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Multi-Sensor Data Fusion with MATLAB.pdf
9781439800058-f
Multi-Sensor Data Fusion with MATLAB®
Contents
Preface
Acknowledgments
Author
Contributors
Introduction
References
9781439800058-p1
Part I: Theory of Data Fusion and Kinematic-Level Fusion
9781439800058-c1
Chapter 1: Introduction
9781439800058-c2
Chapter 2: Concepts and Theory of Data Fusion
2.1 Models of the Data Fusion Process and Architectures
2.1.1 Data Fusion Models
2.1.1.1 Joint Directors of Laboratories Model
2.1.1.2 Modified Waterfall Fusion Model
2.1.1.3 Intelligence Cycle–Based Model
2.1.1.4 Boyd Model
2.1.1.5 Omnibus Model
2.1.2 Fusion Architectures
2.1.2.1 Centralized Fusion
2.1.2.2 Distributed Fusion
2.1.2.3 Hybrid Fusion
2.2 Unified Estimation Fusion Models and Other Methods
2.2.1 Definition of the Estimation Fusion Process
2.2.2 Unified Fusion Models Methodology
2.2.2.1 Special Cases of the Unified Fusion Models
2.2.2.2 Correlation in the Unified Fusion Models
2.2.3 Unified Optimal Fusion Rules
2.2.3.1 Best Linear Unbiased Estimation Fusion Rules with Complete Prior Knowledge
2.2.3.2 Best Linear Unbiased Estimation Fusion Rules without Prior Knowledge
2.2.3.3 Best Linear Unbiased Estimation Fusion Rules with Incomplete Prior Knowledge
2.2.3.4 Optimal-Weighted Least Squares Fusion Rule
2.2.3.5 Optimal Generalized Weighted Least Squares Fusion Rule
2.2.4 Kalman Filter Technique as a Data Fuser
2.2.4.1 Data Update Algorithm
2.2.4.2 State-Propagation Algorithm
2.2.5 Inference Methods
2.2.6 Perception, Sensing, and Fusion
2.3 Bayesian and Dempster–Shafer Fusion Methods
2.3.1 Bayesian Method
2.3.1.1 Bayesian Method for Fusion of Data from Two Sensors
2.3.2 Dempster–Shafer Method
2.3.3 Comparison of the Bayesian Inference Method and the Dempster–Shafer Method
2.4 Entropy-Based Sensor Data Fusion Approach
2.4.1 Definition of Information
2.4.2 Mutual Information
2.4.3 Entropy in the Context of an Image
2.4.4 Image-Noise Index
2.5 Sensor Modeling, Sensor Management, and Information Pooling
2.5.1 Sensor Types and Classification
2.5.1.1 Sensor Technology
2.5.1.2 Other Sensors and their Important Features and Usages
2.5.1.3 Features of Sensors
2.5.1.4 Sensor Characteristics
2.5.2 Sensor Management
2.5.2.1 Sensor Modeling
2.5.2.2 Bayesian Network Model
2.5.2.3 Situation Assessment Process
2.5.3 Information-Pooling Methods
2.5.3.1 Linear Opinion Pool
2.5.3.2 Independent Opinion Pool
2.5.3.3 Independent Likelihood Pool
9781439800058-c3
Chapter 3: Strategies and Algorithms for Target Tracking and Data Fusion
3.1 State-Vector and Measurement-Level Fusion
3.1.1 State-Vector Fusion
3.1.2 Measurement Data–Level Fusion
3.1.3 Results with Simulated and Real Data Trajectories
3.1.4 Results for Data from a Remote Sensing Agency with Measurement Data–Level Fusion
3.2 Factorization Kalman Filters for Sensor Data Characterization and Fusion
3.2.1 Sensor Bias Errors
3.2.2 Error State-Space Kalman Filter
3.2.3 Measurement and Process Noise Covariance Estimation
3.2.4 Time Stamp and Time Delay Errors
3.2.5 Multisensor Data Fusion Scheme
3.2.5.1 UD Filters for Trajectory Estimation
3.2.5.2 Measurement Fusion
3.2.5.3 State-Vector Fusion
3.2.5.4 Fusion Philosophy
3.3 Square-Root Information Filtering and Fusion in Decentralized Architecture
3.3.1 Information Filter
3.3.1.1 Information Filter Concept
3.3.1.2 Square Root Information Filter Algorithm
3.3.2 Square Root Information Filter Sensor Data Fusion Algorithm
3.3.3 Decentralized Square Root Information Filter
3.3.4 Numerical Simulation Results
3.4 Nearest Neighbor and Probabilistic Data Association Filter Algorithms
3.4.1 Nearest Neighborhood Kalman Filter
3.4.2 Probabilistic Data Association Filter
3.4.3 Tracking and Data Association Program for Multisensor, Multitarget Sensors
3.4.3.1 Sensor Attributes
3.4.3.2 Data Set Conversion
3.4.3.3 Gating in Multisensor, Multitarget
3.4.3.4 Measurement-to-Track Association
3.4.3.5 Initiation of Track and Extrapolation of Track
3.4.3.6 Extrapolation of Tracks into Next Sensor Field of View
