Data Fusion Mathematics : Theory and Practice / Jitendra R. Raol [and three others].

Format:

Book

Author/Creator:

Raol, J. R. (Jitendra R.), 1947- author.

Language:

English

Subjects (All):

Multisensor data fusion--Mathematics.

Multisensor data fusion.

Signal processing--Mathematics.

Signal processing.

Statistical matching.

Wireless sensor nodes.

Wireless sensor networks.

Physical Description:

1 online resource (695 pages)

Edition:

Second edition.

Place of Publication:

Boca Raton, FL : CRC Press, [2025]

Summary:

Data Fusion Mathematics: Theory and Practice offers a comprehensive overview of data fusion (DF) and provides a proper and adequate understanding of the basic mathematics directly related to DF.

Contents:

Cover

Half Title

Title Page

Copyright Page

Dedication

Table of Contents

Preface

Acknowledgments

Authors

Introduction

Chapter 1 Introduction to Data Fusion Process

1.1 Data Fusion Aspects

1.2 Data Fusion Models

1.2.1 Joint Directors of Laboratories Model

1.2.2 Modified Waterfall Fusion Model

1.2.3 The Intelligence Cycle-Based Model

1.2.4 Boyd Model

1.2.5 Omnibus Model

1.2.6 Dasarathy Model

1.3 Sensor Data Fusion Configurations

1.3.1 Complementary

1.3.2 Competitive

1.3.3 Cooperative

1.4 Sensor-Data Fusion Architectures

1.4.1 Centralized Fusion

1.4.2 Distributed Fusion

1.4.3 Hybrid Fusion

1.5 Data Fusion Process

Exercises

References

Chapter 2 Statistics, Probability Models, and Reliability: Towards Probabilistic Data Fusion

