Networked Multisensor Decision and Estimation Fusion : Based on Advanced Mathematical Methods book cover
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Networked Multisensor Decision and Estimation Fusion
Based on Advanced Mathematical Methods




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ISBN 9781439874523
Published July 5, 2012 by CRC Press
437 Pages 79 B/W Illustrations

 
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Book Description

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.

Table of Contents

Introduction
Fundamental 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 Optimization 
     Convex 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 Algorithm 
Unified Fusion Rule 
     Expression of the Unified Fusion Rule 
     Numerical Examples 
          Two Sensors
          Three Sensors 
          Four Sensors 
Extension 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) Network
Formulation of Fusion Rule via Polynomials of Sensor Rules
Fixed-Point Type Necessary Condition for Optimal Sensor Rules 
Iterative 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 System
Optimal 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 3.3
Performance 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 Function 
     Results 
     Numerical Examples 
Network 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 Errors
          Unified Fusion Rule in Parallel Bayesian Binary Decision System
          Unified Fusion rules for General Network Decision Systems with Channel Errors 
     Numerical Examples 
          Parallel Bayesian Binary Decision System 
          Three-Sensor Decision System

Some Uncertain Decision Combinations
Representation 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 Rule
Fuzzy 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 Rules 
     Using the Operations of Sets Only 
     Using the More General Correlation of the Random Variables 
     Relationship between the t-Norm and Two-Dimensional Distribution Function 
     Examples 
Hybrid Combination Rule Based on Random Set Formulation

Convex Linear Estimation Fusion
LMSE 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
     Examples
Recursion 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 Example 
Quantization 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 Fusion
Distributed 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 Feedback 
Distributed Kalman Filtering Fusion with Singular Covariances of Filtering Error and Measurement Noises
     Equivalence Fusion Algorithm 
     LMSE Fusion Algorithm 
     Numerical Examples 
Optimal Kalman Filtering Trajectory Update with Unideal Sensor Messages 
     Optimal 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 Updates 
Random Parameter Matrices Kalman Filtering Fusion 
     Random 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 Center 
          Sensors 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 Noise 
     Optimal 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 Fusion 
          State Bounding Box Estimation Based on Centralized Fusion
          State 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 Algorithms
Minimized Euclidean Error Data Association for Uncertain Dynamic System
     Formulation of Data Association 
     MEEDA Algorithms
     Numerical Examples

References

Index

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