3.4.3.7 Extrapolation of Tracks into Next Scan
3.4.3.8 Track Management Process
3.4.4 Numerical Simulation
3.5 Interacting Multiple Model Algorithm for Maneuvering Target Tracking
3.5.1 Interacting Multiple Model Kalman Filter Algorithm
3.5.1.1 Interaction and Mixing
3.5.1.2 Kalman Filtering
3.5.1.3 Mode Probability Update
3.5.1.4 State Estimate and Covariance Combiner
3.5.2 Target Motion Models
3.5.2.1 Constant Velocity Model
3.5.2.2 Constant Acceleration Model
3.5.3 Interacting Multiple Model Kalman Filter Implementation
3.5.3.1 Validation with Simulated Data
3.6 Joint Probabilistic Data Association Filter
3.6.1 General Version of a Joint Probabilistic Data Association Filter
3.6.2 Particle Filter Sample–Based Joint Probabilistic Data Association Filter
3.7 Out-of-Sequence Measurement Processing for Tracking
3.7.1 Bayesian Approach to the Out-of-Sequence Measurement Problem
3.7.2 Out-of-Sequence Measurement with Single Delay and No Clutter
3.7.2.1 Y Algorithm
3.7.2.2 Augmented State Kalman Filters
3.8 Data Sharing and Gain Fusion Algorithm for Fusion
3.8.1 Kalman Filter–Based Fusion Algorithm
3.8.2 Gain Fusion–Based Algorithm
3.8.3 Performance Evaluation
3.9 Global Fusion and H-Infinity Filter–Based Data Fusion
3.9.1 Sensor Data Fusion using H-Infinity Filters
3.9.2 H-Infinity a Posteriori Filter–Based Fusion Algorithm
3.9.3 H-Infinity Global Fusion Algorithm
3.9.4 Numerical Simulation Results
3.10 Derivative-Free Kalman Filters for Fusion
3.10.1 Derivative-Free Kalman Filters
3.10.2 Numerical Simulation
3.10.2.1 Initialization of the Data Fusion-Derivative Free Kalman Filter Algorithm
3.10.2.2 Computation of the Sigma Points
3.10.2.3 State and Covariance Propagation
3.10.2.4 State Covariance Updateand
3.11 Missile Seeker Estimator
3.11.1 Interacting Multiple Model–Augmented Extended Kalman Filter Algorithm
3.11.1.1 State Model
3.11.1.2 Measurement Model
3.11.2 Interceptor–Evader Engagement Simulation
3.11.2.1 Evader Data Simulation
3.11.3 Performance Evaluation of Interacting Multiple Model–Augmented Extended Kalman Filter
3.12 Illustrative Examples
9781439800058-c4
Chapter 4: Performance Evaluation of Data Fusion Systems, Software, and Tracking
4.1 Real-Time Flight Safety Expert System Strategy
4.1.1 Autodecision Criteria
4.1.2 Objective of a Flight Test Range
4.1.3 Scenario of the Test Range
4.1.3.1 Tracking Instruments
4.1.3.2 Data Acquisition
4.1.3.3 Decision Display System
4.1.4 Multisensor Data Fusion System
4.1.4.1 Sensor Fusion for Range Safety Computer
4.1.4.2 Algorithms for Fusion
4.1.4.3 Decision Fusion
4.2 Multisensor Single-Target Tracking
4.2.1 Hierarchical Multisensor Data Fusion Architecture and Fusion Scheme
4.2.2 Philosophy of Sensor Fusion
4.2.3 Data Fusion Software Structure
4.2.3.1 Fusion Module 1
4.2.3.2 Fusion Modules 2 and 3
4.2.4 Validation
4.3 Tracking of a Maneuvering Target—Multiple-Target Tracking Using Interacting Multiple Model Probability Data Association Filter and Fusion
4.3.1 Interacting Multiple Model Algorithm
4.3.1.1 Automatic Track Formation
4.3.1.2 Gating and Data Association
4.3.1.3 Interaction and Mixing in Interactive Multiple Model Probabilistic Data Association Filter
4.3.1.4 Mode-Conditioned Filtering
4.3.1.5 Probability Computations
4.3.1.6 Combined State and Covariance Prediction and Estimation
4.3.2 Simulation Validation
4.3.2.1 Constant Velocity Model
4.3.2.2 Constant Acceleration Model
4.3.2.3 Performance Evaluation and Discussions
4.3.2.3.1 Evaluation of Interacting Multiple Models Probability Data Association Filter
4.3.2.3.2 Multiple Sensors—Fusion of Data
4.4 Evaluation of Converted Measurement and Modified Extended Kalman Filters
4.4.1 Error Model Converted Measurement Kalman Filter and Error Model Modified Extended Kalman Filter Algorithms
4.4.1.1 Error Model Converted Measurement Kalman Filter Algorithm
4.4.1.1.1 Error Model Kalman Filter
4.4.1.2 Error Model Modified Extended Kalman Filter Algorithm
4.4.2 Discussion of Results
4.4.2.1 Sensitivity Study on Error Model Modified Extended Kalman Filter