2.1 Introduction

2.2 Statistics

2.2.1 Mathematical Expectation

2.2.2 Variance, Co-Variance, and Standard Deviation

2.2.3 Correlations and Autocorrelation Function

2.3 Probability Models

2.4 Probabilistic Methods for Data Fusion

2.4.1 Bayesian Formula

2.4.2 Data Fusion Based on Bayesian Rule

2.4.3 Distributed Data Fusion Based on Bayesian Rule

2.4.4 Log-Likelihoods Based Data Fusion

2.5 Reliability in Data Fusion

2.5.1 Bayesian Method

2.5.2 Evidential Method

2.5.3 Fuzzy Logic-Based Approach

2.5.4 Markov Models for Reliability Evaluation

2.5.5 Reliability in Least Squares Estimation

2.6 Information Methods

2.6.1 Entropy and Information

2.6.2 Fisher Information

2.6.3 Information Pooling Methods

2.7 Probability Concepts for Expert System and Data Fusion

2.7.1 Probabilistic Rules and Evidence

2.7.2 Propagation of Confidence Limits

2.7.3 Combining-Fusion of Multiple Reports

2.8 Probabilistic Methods for Data Fusion - Theoretical Examples

2.8.1 Maximum Entropy Method.

2.8.2 Maximum Likelihood Method

2.8.3 Maximum Likelihood and Incomplete Data

2.8.4 Bayesian Approach

2.8.5 Data Fusion Aspects/Examples

2.8.6 Some Realistic Data Fusion Problems

2.9 Bayesian Formula and Sensor/Data Fusion-Illustrative Example

Appendix 2A Unified Estimation Fusion

Chapter 3 Fuzzy Logic and Possibility Theory Based Fusion

3.1 Introduction

3.2 Fuzzy Logic Type I

3.2.1 Membership Functions for Fuzzification

3.2.2 Fuzzy Set Operations

3.2.3 Fuzzy Inference System

3.2.4 Triangular-Norm (T-Norms)

3.2.5 S-Norm (Triangular-Conorm)

3.2.6 Defuzzification

3.2.7 Fuzzy Implication Functions

3.3 Adaptive Neuro-Fuzzy Inference System-ANFIS

3.4 Fuzzy Logic Type 2

3.4.1 Type 2 and Interval Type 2 Fuzzy Sets

3.4.2 Interval Type 2 Fuzzy Logic Mathematics

3.4.3 The Set-Theoretic Operations for IT2FS

3.4.4 Further Operations on IT2FS

3.5 Fuzzy Intelligent Sensor Fusion

3.6 FL-Based Procedure for Generating the Weights for a DF Rule

3.6.1 Fuzzification

3.6.2 Rule Generation Using FIS

3.6.3 Defuzzification

3.7 FL-ANFIS for Parameter Estimation and Generation of DF Weights-Illustrative Examples

3.7.1 ANIFS Based Parameter Estimation

3.7.2 ANIFS for Deciphering a Linear DF Rule for Images

3.8 Possibility Theory

3.8.1 Possibility Distribution

3.8.2 Possibility Set Functions

3.8.3 Joint Possibility Distribution, Specificity, and Non-Interactivity

3.8.4 Possibility and Necessity of Fuzzy Events

3.8.5 Conditional Possibility

3.9 Fusion of Long Wave IR and EOT Images Using Type 1 and Type 2 Fuzzy Logics - Illustrative Examples

3.9.1 Fuzzy Logic Systems - Takagi-Sugeno-Kang Inference Method

3.9.2 IT2 Fuzzy Set Operations and Inference

3.9.3 Fuzzy Sets Type Reduction.

3.9.4 Implementation of Image Fusion Using MATLAB FLS Toolbox

3.9.5 Results and Discussion

3.10 Data Fusion Using D-S and Possibility Theory - Illustrative Example

3.10.1 Information Fusion for Close Range Mine Detection

3.10.2 Close-Range Mine Detection Measures

3.10.3 Fusion Combination Evaluation

3.10.4 Comparison and Decision Results

Appendix 3A Type 1-Triangular MF-MATLAB Code

Appendix 3B Type 2-Gaussian MF-MATLAB Code

Appendix 3C Fuzzy Inference Calculations-MATLAB Code

Chapter 4 Filtering, Target-Tracking, and Kinematic Data Fusion

4.1 Introduction

4.2 The Kalman Filter

4.2.1 State and Sensor Models

4.2.2 The Kalman Filter Algorithm

4.2.3 The Innovations - Kalman Filter Residuals

4.2.4 Steady-State Filters

4.2.5 Asynchronous, Delayed, and A-Sequent Measurements

4.2.6 The Extended Kalman Filter

4.2.7 Kalman Filter - A Natural Data-Level Fuser

4.3 The Multi-Sensor Data Fusion and Kalman Filter

4.3.1 Measurement Models

4.3.2 Group-Sensor Method

4.3.3 Sequential-Sensor Method

4.3.4 Inverse-Covariance Form

4.3.5 Track-to-Track Fusion

4.4 Non-Linear Data Fusion Methods

4.4.1 Likelihood Estimation Methods

4.4.2 Derivative-Free Filtering and Fusion

4.4.3 Other Nonlinear Tracking Filters

4.5 Data Association in Multisensory Systems

4.5.1 Nearest-Neighbor Standard Filter

4.5.2 Probabilistic Data Association Filter-PDAF

