CRANFIELD UNIVERSITY LEIGH MOODY SENSORS, SENSOR MEASUREMENT FUSION AND MISSILE TRAJECTORY OPTIMISATION COLLEGE OF DEFENCE TECHNOLOGY PhD THESIS CRANFIELD UNIVERSITY COLLEGE OF DEFENCE TECHNOLOGY DEPARTMENT OF AEROSPACE, POWER AND SENSORS PhD THESIS Academic Year 2002 - 2003 Leigh Moody Sensors, Measurement Fusion and Missile Trajectory Optimisation Supervisor: Professor B.A. White July 2003 Leigh Moody asserts his right to be identified as the author. © Cranfield University 2003 All rights reserved. No part of this publication may be reproduced without the written permission of Cranfield University and without acknowledging that it may contain copyright material owned by MBDA UK Limited. i ii ABSTRACT When considering advances in “smart” weapons it is clear that air-launched systems have adopted an integrated approach to meet rigorous requirements, whereas air-defence systems have not. The demands on sensors, state observation, missile guidance, and simulation for air-defence is the subject of this research. Historical reviews for each topic, justification of favoured techniques and algorithms are provided, using a nomenclature developed to unify these disciplines. Sensors selected for their enduring impact on future systems are described and simulation models provided. Complex internal systems are reduced to simpler models capable of replicating dominant features, particularly those that adversely effect state observers. Of the state observer architectures considered, a distributed system comprising ground based target and own-missile tracking, data up-link, and on-board missile measurement and track fusion is the natural choice for air-defence. An IMM is used to process radar measurements, combining the estimates from filters with different target dynamics. The remote missile state observer combines up-linked target tracks and missile plots with IMU and seeker data to provide optimal guidance information. The performance of traditional PN and CLOS missile guidance is the basis against which on-line trajectory optimisation is judged. Enhanced guidance laws are presented that demand more from the state observers, stressing the importance of time-to-go and transport delays in strap-down systems employing staring array technology. Algorithms for solving the guidance two- point boundary value problems created from the missile state observer output using gradient projection in function space are presented. A simulation integrating these aspects was developed whose infrastructure, capable of supporting any dynamical model, is described in the air-defence context. MBDA have extended this work creating the Aircraft and Missile Integration Simulation (AMIS) for integrating different launchers and missiles. The maturity of the AMIS makes it a tool for developing pre-launch algorithms for modern air-launched missiles from modern military aircraft. iii iv ACKNOWLEDGEMENTS Professor B.A. White from the Royal Military College of Science (Shrivenham) kindly supervised this research, leading to PhD thesis submission in July 2003. Many of the ideas explored in this research were formulated when I was a member of the MBDA Guidance and Control research department at Bristol. During this time the work on missile guidance with Dr. D. Vorley was particularly stimulating; I am indebted to him for the many useful ideas in the field of weave tuning and trajectory optimisation. Although it is difficult to isolate individuals from those researchers referenced and whose work has contributed fundamental to my own, I feel that Kerr, Fitzgerald, Lobia, Li, and Pulford, et. al. deserve a special mention. Having created a simulation infrastructure for this research it was gratifying that MBDA were prepared to take a radical approach, build upon it, and create a Pan-Project Aircraft and Missile Integration Simulation (AMIS); Akram Ghulam being the most prominent supporter. The synergy between the programs has I believe resulted in two robust, flexible and complimentary simulations; thanks to all those involved in developing the AMIS, for their suggestions and patience during software testing. I would especially like to thank Ian McBride and Rob Zukowski without whom the AMIS would not have flourished; and in particular Paul Heath who alone is responsible for the excellent interactive interface. Finally, I would like to acknowledge the financial support provided by MBDA and the patience shown over the many years it has taken to produce this work. v vi Contents _ _ LIST OF CONTENTS 1 INTRODUCTION 1.1 Politics and Markets 1.2 Research Objectives 1.3 Document Structure 2 TARGET MODELLING 2.1 Target Simulator 2.2 Generic Target Models 2.3 Programmed Target Trajectories 2.4 Target Trajectories for IMM Filter Tuning 2.5 Target Trajectories for