4.4.2.2 Comparison of Debiased Converted Measurements Kalman Filter, Error Model Converted Measurement Kalman Filter, and Error Model Modified Extended Kalman Filter Algorithms
4.5 Estimation of Attitude Using Low-Cost Inertial Platforms and Kalman Filter Fusion
4.5.1 Hardware System
4.5.2 Sensor Modeling
4.5.2.1 Misalignment Error Model
4.5.2.2 Temperature Drift Model
4.5.2.3 CG Offset Model
4.5.3 MATLAB®/Simulink Implementation
4.6.3.1 State Model
4.6.3.2 Measurement Model
4.5.4 Microcontroller Implementation
Epilogue
Exercises
References
9781439800058-p2
Part II: Fuzzy Logic and Decision Fusion
9781439800058-c5
Chapter 5: Introduction
9781439800058-c6
Chapter 6: Theory of Fuzzy Logic
6.1 Interpretation and Unification of Fuzzy Logic Operations
6.1.1 Fuzzy Sets and Membership Functions
6.1.2 Types of Fuzzy Membership Functions
6.1.2.1 Sigmoid-Shaped Function
6.1.2.1 Gaussian-Shaped Function
6.1.2.3 Triangle-Shaped Function
6.1.2.4 Trapezoid-Shaped Function
6.1.2.5 S-Shaped Function
6.1.2.6 Π-Shaped Function
6.1.2.7 Z-Shaped Function
6.1.3 Fuzzy Set Operations
6.1.3.1 Fuzzy Logic Operators
6.1.4 Fuzzy Inference System
6.1.4.1 Triangular Norm or T-norm
6.1.4.2 Fuzzy Implication Process Using T-norm
6.1.4.3 Triangular Conorm or S-norm
6.1.4.4 Fuzzy Inference Process Using S-norm
6.1.4.4.1 Fuzzy Complements
6.1.5 Relationships between Fuzzy Logic Operators
6.1.6 Sup (max)–Star (T-norm) Composition
6.1.6.1 Maximum–Minimum Composition (Mamdani)
6.1.6.2 Maximum Product Composition (Larsen)
6.1.7 Interpretation of the Connective “and”
6.1.8 Defuzzification
6.1.8.1 Centroid Method, or Center of Gravity or Center of Area
6.1.8.2 Maximum Decomposition Method
6.1.8.3 Center of Maxima or Mean of Maximum
6.1.8.4 Smallest of Maximum
6.1.8.5 Largest of Maximum
6.1.8.6 Height Defuzzification
6.1.9 Steps of the Fuzzy Inference Process
6.2 Fuzzy Implication Functions
6.2.1 Fuzzy Implication Methods
6.2.2 Comparative Evaluation of the Various Fuzzy Implication Methods s with Numerical Data
6.2.3 Properties of Fuzzy If-Then Rule Interpretations
6.3 Forward- and Backward-Chain Logic Criteria
6.3.1 Generalization of Modus Ponens Rule
6.3.2 Generalization of Modus Tollens Rule
6.4 Tool for the Evaluation of Fuzzy Implication Functions
6.4.1 Study of Criteria Satisfaction Using MATLAB® Graphics
6.5 Development of New Implication Functions
6.5.1 Study of Criteria Satisfaction by New Implication Function Using MATLAB and GUI Tools
6.6 Fuzzy Logic Algorithms and Final Composition Operations
6.7 Fuzzy Logic and Fuzzy Integrals in Multiple Network Fusion
9781439800058-c7
Chapter 7: Decision Fusion
7.1 Symbol- or Decision-Level Fusion
7.2 Soft Decisions in Kalman Filtering
7.3 Fuzzy Logic–Based Kalman Filter and Fusion Filters
7.3.1 Fuzzy Logic–Based Process and Design
7.3.2 Comparison of Kalman Filter and Fuzzy Kalman Filter
7.3.3 Comparison of Kalman Filter and Fuzzy Kalman Filter for Maneuvering Target Tracking
7.3.3.1 Training Set and Check-Set Data
7.3.3.2 Mild and Evasive Maneuver Data
7.3.4 Fuzzy Logic–Based Sensor Data Fusion
7.3.4.1 Kalman Filter Fuzzification
7.3.4.2 Fuzzy Kalman Filter Fuzzification
7.3.4.3 Numerical Simulation Results
7.4 Fuzzy Logic in Decision Fusion
7.4.1 Methods Available to Perform Situation Assessments
7.4.2 Comparison between Bayesian Network and Fuzzy Logic
7.4.2.1 Situation Assessment Using Fuzzy Logic
7.4.3 Level-3 Threat Refinement and Level-4 Process Refinement
7.4.4 Fuzzy Logic–Based Decision Fusion Systems
7.4.4.1 Various Attributes and Aspects of Fuzzy Logic–Based Decision Fusion Systems
7.5 Fuzzy Logic Bayesian Network for Situation Assessment
7.5.1 Description of Situation Assessment in Air Combat
7.5.1.1 Exercise Controller
7.5.1.2 Integrated Sensor Model
7.5.1.3 Data Processor
7.5.1.4 Pilot Mental Model
7.5.2 Bayesian Mental Model
7.5.2.1 Pair Agent Bayesian Network
7.5.2.2 Along Agent Bayesian Network
7.5.2.3 Attack Agent Bayesian Network
7.5.3 Results and Discussions
7.6 Fuzzy Logic–Based Decision Fusion in a Biometric System
7.6.1 Fusion in Biometric Systems
