vegetation, waterways, cultural features, system performance characteristics, and coefficients of fixed-parameter signal filters, or context-free knowledge that simply ignores any domain sensitivity. Context-sensitive long-term knowledge is specialized knowledge, such as enemy Tables of Equipment, FIGURE 6.7 Biologically motivated metaphor for the data fusion process. Sensor input Short-term declarative Fusion Process, F Long-term procedural Database Long-term declarative Situation Description Medium-term declarative Update Learning ©2001 CRC Press LLC 7 Contrasting Approaches to Combine Evidence 7.1 Introduction 7.2 Alternative Approaches to Combine Evidence The Probability Theory Approach • The Possibility Theory Approach • The Belief Theory Approach • Methods of Combining Evidence 7.3 An Example Data Fusion System. System Context • Collections of Spaces • The System in Operation • Summary 7.4 Contrasts and Conclusion Appendix 7.A The Axiomatic Definition of Probability References 7.1 Introduction A broad consensus holds that a probabilistic approach to evidence accumulation is appropriate because it enjoys a powerful theoretical foundation and proven guiding principles. Nevertheless, many would argue that probability theory is not suitable for practical implementation on complex real-world prob- lems. Further debate arises when considering people’s subjective opinions regarding events of interest. Such debate has resulted in the development of several alternative approaches to combining evidence. 1-3 Two of these alternatives, possibility theory (or fuzzy logic) 4-6 and belief theory (or Dempster-Shafer theory), 7-10 have each achieved a level of maturity and a measure of success to warrant their comparison with the historically older probability theory. This chapter first provides some background on each of the three approaches to combining evidence in order to establish notation and to collect summary results about the approaches. Then an example system that accumulates evidence about the identity of an aircraft target is introduced. The three methods of combining evidence are applied to the example system, and the results are contrasted. At this point, possibility theory is dropped from further consideration in the rest of the chapter because it does not seem well suited to the sequential combination of information that the example system requires. Finally, an example data fusion system is constructed that determines the presence and location of mobile missile batteries. The evidence is derived from multiple sensors and is introduced into the system in temporal sequence, and a software component approach is adopted for its implementation. Probability and belief theories are contrasted within the context of the example system. One key idea that emerges for simplifying the solution of complex, real-world problems involves collections of spaces. This is in contradistinction to collections of events in a common space. Although Joseph W. Carl Harris Corporation II Advanced Tracking and Association Methods 8 Target Tracking Using Probabilistic Data Association-Based Techniques with Applications to Sonar, Radar, and EO Sensors T. Kirubarajan and Yaakov Bar-Shalom Introduction • Probabilistic Data Association • Low Observable TMA Using the ML-PDA Approach with Features • The IMMPDAF for Tracking Maneuvering Targets • A Flexible- Window ML-PDA Estimator for Tracking Low Observable (LO) Targets • Summary 9 An Introduction to the Combinatorics of Optimal and Approximate Data Association Jeffrey K. Uhlmann Introduction • Background • Most Probable Assignments • Optimal Approach • Computational Considerations • Efficient Computation of the JAM • Crude Permanent Approximations • Approximations Based on Permanent Inequalities • Comparisons of Different Approaches • Large-Scale Data Associations • Generalizations • Conclusions • Acknowledgments • Appendix 9.A Algorithm for Data Association Experiment 10 A Bayesian Approach to Multiple-Target Tracking Lawrence D. Stone Introduction • Bayesian Formulation of the Single-Target Tracking Problem • Multiple- Target Tracking without Contacts or Association (Unified Tracking) • Multiple-Hypothesis Tracking (MHT) • Relationship of Unified Tracking to MHT and Other Tracking Approaches • Likelihood Ratio Detection and Tracking 11 Data Association Using Multiple Frame Assignments Aubrey B. Poore, Suihua Lu, and Brian J. Suchomel Introduction • Problem Background • Assignment Formulation of Some General Data Association Problems • Multiple Frame Track Initiation and Track Maintenance • Algorithms • Future Directions 12 General Decentralized Data Fusion with Covariance Intersection (CI) Simon Julier and Jeffrey K. Uhlmann Introduction • Decentralized Data Fusion • Covariance Intersection • Using Covariance Intersection for Distributed Data Fusion • Extended Example • Incorporating Known Independent Information • Conclusions • Appendix 12.A The Consistency of CI • Appendix 12.B MATLAB Source Code (Conventional CI and Split CI) ©2001 CRC Press LLC ©2001 CRC Press LLC 8 Target Tracking Using Probabilistic Data Association-Based Techniques with Applications to Sonar, Radar, and EO Sensors 8.1 Introduction 8.2 Probabilistic Data Association Assumptions • The PDAF Approach • Measurement Validation • The State Estimation • The State and Covariance Update • The Prediction Equations • The Probabilistic Data Association • The Parametric PDA • The Nonparametric PDA 8.3 Low Observable TMA Using the ML-PDA Approach with Features Amplitude Information Feature • Target Models • Maximum Likelihood Estimator Combined with PDA — The ML- PDA • Cramér-Rao Lower Bound for the Estimate • Results 8.4 The IMMPDAF for Tracking Maneuvering Targets Coordinate Selection • Track Formation • Track Maintenance • Track Termination • Simulation Results 8.5 A Flexible-Window ML-PDA Estimator for Tracking Low Observable (LO) Targets The Scenario • Formulation of the ML-PDA Estimator • Adaptive ML-PDA • Results 8.6 Summary References 8.1 Introduction In tracking targets with less-than-unity probability of detection in the presence of false alarms (clutter), data association — deciding which of the received multiple measurements to use to update each track — is crucial. A number of algorithms have been developed to solve this problem. 1-4 Two simple solutions are the Strongest Neighbor Filter (SNF) and the Nearest Neighbor Filter (NNF). In the SNF, the signal T. Kirubarajan University of Connecticut Yaakov Bar-Shalom University of Connecticut . enemy Tables of Equipment, FIGURE 6.7 Biologically motivated metaphor for the data fusion process. Sensor input Short-term declarative Fusion Process, F Long-term procedural Database Long-term. Theory Approach • The Belief Theory Approach • Methods of Combining Evidence 7 .3 An Example Data Fusion System. System Context • Collections of Spaces • The System in Operation • Summary 7.4. maintenance of the current relevant percep- tion of the environment, the dynamic situation description represents medium-term memory. In both biological and tactical data fusion systems,