Performance Assessment 2.6 Discussion 3 SENSORS 3.1 Simulation Sensor Initialisation and Control 3.2 Generic Sensor Modelling 3.3 Inertial Navigation and Airframe Stabilisation 3.4 Gyroscopes 3.5 Accelerometer Triad 3.6 Barometric Altimeter 3.7 Radar Altimeter 3.8 Radar 3.9 Missile Seeker 3.10 Missile Fin Position Transducers 3.11 NAVSTAR Global Positioning Service 3.12 Helmet Mounted Sight 3.13 Air Data System 3.14 Discussion 4 TARGET TRACKING 4.1 Multiple-Model Architectures 4.2 Tracking Filter States 4.3 Tracking Filter Initialisation 4.4 Stochastic Filtering 4.5 IMM Mode Conditioned Filters 4.6 IMM Filter Measurement Updates 4.7 IMM Initialisation 4.8 IMM Filter Mixing 4.9 IMM Filter Propagation and Update vii Contents _ _ 4.10 IMM Filter Combination 4.11 Target Tracking Simulator 4.12 Discussion 5 MISSILE STATE OBSERVER 5.1 Data Fusion Architectures 5.2 Up-Link Interface 5.3 Sensor Measurements 5.4 States and Partitioning 5.5 Initialisation 5.6 Process Model 5.7 Up-Linked Target Track Update 5.8 Missile Measurement Updates 5.9 Pseudo-Measurements 5.10 Filter integrity 5.11 Missile State Observer Simulator 5.12 Discussion 6 CONVENTIONAL MISSILE GUIDANCE 6.1 Review 6.2 Missile Guidance Simulator 6.3 Missile Airframe 6.4 Missile Thrust 6.5 Missile Drag 6.6 Missile Guidance - Proportional Navigation 6.7 Missile Guidance - Command to Line-of-Sight 6.8 Missile Autopilots 6.9 Simulation Guidance and Autopilot Implementation 6.10 Launcher Dynamics 6.11 Missile Dynamics 6.12 Discussion 7 MISSILE TRAJECTORY OPTIMISATION 7.1 Control Sequence 7.2 Dynamic Model 7.3 Missile Controls 7.4 Cost Function 7.5 Dynamic Constrains 7.6 TPBVP Formulation 7.7 Gradients 7.8 Search Direction 7.9 Univariate Search and Termination 7.10 Algorithm Implementation 7.11 Trajectory Optimisation Simulator 7.12 Discussion 8 SIMULATION 8.1 The Role of Simulation viii Contents _ _ 8.2 The Scope of Modern Simulation 8.3 The AMIS Philosophy 8.4 The Research Simulation Infrastructure 8.5 Internal Data Communication between Software Modules 8.6 Simulation Infrastructure Control 8.7 Interactive X-Windows Interface 8.8 Discussion 9 PERFORMANCE 9.1 Air-To-Air Engagement Scenario 9.2 Performance Metrics 9.3 PN Guidance 9.4 CLOS Performance 9.5 IMM Filter Tuning and Verification 9.6 Discussion 10 CONCLUSIONS 10.1 Targets 10.2 Sensor Technology 10.3 State Observer Data Fusion 10.4 Conventional Missile Guidance 10.5 Trajectory Optimisation 10.6 Weapon System Simulation 11 FUTURE RESEARCH 11.1 Targets 11.2 Sensor Technology 11.3 State Observer Data Fusion 11.4 Conventional Missile Guidance 11.5 Trajectory Optimisation 11.6 Weapon System Simulation 12 REFERENCES 13 BIBLIOGRAPHY 14 APPENDIX A : GEOMETRIC POINTS 14.1 Geometric Earth Centre 14.2 Local Geoid Centre 14.3 Earth Referenced Launcher Position 14.4 NAVSTAR GPS Reference Points 14.5 Missile Centre of Gravity 14.6 Missile IMU Reference Point 14.7 Missile GPS Receiver Reference Point 14.8 Seeker (Missile) Reference Point 14.9 Missile Geodetic Position 14.10 Missile Ground Position 14.11 Target Reference Point ix Contents _ _ 14.12 Target Impact Point 15 APPENDIX B : FRAMES OF REFERENCE 15.1 Celestial Frame 15.2 NAVSTAR GPS Orbital Frames 15.3 Missile to Satellite LOS Frames 15.4 Earth Centred, Earth Fixed Frame 15.5 Alignment Frame 15.6 Local Geodetic Axes 15.7 Missile LOS Frame 15.8 Missile Body Frame 15.9 Missile Velocity Frame 15.10 Missile IMU Frame 15.11 Seeker LOS Frame 15.12 Seeker Head Frame 15.13 Missile Rolled Frame 15.14 Target LOS Frame 15.15 Target Body Frame 15.16 Target Velocity Frame 15.17 Radar Boresight Axes 15.18 Radar-Target Beam Axis 15.19 Radar-Missile Beam Axes 16 APPENDIX C : AXIS TRANSFORMS 16.1 Euler Rotations 16.2 Small Angle Approximations 16.3 Euler Angles as a Function of Direction Cosines 16.4 Transformation Between Co-ordinate Systems 16.5 Simulation Naming Convention 16.6 Satellite Orbital to Celestial Transformations 16.7 Celestial to Satellite LOS Transformations 16.8 Celestial to Earth Transformation 16.9 Earth to Alignment Transformation 16.10 LGA to Earth Position Vector Transformation 16.11 Earth to LGA Transformation 16.12 Alignment to Missile Body Transformation 16.13 Alignment to Missile and Target LOS Transformations 16.14 Alignment to Missile and Target Velocity Transformations 16.15 Missile Body to Missile IMU Transformation 16.16 Missile Body to Missile Velocity Transformation 16.17 Alignment to Seeker LOS Transformation 16.18 Missile Body to Seeker Head Transformation 16.19 LGA to Alignment Transformation 17 APPENDIX D : POINT MASS DYNAMICS 17.1 Transformation from Angular to Euler Rates 17.2 Transformation Time Derivatives 17.3 Average Angular Rates From Direction Cosines x Contents _ _ 17.4 Inertial Velocity Vector 17.5 Inertial Acceleration Vector 17.6 Inertial