7.6.2 Fuzzy Logic Fusion
9781439800058-c8
Chapter 8: Performance Evaluation of Fuzzy Logic–Based Decision Systems
8.1 Evaluation of Existing Fuzzy Implication Functions
8.2 Decision Fusion System 1—Formation Flight
8.2.1 Membership Functions
8.2.2 Fuzzy Rules and the Fuzzy Implication Method
8.2.3 Aggregation and Defuzzification Method
8.2.4 Fuzzy Logic–Based Decision Software Realization
8.3 Decision Fusion System 2—Air Lane
8.3.1 Membership Functions
8.3.2 Fuzzy Rules and Other Methods
8.3.3 Fuzzy Logic–Based Decision Software Realization for System 2
8.4 Evaluation of Some New Fuzzy Implication Functions
8.5 Illustrative Examples
Epilogue
Exercises
References
9781439800058-p3
Part III: Pixel- and Feature-Level Image Fusion
9781439800058-c9
Chapter 9: Introduction
9781439800058-c10
Chapter 10: Pixel- and Feature-Level Image Fusion Concepts and Algorithms
10.1 Image Registration
10.1.1 Area-Based Matching
10.1.1.1 Correlation Method
10.1.1.2 Fourier Method
10.1.1.3 Mutual Information Method
10.1.2 Feature-Based Methods
10.1.2.1 Spatial Relation
10.1.2.2 Invariant Descriptors
10.1.2.3 Relaxation Technique
10.1.2.4 Pyramids and Wavelets
10.1.3 Transform Model
10.1.3.1 Global and Local Models
10.1.3.2 Radial Basis Functions
10.1.3.3 Elastic Registration
10.1.4 Resampling and Transformation
10.1.5 Image Registration Accuracy
10.2 Segmentation, Centroid Detection, and Target Tracking with Image Data
10.2.1 Image Noise
10.2.1.1 Spatial Filter
10.2.1.2 Linear Spatial Filters
10.2.1.3 Nonlinear Spatial Filters
10.2.2 Metrics for Performance Evaluation
10.2.2.1 Mean Square Error
10.2.2.2 Root Mean Square Error
10.2.2.3 Mean Absolute Error
10.2.2.4 Percentage Fit Error
10.2.2.5 Signal-to-Noise Ratio
10.2.2.6 Peak Signal-to-Noise Ratio
10.2.3 Segmentation and Centroid Detection Techniques
10.2.3.1 Segmentation
10.2.3.2 Centroid Detection
10.2.4 Data Generation and Results
10.2.5 Radar and Imaging Sensor Track Fusion
10.3 Pixel-Level Fusion Algorithms
10.3.1 Principal Component Analysis Method
10.3.1.1 Principal Component Analysis Coefficients
10.3.1.2 Image Fusion
10.3.2 Spatial Frequency
10.3.2.1 Image Fusion by Spatial Frequency
10.3.2.2 Majority Filter
10.3.3 Performance Evaluation
10.3.3.1 Results and Discussion
10.3.3.2 Performance Metrics When No Reference Image Is Available
10.3.4 Wavelet Transform
10.3.4.1 Fusion by Wavelet Transform
10.3.4.2 Wavelet Transforms for Similar Sensor Data Fusion
10.4 Fusion of Laser and Visual Data
10.4.1 3D Model Generation
10.4.2 Model Evaluation
10.5 Feature-Level Fusion Methods
10.5.1 Fusion of Appearance and Depth Information
10.5.2 Stereo Face Recognition System
10.5.2.1 Detection and Feature Extraction
10.5.2.2 Feature-Level Fusion Using Hand and Face Biometrics
10.5.3 Feature-Level Fusion
10.5.3.1 Feature Normalization
10.5.3.2 Feature Selection
10.5.3.3 Match Score Generation
10.6 Illustrative Examples
9781439800058-c11
Chapter 11: Performance Evaluation of Image-Based Data Fusion Systems
11.1 Image Registration and Target Tracking
11.1.1 Image-Registration Algorithms
11.1.1.1 Sum of Absolute Differences
11.1.1.2 Normalized Cross Correlation
11.1.2 Interpolation
11.1.3 Data Simulation and Results
11.2 3D Target Tracking with Imaging and Radar Sensors
11.2.1 Passive Optical Sensor Mathematical Model
11.2.2 State-Vector Fusion for Fusing IRST and Radar Data
11.2.2.1 Application of Extended KF
11.2.2.2 State-Vector Fusion
11.2.3 Numerical Simulation
11.2.4 Measurement Fusion
11.2.4.1 Measurement Fusion 1 Scheme
11.2.4.2 Measurement Fusion 2 Scheme
11.2.5 Maneuvering Target Tracking
11.2.5.1 Motion Models
11.2.5.2 Measurement Model
11.2.5.3 Numerical Simulation
11.3 Target Tracking with Acoustic Sensor Arrays and Imaging Sensor Data
11.3.1 Tracking with Multiple Acoustic Sensor Arrays
11.3.2 Modeling of Acoustic Sensors
11.3.3 DoA Estimation
11.3.4 Target-Tracking Algorithms
11.3.4.1 Digital Filter
11.3.4.2 Triangulation
11.3.4.3 Results and Discussion
11.3.5 Target Tracking
11.3.5.1 Joint Acoustic-Image Target Tracking
