1st Edition

Networked Multisensor Decision and Estimation Fusion Based on Advanced Mathematical Methods

    440 Pages 79 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    Yunmin Zhu, Jie Zhou