Mathematical Modelling of Aerospace Dynamic Systems with Practical Applications

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgements
About the Authors
Chapter 1 Introduction
	1.1 Mathematical Modelling Concepts
	1.2 Aircraft Mathematical Models
		1.2.1 For Flight Simulation
		1.2.2 For Flight Control
	1.3 Missile Mathematical Models
	1.4 Rotorcraft Mathematical Models
	1.5 Micro-Mini-Air Vehicles (MAVs)
	1.6 Lighter than Air Vehicles
	1.7 Maneuvering Target Models and Data Fusion
	1.8 Unmanned Aerial Vehicles (UAVs)
		1.8.1 Vision-Assisted Target Tracking
	1.9 Autonomous Underwater Vehicles (AUWVs)
	1.10 Leader-Follower Coordination for Two Vehicles
	1.11 Satellite Orbit Determination
	1.12 Chapter Highlights
	References
Chapter 2 Flight Mechanics Models
	2.1 Introduction
	2.2 Equations of Motion (EOMs) for a Rigid Body
		2.2.1 Resolution of Inertial Forces and Moments
		2.2.2 Resolution of Aerodynamic, Gravity, and Thrust Forces
	2.3 Complete Set of EOM
		2.3.1 Rectangular Form
		2.3.2 Polar Form
	2.4 Missile Dynamic Models
	2.5 Rotorcraft Dynamic Models
		2.5.1 Momentum Theory
		2.5.2 Blade Element Theory
		2.5.3 Rotorcraft Modelling Formulations
			2.5.3.1 Equations for Linear Accelerations
			2.5.3.2 Equations for Angular Accelerations
			2.5.3.3 Kinematic Equations for Euler Rates
			2.5.3.4 Specific Forces
			2.5.3.5 Specific Moments
		2.5.4 Limitations of the Rigid Body Model
	2.6 Aerodynamic Coefficients and Derivatives
		2.6.1 Basic Aerodynamic Forces and Moments
		2.6.2 Aerodynamic Parameters
		2.6.3 Definition of Aerodynamic Derivatives
			2.6.3.1 For Aircraft
			2.6.3.2 For Missiles
			2.6.3.3 For Rotorcraft
	2.7 Aerodynamic Models
	2.8 Simplified State-Space and Transfer Function (TF) Models
		2.8.1 Mathematical Model Structures
		2.8.2 Choice of Coordinate Systems
		2.8.3 Linearization of Model Equations
		2.8.4 Simplification Using Measured Data
			2.8.4.1 Aircraft Models
			2.8.4.2 Missile Aerodynamic TFs
			2.8.4.3 Rotorcraft Linear Modelling
	2.9 UAV Dynamics
	2.10 MAV Dynamics
	2.11 Lighter-Than-Air Vehicle/BLIMP Dynamics
	Appendix 2A: Aircraft Geometry and Coordinate Systems
	2A.1 Aircraft Axis and Notations
	2A.2 Axis/Coordinate Transformations and Quaternions
	2A.3 Transformation from the Body to the Earth Axis
	2A.4 Transformation from the Stability Axis to the Body Axis
	2A.5 Transformation from the Stability Axis to the Wind Axis (w)
	2A.6 Transformation from the Body Axis to the Wind Axis
	Appendix 2B: Transformations of Aerodynamic Derivatives
	Exercises
	References
Chapter 3 Models Used in Target Tracking and Data Fusion
	3.1 Introduction
	3.2 Interacting Multiple Model (IMM) Kalman Filter Algorithm
		3.2.1 IMMKF Algorithm
			3.2.1.1 Interaction and Mixing
			3.2.1.2 Target Motion Models
			3.2.1.3 Implementation and Validation
	3.3 A Missile Seeker Estimator
		3.3.1 IMM-Augmented EKF
			3.3.1.1 State Model
			3.3.1.2 Measurement Model
		3.3.2 Interceptor-Evader Engagement Simulation
			3.3.2.1 Evader Data Simulation
		3.3.3 Performance Evaluation
	3.4 Tracking of Maneuvering Targets with Probability Data Association Filter
		3.4.1 IMM Algorithm
			3.4.1.1 Automatic Track Formation
			3.4.1.2 Gating and Data Association
			3.4.1.3 Interaction and Mixing in IMMPDAF
			3.4.1.4 Mode-Conditioned Filtering
			3.4.1.5 Probability Computations
			3.4.1.6 Combined State and Covariance Prediction/Estimation
		3.4.2 Simulation Validation
			3.4.2.1 Constant Velocity Model (CVM)
			3.4.2.2 Constant Acceleration Model (CAM)
			3.4.2.3 Performance Evaluation and Discussions
			3.4.2.4 Evaluation of IMMPDAF
			3.4.2.5 Multiple Sensors – Fusion of Data
	3.5 Target Tracking with Imaging and Radar Sensors
		3.5.1 Passive Optical Sensor Mathematical Model
			3.5.1.1 State Vector Fusion for Fusing IRST and Radar Data
			3.5.1.2 Extended Kalman Filter
		3.5.2 State Vector Fusion
			3.5.2.1 SVF1
			3.5.2.2 SVF2
			3.5.2.3 Numerical Simulation
		3.5.3 Measurement Fusion
			3.5.3.1 MF1
			3.5.3.2 MF2
		3.5.4 Maneuvering Target Tracking
			3.5.4.1 Motion Models
			3.5.4.2 Measurement Model
			3.5.4.3 Numerical Simulation