11.3.5.2 Decentralized KF
11.3.5.3 3D Target Tracking
11.3.6 Numerical Simulation
Epilogue
Exercises
References
9781439800058-p4
Part IV: A Brief on Data Fusion in Other Systems
9781439800058-c12
Chapter 12: Introduction: Overview of Data Fusion in Mobile Intelligent Autonomous Systems
12.1 Mobile Intelligent Autonomous Systems
12.2 Need for Data Fusion in MIAS
12.3 Data Fusion Approaches in MIAS
9781439800058-c13
Chapter 13: Intelligent Monitoring and Fusion
13.1 The Monitoring Decision Problem
13.2 Command, Control, Communications, and Configuration
13.3 Proximity- and Condition-Monitoring Systems
Epilogue
Exercises
References
9781439800058-a
Appendix: Numerical, Statistical, and Estimation Methods
A.1 Some Definitions and Concepts
A.1.1 Autocorrelation Function
A.1.2 Bias in Estimate
A.1.3 Bayes’ Theorem
A.1.4 Chi-Square Test
A.1.5 Consistency of Estimates Obtained from Data
A.1.6 Correlation Coefficients and Covariance
A.1.7 Mathematical Expectations
A.1.8 Efficient Estimators
A.1.9 Mean-Squared Error (MSE)
A.1.10 Mode and Median
A.1.11 Monte Carlo Data Simulation
A.1.12 Probability
A.2 Decision Fusion Approaches
A.3 Classifier Fusion
A.3.1 Classifier Ensemble Combining Methods
A.3.1.1 Methods for Creating Ensemble Members
A.3.1.2 Methods for Combining Classifiers in Ensembles
A.4 Wavelet Transforms
A.5 Type-2 Fuzzy Logic
A.6 Neural Networks
A.6.1 Feed-Forward Neural Networks
A.6.2 Recurrent Neural Networks
A.7 Genetic Algorithm
A.7.1 Chromosomes, Populations, and Fitness
A.7.2 Reproduction, Crossover, Mutation, and Generation
A.8 System Identification and Parameter Estimation
A.8.1 Least-Squares Method
A.8.2 Maximum Likelihood and Output Error Methods
A.9 Reliability in Information Fusion
A.9.1 Bayesian Method
A.9.1.1 Weighted Average Methods
A.9.2 Evidential Methods
A.9.3 Fuzzy Logic–Based Possibility Approach
A.10 Principal Component Analysis
A.11 Reliability
References
Multi-Sensor
Data Fusion
MATLAB®
with
© 2010 by Taylor and Francis Group, LLC
Multi-Sensor
Data Fusion
MATLAB®
with
Jitendra R. Raol
Boca Raton London New York
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Raol, J. R. (Jitendra R.), 1947-
Multi-sensor data fusion with MATLAB / Jitendra R. Raol.
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ISBN 978-1-4398-0003-4 (hardcover : alk. paper)
1. Multisensor data fusion— Data processing. 2. MATLAB. 3. Detectors. I. Title.
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and
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(University of British Columbia, Canada)
© 2010 by Taylor and Francis Group, LLC
Contents
Preface ................................................................................................... xix
Acknowledgments ................................................................................ xxi
Author .................................................................................................xxiii
Contributors ......................................................................................... xxv
Introduction .......................................................................................xxvii
I: Theory of Data Fusion and Kinematic-Level Fusion
Part
(J. R. Raol, G. Girija, and N. Shanthakumar)
1. Introduction .................................................................................................. 3
2. Concepts and Theory of Data Fusion ..................................................... 11
2.1 Models of the Data Fusion Process and Architectures ..................... 11
2.1.1 Data Fusion Models .................................................................... 13
Joint Directors of Laboratories Model ....................... 13
2.1.1.1
2.1.1.2 Modifi ed Waterfall Fusion Model .............................. 17
2.1.1.3
Intelligence Cycle–Based Model ................................ 18
2.1.1.4 Boyd Model ................................................................... 19
2.1.1.5 Omnibus Model ........................................................... 20
