1st Edition
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.
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
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
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
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
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
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