Multisensor Decision And Estimation Fusion, 2003 The International Series on Asian Studies in Computer and Information Science Series, Vol. 14

YUNMIN ZHU In the past two decades, multi sensor or multi-source information fusion tech­ niques have attracted more and more attention in practice, where observations are processed in a distributed manner and decisions or estimates are made at the individual processors, and processed data (or compressed observations) are then transmitted to a fusion center where the final global decision or estimate is made. A system with multiple distributed sensors has many advantages over one with a single sensor. These include an increase in the capability, reliability, robustness and survivability of the system. Distributed decision or estimation fusion prob­ lems for cases with statistically independent observations or observation noises have received significant attention (see Varshney's book Distributed Detec­ tion and Data Fusion, New York: Springer-Verlag, 1997, Bar-Shalom's book Multitarget-Multisensor Tracking: Advanced Applications, vol. 1-3, Artech House, 1990, 1992,2000). Problems with statistically dependent observations or observation noises are more difficult and have received much less study. In practice, however, one often sees decision or estimation fusion problems with statistically dependent observations or observation noises. For instance, when several sensors are used to detect a random signal in the presence of observation noise, the sensor observations could not be statistically independent when the signal is present. This book provides a more complete treatment of the fundamentals of multi­ sensor decision and estimation fusion in order to deal with general random ob­ servations or observation noises that are correlated across the sensors.

I Decision Fusion.- 1. Introduction.- 1.1 Conventional Statistical Decision.- 1.1.1 Basic model of statistical decision.- 1.1.2 Hypothesis testing.- 1.2 Multisensor Statistical Decision Fusion Summary.- 1.2.1 Brief introduction to multisensor data fusion.- 1.2.2 Some basic issues.- 1.2.3 The previous studies of decision fusion.- 1.3 Three Conventional Single Sensor Decisions.- 1.3.1 Bayes decision.- 1.3.2 Neyman-Pearson decision.- 1.3.3 Sequential decision.- 2. Two Sensor Binary Decisions.- 2.1 Introduction.- 2.1.1 Problem formulation.- 2.1.2 The relationship of distributed and classical decisions.- 2.2 Optimal Sensor Rule of Bayes Decision.- 2.2.1 Fixed point type necessary condition.- 2.2.2 Existence of the optimal sensor rule.- 2.3 An Algorithm for Computing the Optimal Sensor Rule.- 2.3.1 Gauss-Seidel iterative algorithm.- 2.3.2 The finite convergence of the discretized algorithm.- 2.4 Relationships with Likelihood Ratio Sensor Rules.- 2.5 Numerical Examples.- 2.6 Randomized Fusion Rules.- 3. Multisensor Binary Decisions.- 3.1 The Formulation for Bayes Binary Decision Problem.- 3.2 Formulation of Fusion Rules via Polynomials of Sensor Rules.- 3.3 Fixed Point Type Necessary Condition for the Optimal Sensor Rules Given a Fusion Rule.- 3.4 The Finite Convergence of the Discretized Algorithm.- 3.5 The Optimal Fusion Rule and Some Interesting Properties.- 3.6 Numerical Examples of the Above Results.- 3.7 Optimal Sensor Rule of Neyman-Pearson Decision.- 3.7.1 Necessary condition.- 3.7.2 The algorithm to search for optimal sensor rules.- 3.7.3 Numerical examples.- 3.8 Sequential Decision Fusion Given Fusion Rule.- 3.8.1 Algorithm.- 3.8.2 Numerical example.- 4. Multisensor Multi-Hypothesis Network Decision.- 4.1 Elementary Network Structures.- 4.1.1 Parallel network.- 4.1.2 Tandem network and tree network.- 4.1.3 Hybrid (tree) network.- 4.2 Formulation of Fusion Rule via Polynomial of Sensor rules.- 4.3 Fixed Point Type Necessary Condition for Optimal Sensor Rules Given a Fusion Rule.- 4.4 Iterative Algorithm and Convergence.- 5. Optimal Fusion Rule and Design of Network Communication Structures.- 5.1 Optimal Fusion Rule Given Sensor Rules.- 5.1.1 Problem formulation.- 5.1.2 Computation of likelihood ratios.- 5.1.3 Locally optimal sensor rules with communications.- 5.1.4 Extensions to more general systems.- 5.1.5 Numerical examples.- 5.2 The Equivalent Classes of Fusion Rules.- 5.2.1 Preliminary definitions.- 5.2.2 Propositions.- 5.2.3 Applications of propositions.- 5.3 Unified Fusion Rule for Parallel Network.- 5.4 Unified Fusion Rule for Tandem and Tree Networks.- 5.5 Performance Comparison of Parallel and Tandem Networks.- 5.6 Numerical Examples.- 5.6.1 Three sensor system.- 5.6.2 Four sensor system.- 5.7 Optimization Design of Network Decision Systems.- 5.7.1 Selection of a network structure category.- 5.7.2 Allocation of sensors’ positions and communication amounts.- II Estimation Fusion.- 6. Multisensor Point Estimation Fusion.- 6.1 Previous Main Results.- 6.2 Linear Minimum Variance Estimation Fusion.- 6.2.1 Formulation of the LMV fusion as an optimization problem.- 6.2.2 Optimal fusion weights.- 6.2.3 Efficiency of the LMV fusion.- 6.2.4 Extension to a more general model.- 6.2.5 Previous fusion formulae as special cases.- 6.2.6 Discussion.- 6.2.7 Recursive computation of error covariance.- 6.3 The Optimality of Kalman Filtering Fusion with Feedback.- 6.3.1 Problem formulation.- 6.3.2 Global optimality of the feedback filtering fusion.- 6.3.3 Local estimate errors.- 6.3.4 The advantage of the feedback.- 6.3.5 Extension to a hybrid filtering fusion.- 6.4 Fusion of the Forgetting Factor RLS Algorithm.- 6.4.1 Forgetting factor RLS algorithm.- 6.4.2 Two types of distributed EFRLS fusion methods.- 6.4.3 Simulations.- 7. Multisensor.- 7.1 Statistical Interval Estimation Fusion Using Sensor Statistics.- 7.1.1 Problem formulation.- 7.1.2 Optimal convex linear fusion.- 7.1.3 Computation of the optimal weights.- 7.1.4 Nearly optimal linear fusion.- 7.1.5 Numerical examples.- 7.1.6 Inverting a hypothesis testing.- 7.2 Interval Estimation Fusion Using Sensor Estimates.- 7.2.1 Outputs of sensors.- 7.2.2 Combination rule of sensor outputs.- 7.2.3 Optimization criteria.- 7.3 Fault-Tolerant Interval Estimation Fusion.- 7.3.1 Without knowledge of confidence degrees.- 7.3.2 With knowledge of confidence degrees.- 7.3.3 Extension to sensors outputting multiple intervals.- 7.3.4 Conclusion.