2.1.2 Fusion Architectures .................................................................. 21
2.1.2.1 Centralized Fusion ....................................................... 21
2.1.2.2 Distributed Fusion ....................................................... 21
2.1.2.3 Hybrid Fusion ............................................................... 22
2.2 Unifi ed Estimation Fusion Models and Other Methods ................... 23
2.2.1 Defi nition of the Estimation Fusion Process ........................... 24
2.2.2 Unifi ed Fusion Models Methodology ...................................... 25
2.2.2.1 Special Cases of the Unifi ed Fusion Models ............ 25
2.2.2.2 Correlation in the Unifi ed Fusion Models ................ 26
2.2.3 Unifi ed Optimal Fusion Rules .................................................. 27
2.2.3.2
2.2.3.3
2.2.3.1
Best Linear Unbiased Estimation Fusion Rules
with Complete Prior Knowledge ............................... 27
Best Linear Unbiased Estimation Fusion Rules
without Prior Knowledge ........................................... 28
Best Linear Unbiased Estimation Fusion Rules
with Incomplete Prior Knowledge ............................ 28
2.2.3.4 Optimal-Weighted Least Squares Fusion Rule ........ 28
2.2.3.5 Optimal Generalized Weighted Least Squares
Fusion Rule ................................................................... 29
© 2010 by Taylor and Francis Group, LLC
vii
viii
Contents
2.2.4 Kalman Filter Technique as a Data Fuser ............................... 29
2.2.4.1 Data Update Algorithm............................................... 30
2.2.4.2 State-Propagation Algorithm ..................................... 31
2.2.5
Inference Methods ...................................................................... 32
2.2.6 Perception, Sensing, and Fusion ............................................... 32
2.3 Bayesian and Dempster–Shafer Fusion Methods .............................. 33
2.3.1 Bayesian Method ......................................................................... 34
2.3.1.1 Bayesian Method for Fusion of Data from
Two Sensors .................................................................. 36
2.3.2 Dempster–Shafer Method ......................................................... 38
2.3.3
Comparison of the Bayesian Inference Method and
the Dempster–Shafer Method ................................................... 40
2.4 Entropy-Based Sensor Data Fusion Approach ................................... 41
2.4.1 Defi nition of Information .......................................................... 41
2.4.2 Mutual Information .................................................................... 43
2.4.3 Entropy in the Context of an Image ......................................... 44
2.4.4
Image-Noise Index ...................................................................... 44
2.5 Sensor Modeling, Sensor Management, and Information Pooling ..... 45
2.5.1 Sensor Types and Classifi cation ............................................... 45
2.5.1.1 Sensor Technology ....................................................... 46
2.5.1.2 Other Sensors and their Important Features
and Usages .................................................................... 48
2.5.1.3 Features of Sensors ...................................................... 51
2.5.1.4 Sensor Characteristics ............................................... 52
2.5.2 Sensor Management ................................................................... 53
2.5.2.1 Sensor Modeling .......................................................... 55
2.5.2.2 Bayesian Network Model ............................................ 58
2.5.2.3 Situation Assessment Process .................................... 58
Information-Pooling Methods .................................................. 60
2.5.3.1 Linear Opinion Pool .................................................... 60
Independent Opinion Pool ......................................... 61
2.5.3.2
2.5.3.3
Independent Likelihood Pool ..................................... 61
