1st Edition

# Data Fusion Mathematics Theory and Practice

By Jitendra R. Raol Copyright 2016
504 Pages 70 B/W Illustrations
by CRC Press

600 Pages 122 B/W Illustrations
by CRC Press

600 Pages
by CRC Press

Also available as eBook on:

Fills the Existing Gap of Mathematics for Data Fusion

Data fusion (DF) combines large amounts of information from a variety of sources and fuses this data algorithmically, logically and, if required intelligently, using artificial intelligence (AI). Also, known as sensor data fusion (SDF), the DF fusion system is an important component for use in various applications that include the monitoring of vehicles, aerospace systems, large-scale structures, and large industrial automation plants. Data Fusion Mathematics: Theory and Practice offers a comprehensive overview of data fusion, and provides a proper and adequate understanding of the basic mathematics directly related to DF. The material covered can be used for evaluation of the performances of any designed and developed DF systems. It tries to answer whether unified data fusion mathematics can evolve from various disparate mathematical concepts, and highlights mathematics that can add credibility to the data fusion process.

Focuses on Mathematical Tools That Use Data Fusion

This text explores the use of statistical/probabilistic signal/image processing, filtering, component analysis, image algebra, decision making, and neuro-FL–GA paradigms in studying, developing and validating data fusion processes (DFP). It covers major mathematical expressions, and formulae and equations as well as, where feasible, their derivations. It also discusses SDF concepts, DF models and architectures, aspects and methods of type 1 and 2 fuzzy logics, and related practical applications. In addition, the author covers soft computing paradigms that are finding increasing applications in multisensory DF approaches and applications.

This book:

• Explores the use of interval type 2 fuzzy logic and ANFIS in DF
• Covers the mathematical treatment of many types of filtering algorithms, target-tracking methods, and kinematic DF methods
• Presents single and multi-sensor tracking and fusion mathematics
• Considers specific DF architectures in the context of decentralized systems
• Discusses information filtering, Bayesian approaches, several DF rules, image algebra and image fusion, decision fusion, and wireless sensor network (WSN) multimodality fusion

Data Fusion Mathematics: Theory and Practice incorporates concepts, processes, methods, and approaches in data fusion that can help you with integrating DF mathematics and achieving higher levels of fusion activity, and clarity of performance. This text is geared toward researchers, scientists, teachers and practicing engineers interested and working in the multisensor data fusion area.

