Strapdown Inertial Navigation Technology. Second Edition. Volume 207 PROGRESS IN ASTRONAUTICS AND AERONAUTICS
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1 Strapdown Inertial Navigation Technology Second Edition D. H. Titterton Technical leader in Laser Systems at the Defence Science and Technology Laboratory (DSTL) Hampshire, UK J. L. Weston Principal Scientist with Halliburton Sperry-Sun Gloucestershire, UK Volume 207 PROGRESS IN ASTRONAUTICS AND AERONAUTICS Paul Zarchan, Editor-in-Chief MIT Lincoln Laboratory Lexington, Massachusetts Copublished by the American Institute of Aeronautics and Astronautics, Inc Alexander Bell Drive, Reston, VA and the Institution of Electrical Engineers, Michael Faraday House Six Hills Way, Stevenage, Herts, SGI 2AY UK
2 Contents Preface xv Navigation Inertial navigation Strapdown technology Layout of the book 4 2 Fundamental principles and historical developments of inertial navigation Basic concepts Summary Historical developments '" The modern-day inertial navigation system Trends in inertial sensor development 15 3 Basic principles of strapdown inertial navigation systems \ A simple two-dimensional strapdown navigation system Reference frames Three-dimensional strapdown navigation system - general analysis Navigation with respect to a fixed frame Navigation with respect to a rotating frame The choice of reference frame Resolution of accelerometer measurements System example Strapdown system mechanisations Inertial frame mechanisation Earth frame mechanisation Local geographic navigation frame mechanisation 31
3 vi Contents Wander azimuth navigation frame mechanisation Summary of strapdown system mechanisations Strapdown attitude representations Introductory remarks Direction cosine matrix Euler angles Quaternions Relationships between direction cosines, Euler angles and quaternions Detailed navigation equations Navigation equations expressed in component form The shape of the Earth Datum reference models Variation of gravitational attraction over th( h 55 Gyroscope technology Conventional sensors Fundamental principles Components of a mechanical gyroscope Sensor errors Rate-integrating gyroscope Dynamically tuned gyroscope Flex gyroscope Rate sensors Vibratory gyroscopes Dual-axis rate transducer (DART) Magnetohydrodynamic sensor Vibrating wine glass sensor Hemispherical resonator gyroscope Vibrating disc sensor Tuning fork sensor Quartz rate sensor Silicon sensor Vibrating wire rate sensor General characteristics of vibratory sensors Cryogenic devices Nuclear magnetic resonance gyroscope SARDIN Electrostatically suspended gyroscope Other devices for sensing angular motion Fluidic (flueric) sensors
4 Contents vn Fluxgate magnetometers The transmission line gyroscope Gyroscope technology Optical sensors Fundamental principles Ring laser gyroscope Three-axis ring laser gyroscope configuration Fibre optic gyroscope Photonic crystal optical fibre gyroscope Fibre optic ring resonator gyroscope Ring resonator gyroscope Integrated optical gyroscope Cold atom sensors Rotation sensing Measurement of acceleration Gravity gradiometer Summary of gyroscope technology Accelerometer and multi-sensor technology The measurement of translational motion 6.3 Mechanical sensors Principles of operation Sensor errors Force-feedback pendulous accelerometer Pendulous accelerometer hinge elements Two-axes force-feedback accelerometer Open-loop accelerometers Solid-state accelerometers Vibratory devices Surface acoustic wave accelerometer Silicon sensors Fibre optic accelerometer Optical accelerometers u Other acceleration sensors Multi-functional sensors Rotating devices Vibratory multi-sensor Mass unbalanced gyroscope \
5 viii Contents Angular accelerometers Liquid rotor angular accelerometer Gas rotor angular accelerometer Inclinometers Summary of accelerometer and multi-sensor technology MEMS inertial sensors Silicon processing 7.3 MEMS gyroscope technology Tuning fork MEMS gyroscopes '7.3.3 Resonant ring MEMS gyroscopes MEMS accelerometer technology Pendulous mass MEMS accelerometers Resonant MEMS accelerometers Tunnelling MEMS accelerometers Electrostatically levitated MEMS accelerometers Dithered accelerometers MOEMS Multi-axis/rotating structures MEMS based inertial measurement units Silicon IMU Quartz IMU System integration Summary 8 Testing, calibration and compensation Testing philosophy Test equipment Data-logging equipment Gyroscope testing Stability tests - multi-position tests Rate transfer tests Thermal tests Oscillating rate table tests Magnetic sensitivity tests Centrifuge tests Shock tests c Vibration tests Combination tests Aeeine and storaee tests ,