2.5.3
3. Strategies and Algorithms for Target Tracking and Data
Fusion ........................................................................................................... 63
3.1 State-Vector and Measurement-Level Fusion ..................................... 69
3.1.1 State-Vector Fusion ..................................................................... 70
3.1.2 Measurement Data–Level Fusion ............................................. 71
3.1.3 Results with Simulated and Real Data Trajectories ............... 71
3.1.4
Results for Data from a Remote Sensing Agency with
Measurement Data–Level Fusion ............................................. 72
3.2
Factorization Kalman Filters for Sensor Data Characterization
and Fusion ................................................................................................ 73
3.2.1 Sensor Bias Errors ....................................................................... 73
© 2010 by Taylor and Francis Group, LLC
Contents
ix
3.3
3.4
3.5
3.2.2 Error State-Space Kalman Filter ............................................... 75
3.2.3 Measurement and Process Noise Covariance
Estimation .................................................................................... 76
3.2.4 Time Stamp and Time Delay Errors ......................................... 77
3.2.5 Multisensor Data Fusion Scheme ............................................. 77
3.2.5.1 UD Filters for Trajectory Estimation ......................... 80
3.2.5.2 Measurement Fusion ................................................... 81
3.2.5.3 State-Vector Fusion ....................................................... 82
3.2.5.4 Fusion Philosophy ........................................................ 82
Square-Root Information Filtering and Fusion in
Decentralized Architecture ................................................................... 86
Information Filter ........................................................................ 87
3.3.1
3.3.1.1
Information Filter Concept ......................................... 87
3.3.1.2 Square Root Information Filter Algorithm .............. 88
3.3.2 Square Root Information Filter Sensor Data Fusion
Algorithm ..................................................................................... 88
3.3.3 Decentralized Square Root Information Filter ....................... 89
3.3.4 Numerical Simulation Results .................................................. 91
Nearest Neighbor and Probabilistic Data Association Filter
Algorithms ............................................................................................... 93
3.4.1 Nearest Neighborhood Kalman Filter ..................................... 94
3.4.2 Probabilistic Data Association Filter ........................................ 96
3.4.3
Tracking and Data Association Program for
Multisensor, Multitarget Sensors ............................................. 97
3.4.3.1 Sensor Attributes.......................................................... 99
3.4.3.2 Data Set Conversion ..................................................... 99
3.4.3.3 Gating in Multisensor, Multitarget .......................... 100
3.4.3.4 Measurement-to-Track Association ......................... 100
3.4.3.5
Initiation of Track and Extrapolation of Track ....... 101
3.4.3.6 Extrapolation of Tracks into Next Sensor Field
of View ......................................................................... 101
3.4.3.7 Extrapolation of Tracks into Next Scan ................... 102
3.4.3.8 Track Management Process ...................................... 102
3.4.4 Numerical Simulation .............................................................. 103
Interacting Multiple Model Algorithm for Maneuvering
Target Tracking ..................................................................................... 106
Interacting Multiple Model Kalman Filter Algorithm ........ 106
3.5.1
3.5.1.1
Interaction and Mixing ............................................. 108