	3.6 Target Tracking with Acoustic Array Sensors and Imaging Sensor Data
		3.6.1 Tracking with Multi-Acoustic Array Sensors
			3.6.1.1 Modelling of Acoustic Sensors
			3.6.1.2 Target Tracking Algorithms
			3.6.1.3 Simulation Results
	Exercises
	References
Chapter 4 Mathematical Modelling for Two-Vehicle Coordination
	4.1 Introduction
	4.2 Problem Formulation for UAV Coordination
		4.2.1 Math Model of the Measurements
		4.2.2 Covariance of Geolocation Error
		4.2.3 UAV Modelling
	4.3 Dynamic Programming
		4.3.1 State Space and Quantization
		4.3.2 Cost Function
	4.4 Simulation Results
		4.4.1 Scenario 1
		4.4.2 Scenario 2
		4.4.3 Static Interpretation
	4.5 Dynamic Equations of Wheeled Mobile Robot
		4.5.1 Mathematical Modelling
	4.6 Kalman and RLS Filtering
		4.6.1 State Propagation/Evolution
		4.6.2 Measurements/Data Update
		4.6.3 Simple RLS Filter Updates
	4.7 Implementation and Results
	Exercises
	References
Chapter 5 Vision-Aided Inertial Navigation
	5.1 Introduction
	5.2 Estimator Description
		5.2.1 Algorithm: Multistate Constraint Filter
		5.2.2 State Vector Model
		5.2.3 State Propagation
	5.3 State Augmentation
		5.3.1 Measurement Model
		5.3.2 EKF Updates
	5.4 Discussion of Experimental Results
	Exercises
	References
Chapter 6 Terrain-Assisted Underwater Vehicle Navigation
	6.1 Terrain Navigation Models
		6.1.1 State Space Model
		6.1.2 Measurement Model
	6.2 Recursive Bayesian Estimation Method
		6.2.1 Bayesian Update Equations
		6.2.2 2D Point Mass Filter
		6.2.3 Marginalized Point Mass Filter in Three Dimensions
			6.2.3.1 Marginalized Point Mass Filter
			6.2.3.2 Design of Grid and Adaptation
	6.3 Simulation Experiment
	6.4 Analysis of Real-Time Terrain-Assisted Navigation
		6.4.1 Navigation Algorithm
			6.4.1.1 System Model
			6.4.1.2 Filter Model
			6.4.1.3 The Recursive Bayesian Filter Equations
			6.4.1.4 Point Mass and Particle Filter
		6.4.2 Underwater Terrain Navigation Sensors
			6.4.2.1 Building the Map
			6.4.2.2 Localization and Navigation
			6.4.2.3 Obstacle Avoidance and Path Planning
			6.4.2.4 Sensor Fusion
		6.4.3 The Hugin Real-Time Terrain Navigation System
			6.4.3.1 Understanding the HUGIN
			6.4.3.2 Features and Capabilities
			6.4.3.3 Applications and Implications
			6.4.3.4 Future Directions
		6.4.4 Results and Discussion
	Exercises
	References
Chapter 7 Object Detection and Tracking from UAV with Thermal Camera
	7.1 Introduction
	7.2 System Overview
	7.3 Object Detection and Recognition
	7.4 Object Tracking
		7.4.1 Kalman Filter
		7.4.2 Data Association
	7.5 Results
		7.5.1 Flight 1
		7.5.2 Flight 2
		7.5.3 Flight 3
		7.5.4 Flight 4
	7.6 Conclusion
	Exercises
	References
Chapter 8 Feature Tracking/Mapping Using a Vision and GPS/INS System on a UAV Platform
	8.1 Introduction
	8.2 Vision System
		8.2.1 Passive Vision Camera
		8.2.2 Feature Tracking Algorithm
	8.3 Navigation System
		8.3.1 Inertial Navigation
		8.3.2 GPS/INS Integration
	8.4 Physical System
	8.5 Results
	Exercises
	References
Chapter 9 Satellite Orbit Determination
	9.1 Introduction
	9.2 Orbit Determination Problem and Process
		9.2.1 Systems Models—Orbital Trajectory Dynamics
			9.2.1.1 Classical Orbital Parameters
			9.2.1.2 Inertial coordinates
			9.2.1.3 Unified State Model
		9.2.2 Measurement Equations
			9.2.2.1 Types of Measurements
			9.2.2.2 Measurement Models
		9.2.3 Hardware and Software
			9.2.3.1 Vehicle-Mounted Sensor System (VMSS)
			9.2.3.2 Electronics and Space-Borne Computers (SBC)
			9.2.3.3 Software
	9.3 Orbit Estimators
		9.3.1 Generalized Least Squares Differential Correction Technique (GLSDCT)
		9.3.2 Factorization Method and Smoother
			9.3.2.1 UD Factorization Filter
			9.3.2.2 RTS Smoother
	9.4 Computational Aspects
	9.5 Search and Rescue Satellite Orbit Estimation
		9.5.1 System Overview
		9.5.2 System-Filter Configuration
		9.5.3 Basic Simulation Studies
		9.5.4 Study of Measurement Data Outliers
	Exercises
	References
Appendix A: Modelling Based on Soft Computing
Appendix B: Obstacle Avoidance in Robot Path Planning
Appendix C: Enhanced Occlusion Detection Algorithm for Surveillance Cameras
Index