Introduction to Data Fusion Process
Data Fusion Aspects
Data Fusion Models
Sensor Data Fusion Configurations
Sensor Data Fusion Architectures
Data Fusion Process
References
Statistics, Probability Models and Reliability: Towards Probabilistic Data Fusion
Introduction
Statistics
Probability Models
Probabilistic Methods for DF
Reliability in DF
Information Methods
Probability Concepts for Expert System and DF
Probabilistic Methods for DF: Theoretical Examples
Bayesian Formula and Sensor/DF: Illustrative Example
References
Fuzzy Logic and Possibility Theory-Based Fusion
Introduction
Fuzzy Logic Type I
Fuzzy Logic Type
Fuzzy Intelligent Sensor Fusion
FL-based Procedure for Generating the Weights for a DF Rule
FL-ANFIS for Parameter Estimation and Generation of DF Weights: Illustrative Examples
Possibility Theory
Fusion of Long-Wave IR and EOT Images Using Type 1 and Type 2 Fuzzy Logics: Illustrative Examples
DF Using Dempster-Shafer and Possibility Theory: Illustrative Example
A: Type 1 - Triangular MF-MATLAB Code
B: Type 2 - Gaussian MF-MATLAB Code
Fuzzy Inference Calculations - MATLAB Code
References
Filtering, Target Tracking and Kinematic Data Fusion
Introduction
The Kalman Filter
The Multi-Sensor Data Fusion and Kalman Filter
Non-linear Data Fusion Methods
Data Association in MS Systems
Information Filtering
HI Filtering-Based DF
Optimal Filtering for Data Fusion with Missing Measurements
Factorisation Filtering and Sensor DF: Illustrative Example
References
Decentralised Data Fusion Systems
Introduction
Data Fusion Architectures
Decentralised Estimation and Fusion
Decentralised Multi-Target Tracking
Millman's Formulae in Sensor Data Fusion
SRIF for Data Fusion in Decentralised Network with Four Sensor Nodes: Illustrative Example
References
Component Analysis and Data Fusion
Introduction
Independent Component Analysis
An Approach to Image Fusion Using ICA Bases
Principal Component Analysis
Discrete-Cosine Transform
WT: A Brief Theory
An Approach to Image Fusion Using ICA and Wavelets
Non-Linear ICA and PCA
Image Fusion Using MR Singular Value Decomposition
References
Image Algebra and Image Fusion
S. Sethu Selvi
Introduction
Image Algebra
Pixels and Features of an Image
Inverse Image
Red, Green and Blue, Grey Images and Histograms
Image Segmentation
Noise Processes in an Observed/Acquired Image
Image Feature Extraction Methods
Image Transformation and Filtering Approaches
Image Fusion Mathematics
Image Fusion Algorithms
Performance Evaluation
Multimodal Biometric Systems and Fusion: Illustrative Examples
References
Decision Theory and Fusion
Introduction
Loss and Utility Functions
Bayesian DT
Decision Making with Multiple Information Sources
Fuzzy Modelling Approach for Decision Analysis/Fusion
Fuzzy-Evolutive Integral Approach
Decision Making Based on Voting
DeF Using FL for Aviation Scenarios
DeF Strategies
SA with FL and DeF for Aviation Scenarios: Illustrative Examples
References
Wireless Sensor Networks and Multimodal Data Fusion
Introduction
Communication Networks and Their Topologies in WSNs
Sensor/Wireless Sensor Networks
Wireless Sensor Networks and Architectures
Sensor Data Fusion in WSN
Multimodality Sensor Fusion
Decision Fusion Rules in WSN
Data Aggregation in WSN
Hybrid Data and Decision Fusion in WSN
Optimal Decision Fusion in WSN
References
Soft Computing Approaches to Data Fusion
Introduction
Artificial Neural Networks
Recurrent Neural Networks
FL and Systems as SC Paradigm
FL in Kalman Filter for Image-Centroid Tracking: A Type of Fusion
Genetic Algorithms
SDF Approaches Using SC Methods: Illustrative Examples
Machine Learning
Neural-Fuzzy-Genetic Algorithm Fusion
Image Analysis Using ANFIS: Illustrative Example
Acknowledgement
References
A: Some Algorithms and/or Their Derivations
B: Other Methods of DF and Fusion Performance Evaluation Metrics
C:Automatic Data Fusion
D: Notes and Information on Data Fusion Software Tools
E: Definitions of Sensor DF in Literature
F: Some Current Research Topics in DF

### Biography

Jitendra R. Raol received a BE and ME in electrical engineering from the MS University of Baroda, Vadodara in 1971 and 1973, respectively, and a PhD (in electrical and computer engineering) from McMaster University, Hamilton, Canada in 1986. He taught for two years at the MS University of Baroda before joining the National Aeronautical Laboratory in 1975. He retired in 2007 as Scientist G and head, flight mechanics and control division at CSIR-NAL. His main research interests are DF, system identification, state/parameter estimation, flight mechanics–flight data analysis, H-infinity filtering, ANNs, fuzzy systems, genetic algorithms, and soft technologies for robotics.

"An application's guide to sensor fusion - Raol's comprehensive yet succinct handling of the mathematical fundamentals of sensor fusion make this a reference source for every practitioner."
—Ajith K. Gopal, The Council for Scientific and Industrial Research in South Africa

"… comprehensively presents tools for data fusions. Initial two chapters cover basic of data fusion and state estimations, especially Bayesian framework. The rest of chapters deal with advance topics that include fuzzy-logic based design, centralized and decentralized strategies, and image fusion. I feel the content of the book will useful both academia and industry."
—Dr. Mangal Kothari, Indian Institute of Technology Kanpur