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Networked Multisensor Decision and Estimation Fusion

Based on Advanced Mathematical Methods

By Yunmin Zhu, Jie Zhou, Xiaojing Shen, Enbin Song, Yingting Luo

CRC Press – 2012 – 437 pages

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    978-1-43-987452-3
    July 5th 2012

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.

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

Name: Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods (Hardback)CRC Press 
Description: By Yunmin Zhu, Jie Zhou, Xiaojing Shen, Enbin Song, Yingting Luo. 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,...
Categories: Systems & Controls, Mathematics & Statistics for Engineers, Instrumentation, Measurement & Testing