6 Contents ix Accelerometer testing Multi-position tests Long-term stability Thermal tests Magnetic sensitivity tests Centrifuge tests Shock tests Vibration tests Combination tests Ageing and storage tests Calibration and error compensation Gyroscope error compensation Accelerometer error compensation Further comments on error compensation Testing of inertial navigation systems Hardware in the loop tests Strapdown system technology The components of a strapdown navigation system The instrument cluster Orthogonal sensor configurations Skewed sensor configurations A skewed sensor configuration using dual-axis gyroscopes Redundant sensor configurations- - Instrument electronics The attitude computer The navigation computer Power conditioning \ Anti-vibration mounts Concluding remarks 0 Inertial navigation system alignment Basic principles Alignment on a fixed platform Alignment on a moving platform 10.3 Alignment on the ground Ground alignment methods Northfinding techniques 10.4 In-flight alignment
7 x Contents Sources of error In-flight alignment methods Alignment at sea Sources of error Shipboard alignment methods Strapdown navigation system computation Attitude computation Direction cosine algorithms Rotation angle computation Rotation vector compensation Body and navigation frame rotations Quaternion algorithms Orthogonalisation and normalisation algorithms The choice of attitude representation 11.3 Acceleration vector transformation algorithm Navigation algorithm 11.5 Summary Acceleration vector transformation using direction cosines Rotation correction Dynamic correction Acceleration vector transformation using quaternions Generalised system performance analysis Propagation of errors in a two-dimensional strapdown navigation system Navigation in a non-rotating reference frame Navigation in a rotating reference frame The Schuler pendulum Propagation of errors in a Schuler tuned system Discussion of results General error equations Derivation of error equations Discussion Analytical assessment Single channel error model Derivation of single channel error propagation equations Single-channel error propagation examples 358
8 Contents xi 12.5 Assessment by simulation Introductory remarks Error modelling Simulation techniques Motion dependence of strapdown system performance Manoeuvre-dependent error terms Vibration dependent error terms Summary Integrated navigation systems Basic principles External navigation aids Radio navigation aids Satellite navigation aids Star trackers Surface radar trackers On-board measurements Doppler radar Magnetic measurements Altimeters Terrain referenced navigation Scene matching Continuous visual navigation System integration Application of Kalman filtering to aided inertial navigation systems ' Design example of aiding INS-GPS integration Uncoupled systems ' Loosely coupled integration Tightly coupled integration Deep integration Concluding remarks INS aiding of GPS signal tracking Multi-sensor integrated navigation Summary Design example Background to the requirement The navigation system requirement Navigation data required Operating and storage environment 423
9 xii Contents Performance System reaction time Physical characteristics Why choose strapdown inertial navigation? Navigation system design and analysis process Choice of system mechanisation Error budget calculations System alignment Choice of inertial instruments Computational requirements Electrical and mechanical interfaces Testing, calibration and compensation requirements Performance enhancement by aiding Concluding remarks Alternative applications of IN sensors and systems Borehole surveying Historical background Inertial survey system System design requirements System design issues System calibration and test Concluding remarks Ship's inertial navigation systems (SINS) NATO SINS Vehicle stabilisation and control Autopilots Passive missile roll control (rollerons) Intelligent transport systems - automotive applications Intelligent transport systems - trains Personal transport Equipment stabilisation Aero-flexure compensation Laser beam director Laser radar Seeker-head stabilisation Sightline stabilisation Relative angular alignment Calibration and measurement 15.6 Geodetic and geophysical measurements and observation of fundamental physical phenomena 495
10 Contents xiii 15.7 Other applications Moving-map displays Safety and arming units Aircraft ejection seats Agricultural survey Artillery pointing Other unusual applications 15.8 Concluding remarks Appendix A Appendix B Appendix C Appendix D Kalman filtering Inertial navigation system error budgets Inertial system configurations Comparison of GPS and GLONASS satellite navigation systems List of symbols Glossary of principal terms Index
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