Networked Multisensor Decision and Estimation Fusion Based on Advanced Mathematical Methods

Due to the increased capability, reliability, robustness, and survivability of systems with multiple distributed sensors, multi-source information fusion has become a crucial technique in a growing number of areas—including sensor networks, space technology, air traffic control, military engineering, agriculture and environmental engineering, and industrial control. Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods presents advanced mathematical descriptions and methods to help readers achieve more thorough results under more general conditions than what has been possible with previous results in the existing literature. Examining emerging real-world problems, this book summarizes recent research developments in problems with unideal and uncertain frameworks. It presents essential mathematical descriptions and methods for multisensory decision and estimation fusion. Deriving thorough results under general conditions, this reference book: Corrects several popular but incorrect results in this area with thorough mathematical ideas Provides advanced mathematical methods, which lead to more general and significant results Presents updated systematic developments in both multisensor decision and estimation fusion, which cannot be seen in other existing books Includes numerous computer experiments that support every theoretical result The book applies recently developed convex optimization theory and high efficient algorithms in estimation fusion, which opens a very attractive research subject on minimizing Euclidean error estimation for uncertain dynamic systems. Supplying powerful and advanced mathematical treatment of the fundamental problems, it will help to greatly broaden prospective applications of such developments in practice.

IntroductionFundamental Problems Core of Fundamental Theory and General Mathematical Ideas Classical Statistical Decision Bayes Decision Neyman–Pearson Decision Neyman–Pearson Criterion Minimax Decision Linear Estimation and Kalman Filtering Basics of Convex OptimizationConvex Optimization Basic Terminology of Optimization Duality Relaxation S-Procedure Relaxation SDP Relaxation Parallel Statistical Binary Decision Fusion Optimal Sensor Rules for Binary Decision Given Fusion Rule Formulation for Bayes Binary Decision Formulation of Fusion Rules via Polynomials of Sensor Rules Fixed-Point Type Necessary Condition for the Optimal Sensor Rules Finite Convergence of the Discretized AlgorithmUnified Fusion Rule Expression of the Unified Fusion Rule Numerical Examples Two Sensors Three Sensors Four SensorsExtension to Neyman–Pearson Decision Algorithm Searching for Optimal Sensor Rules Numerical Examples General Network Statistical Decision Fusion Elementary Network Structures Parallel Network Tandem Network Hybrid (Tree) NetworkFormulation of Fusion Rule via Polynomials of Sensor Rules Fixed-Point Type Necessary Condition for Optimal Sensor RulesIterative Algorithm and Convergence Unified Fusion Rule Unified Fusion Rule for Parallel Networks Unified Fusion Rule for Tandem and Hybrid Networks Numerical Examples Three-Sensor System Four-Sensor SystemOptimal Decision Fusion with Given Sensor Rules Problem Formulation Computation of Likelihood Ratios Locally Optimal Sensor Decision Rules with Communications among Sensors Numerical Examples Two-Sensor Neyman–Pearson Decision System Three-Sensor Bayesian Decision System Simultaneous Search for Optimal Sensor Rules and Fusion Rule Problem Formulation Necessary Conditions for Optimal Sensor Rules and an Optimal Fusion Rule Iterative Algorithm and Its Convergence Extensions to Multiple-Bit Compression and Network Decision Systems Extensions to theMultiple-Bit Compression Extensions to Hybrid Parallel Decision System and Tree Network Decision System Numerical Examples Two Examples for Algorithm 3.2 An Example for Algorithm 3.3Performance Analysis of Communication Direction for Two-Sensor Tandem Binary Decision System Problem Formulation SystemModel Bayes Decision Region of Sensor 2 Bayes Decision Region of Sensor 1 (Fusion Center) Bayes Cost FunctionResults Numerical ExamplesNetwork Decision Systems with Channel Errors Some Formulations about Channel Error Necessary Condition for Optimal Sensor Rules Given a Fusion Rule Special Case: Mutually Independent Sensor Observations Unified Fusion Rules for Network Decision Systems Network Decision Structures with Channel ErrorsUnified Fusion Rule in Parallel Bayesian Binary Decision System Unified Fusion rules for General Network Decision Systems with Channel Errors Numerical ExamplesParallel Bayesian Binary Decision System Three-Sensor Decision System Some