3.5.1.2 Kalman Filtering ........................................................ 108
3.5.1.3 Mode Probability Update .......................................... 109
3.5.1.4 State Estimate and Covariance Combiner .............. 109
3.5.2 Target Motion Models ...............................................................110
3.5.2.1 Constant Velocity Model ............................................110
3.5.2.2 Constant Acceleration Model ....................................110
© 2010 by Taylor and Francis Group, LLC
Contents
x
3.6
3.5.3
Interacting Multiple Model Kalman Filter
Implementation ..........................................................................111
3.5.3.1 Validation with Simulated Data ............................... 112
Joint Probabilistic Data Association Filter ..........................................116
3.6.1 General Version of a Joint Probabilistic Data
3.6.2
Association Filter .......................................................................117
Particle Filter Sample–Based Joint Probabilistic Data
Association Filter .......................................................................119
3.7 Out-of-Sequence Measurement Processing for Tracking ................ 120
3.7.1
3.7.2
Bayesian Approach to the Out-of-Sequence
Measurement Problem ............................................................. 120
Out-of-Sequence Measurement with Single Delay and
No Clutter .................................................................................. 121
3.7.2.1 Y Algorithm ................................................................ 121
3.7.2.2 Augmented State Kalman Filters ............................. 122
3.8 Data Sharing and Gain Fusion Algorithm for Fusion ..................... 124
3.8.1 Kalman Filter–Based Fusion Algorithm ................................ 124
3.8.2 Gain Fusion–Based Algorithm ............................................... 125
3.8.3 Performance Evaluation ........................................................... 126
3.9 Global Fusion and H-Infi nity Filter–Based Data Fusion ................. 127
3.9.1 Sensor Data Fusion using H-Infi nity Filters ......................... 127
3.9.2 H-Infi nity a Posteriori Filter–Based Fusion
Algorithm ................................................................................... 130
3.9.3 H-Infi nity Global Fusion Algorithm ...................................... 131
3.9.4 Numerical Simulation Results ................................................ 132
3.10 Derivative-Free Kalman Filters for Fusion ........................................ 134
3.10.1 Derivative-Free Kalman Filters ............................................... 136
3.10.2 Numerical Simulation .............................................................. 137
3.10.2.1 Initialization of the Data Fusion-Derivative
Free Kalman Filter Algorithm .................................. 140
3.10.2.2 Computation of the Sigma Points ............................ 140
3.10.2.3 State and Covariance Propagation............................141
3.10.2.4 State and Covariance Update ....................................141
3.11 Missile Seeker Estimator ...................................................................... 143
3.11.1 Interacting Multiple Model–Augmented Extended
Kalman Filter Algorithm ......................................................... 143
3.11.1.1 State Model .................................................................. 144
3.11.1.2 Measurement Model .................................................. 145
3.11.2 Interceptor–Evader Engagement Simulation ........................ 146
3.11.2.1 Evader Data Simulation............................................. 147
3.11.3 Performance Evaluation of Interacting
Multiple Model–Augmented Extended
Kalman Filter ............................................................................. 147
3.12 Illustrative Examples ............................................................................ 151
© 2010 by Taylor and Francis Group, LLC
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