4.5.3 Multiple-Hypothesis Filter-MHT

4.6 Information Filtering

4.6.1 Square-Root Information Filtering

4.6.2 Data Fusion Based on Square Root Information Filtering

4.7 H-Infinity Filtering Based Data Fusion

4.7.1 H-Infinity Posterior Filter

4.7.2 Risk-Sensitive H-Infinity Filter

4.7.3 Global H-Infinity Filter for Data Fusion

4.7.4 Hybrid H[sub(2)] and H-Infinity Filter.

4.8 Optimal Filtering for Data Fusion with Missing Measurements

4.8.1 Basic Filter for Missing Measurements - State Vector Fusion

4.8.2 Optimal Filter for Missing Measurements-Measurement Level Fusion

4.8.3 Optimal Filter in Two Parts for State Vector Fusion

4.8.4 Optimal Filter in Two Parts for Measurement Level Fusion

4.8.5 Performance Evaluation of the Filters for Handling Missing Data-Illustrative Examples

4.9 Factorization Filtering and Sensor Data Fusion - Illustrative Example

4.9.1 Kalman U-D Factorization Filter

4.9.2 UD Factorization Filter for Correlated Process Noise and Bias Parameters

4.9.3 Sensor Fusion Scheme

4.9.4 Performance Evaluation of UD and UDCB Filters for Tracking and Fusion

Chapter 5 Decentralized Data Fusion Systems

5.1 Introduction

5.2 Data Fusion Architectures

5.2.1 Hierarchical Data Fusion Architectures

5.2.2 Distributed Data Fusion Architectures

5.2.3 Decentralized Data Fusion Architectures

5.3 Decentralized Estimation and Fusion

5.3.1 Information Filter

5.3.2 Information Filter and Bayesian Theorem

5.3.3 Information Filter in Multi-Sensor Estimation

5.3.4 Hierarchical Information Filter

5.3.5 The Decentralized Information Filter

5.4 Decentralized Multi-Target Tracking

5.4.1 Decentralized Data Association

5.4.2 Decentralized Identification and Bayesian Theorem

5.5 Millman's Formulae in Sensor Data Fusion

5.5.1 Generalized Millman's Formula

5.5.2 Millman's Fusion Formulae in Filtering Algorithms

5.5.3 Millman's Fusion Formulae in Smoothing Algorithms

5.5.4 Generalized Millman's Formula in State Estimation

5.6 SRIF for Data Fusion in Decentralized Network with Four Sensor Nodes - Illustrative Example

Chapter 6 Component Analysis and Data Fusion

6.1 Introduction.

6.2 Independent Component Analysis

6.2.1 Independence

6.2.2 Non-Gaussian Property

6.2.3 Determination of Non-Gaussian Property

6.2.4 Determination of Independent Components Based on Information Theory

6.2.5 Maximum Likelihood Estimation

6.2.6 Demonstration of FastICA Code - Illustrative Example

6.3 An Approach to Image Fusion Using ICA Bases

6.3.1 Fusion Preliminaries

6.3.2 Major Fusion Strategies

6.3.3 Independent Component Analysis and Topographic ICA Bases

6.3.4 Training and Properties of ICA Bases

6.3.5 Image Fusion Using ICA Bases

6.3.6 Pixel- and Region-Based Fusion Rules Using ICA Bases

6.4 Principal Component Analysis

6.4.1 Image Fusion Using PCA Coefficients

6.4.2 Image Fusion of Blurred Aircraft Images Using PCA Coefficients - Illustrative Example

6.5 Discrete Cosine Transform

6.5.1 Multi-Resolution Discrete Cosine Transform

6.5.2 Multi Sensor Image Fusion

6.6 Wavelet Transform - A Brief Theory

6.6.1 Image Analysis for Image Fusion by WT

6.6.2 Image Fusion of Blurred Aircraft Images Using WT Coefficients - Illustrative Example

6.7 An Approach to Image Fusion Using ICA and Wavelets

6.8 Nonlinear ICA and PCA

6.8.1 Nonlinear ICA

6.8.2 Nonlinear PCA

6.9 Curve-Let Transform for Image Fusion

6.10 Image Fusion Using Multi-resolution Singular Value Decomposition

6.10.1 Multi-Resolution SVD

6.10.2 Image Fusion Using MRSVD - Illustrative Example

Appendix 6A Illustrative Example: Image Fusion Using Independent Component Analysis

Chapter 7 Image Algebra and Image Fusion

7.1 Introduction

7.1.1 A Digital Image

7.1.2 Needs of Image Fusion

7.2 Image Algebra

7.2.1 Point and Value Sets

7.2.2 Images and Templates

7.2.3 Recursive Templates

7.2.4 Neighborhoods and the p-Product-Illustrative Examples.

7.3 Pixels and Features of an Image.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

ISBN:

1-04-036262-1

1-04-036256-7

1-003-56026-1

9781003560265

OCLC:

1515074967

Publisher Number:

CIPO000247268