Uncertain Decision CombinationsRepresentation of Uncertainties Dempster Combination Rule Based on Random Set Formulation Dempster’s Combination Rule Mutual Conversion of the Basic Probability Assignment and the Random Set Combination Rules of the Dempster–Shafer Evidences via Random Set Formulation All Possible Random Set Combination Rules Correlated Sensor Basic Probabilistic Assignments Optimal Bayesian Combination Rule Examples of Optimal Combination RuleFuzzy Set Combination Rule Based on Random Set Formulation Mutual Conversion of the Fuzzy Set and the Random Set Some Popular Combination Rules of Fuzzy Sets General Combination RulesUsing the Operations of Sets Only Using the More General Correlation of the Random Variables Relationship between the t-Norm and Two-Dimensional Distribution Function ExamplesHybrid Combination Rule Based on Random Set Formulation Convex Linear Estimation FusionLMSE Estimation Fusion Formulation of LMSE Fusion Optimal FusionWeights Efficient Iterative Algorithm for Optimal Fusion AppropriateWeightingMatrix Iterative Formula of OptimalWeightingMatrix Iterative Algorithm for Optimal Estimation Fusion ExamplesRecursion of Estimation Error Covariance in Dynamic Systems Optimal Dimensionality Compression for Sensor Data in Estimation Fusion Problem Formulation Preliminary Analytic Solution for Single-Sensor Case Search for Optimal Solution in the Multisensor Case Existence of the Optimal Solution Optimal Solution at a Sensor While Other Sensor Compression Matrices Are Given Numerical ExampleQuantization of Sensor Data Problem Formulation Necessary Conditions for Optimal Sensor Quantization Rules and Optimal Linear Estimation Fusion Gauss–Seidel Iterative Algorithm for Optimal Sensor Quantization Rules and Linear Estimation Fusion Numerical Examples Kalman Filtering FusionDistributed Kalman Filtering Fusion with Cross-Correlated Sensor Noises Problem Formulation Distributed Kalman Filtering Fusion without Feedback Optimality of Kalman Filtering Fusion with Feedback Global Optimality of the Feedback Filtering Fusion Local Estimate Errors The Advantages of the FeedbackDistributed Kalman Filtering Fusion with Singular Covariances of Filtering Error and Measurement NoisesEquivalence Fusion Algorithm LMSE Fusion Algorithm Numerical ExamplesOptimal Kalman Filtering Trajectory Update with Unideal Sensor MessagesOptimal Local-processor Trajectory Update with Unideal Measurements Optimal Local-Processor Trajectory Update with Addition of OOSMs Optimal Local-Processor Trajectory Update with emoval of Earlier Measurement Optimal Local-Processor Trajectory Update with Sequentially Processing Unideal Measurements Numerical Examples Optimal Distributed Fusion Trajectory Update with Local-Processor Unideal Updates Optimal Distributed Fusion Trajectory Update with Addition of Local OOSMUpdate Optimal Distributed State Trajectory Update with Removal of Earlier Local Estimate Optimal Distributed Fusion Trajectory Update with Sequential Processing of Local Unideal UpdatesRandom Parameter Matrices Kalman Filtering FusionRandom Parameter Matrices Kalman Filtering Random Parameter Matrices Kalman Filtering with Multisensor Fusion Some Applications Application to Dynamic Process with False Alarm Application to Multiple-Model Dynamic Process Novel Data Association Method Based on the Integrated Random Parameter Matrices Kalman Filtering Some Traditional Data Association Algorithms Single-Sensor DAIRKF Multisensor DAIRKF Numerical Examples Distributed Kalman Filtering Fusion with Packet Loss/Intermittent Communications Traditional Fusion Algorithms with Packet Loss Sensors Send Raw Measurements to Fusion CenterSensors Send Partial Estimates to Fusion Center Sensors Send Optimal Local Estimates to Fusion Center RemodeledMultisensor System Distributed Kalman Filtering Fusion with Sensor Noises Cross-Correlated and Correlated to Process NoiseOptimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss Suboptimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss Robust Estimation Fusion Robust LinearMSE Estimation Fusion Minimizing Euclidean Error Estimation Fusion for Uncertain Dynamic System Preliminaries Problem Formulation of Centralized FusionState Bounding Box Estimation Based on Centralized FusionState Bounding Box Estimation Based on Distributed Fusion Measures of Size of an Ellipsoid or a Box Centralized Fusion Distributed Fusion Fusion of Multiple Algorithms Numerical Examples Figures 7.4 through 7.7 for Comparisons between Algorithms 7.1 and 7.2 Figures 7.8 through 7.10 for Fusion of Multiple AlgorithmsMinimized Euclidean Error Data Association for Uncertain Dynamic System Formulation of Data Association MEEDA Algorithms Numerical Examples References Index