Lawrence A. Modern Inertial Technology. Navigation, Guidance, and Control

New York: Springer-Verlag, 1993. — 268 p. With 129 Illustrations.The purpose of this book is to present the technology of the gyroscopes and accelerometers used in inertial navigation so that the reader can understand how they work, the advantages and disadvantages of the different types available, and where the field is headed. It should be useful to systems engineers who specify and select navigation, guidance, and control systems and sensors; project managers seeking background knowledge which will help them to sift the wheat from the chaff when listening to competing claims (not always objectively presented) from equipment manufacturers; new engineers of all ages beginning or moving into a career in the field; engineers and scientists deeply immersed in one area of the field who wish to comprehend the scope of the whole; and the curious reader, schooled in science, who wants to know how inertial sensors work.An Outline of Inertial Navigation
Navigation's Beginnings
Inertial Navigation
Maps and Reference Frames
The Inertial Navigation Process
Inertial Platforms
Heading and Attitude Reference Systems
Schuler Tuning
Gimbal Lock
Strapdown Systems
System Alignment
Gyrocompassing
Transfer Alignment
Advantages and Disadvantages of Platform Systems
Advantages
Disadvantages
Advantages and Disadvantages of Strapdown Systems
Advantages
Disadvantages
Star Trackers
The Global Positioning System
Applications of Inertial Navigation
ConclusionsGyro and Accelerometer Errors and Their Consequences
Effect of System Heading Error
Scale Factor
Non-linearity and Composite Error
System Error from Gyro Scale Factor
Asymmetry
Bias
System Error from Accelerometer Bias
Tilt Misalignment
System Error from Accelerometer Scale Factor Error
System Error from Gyro Bias
Random Drift
Random Walk
Dead Band, Threshold, and Resolution
Hysteresis
Day-to-Day Uncertainty
Gyro Acceleration Sensitivities
g-Sensitivity
Anisoelasticity
Rotation Induced Errors
Angular Acceleration Sensitivity
Anisoinertia
Angular Accelerometers
Angular Accelerometer Threshold Error
The Statistics of Instrument Performance
Typical Instrument SpecificationsThe Principles of Accelerometers
The Parts of an Accelerometer
The Spring-Mass System
Q Factor
Bandwidth
Open-Loop Pendulous Sensors
Cross-Coupling and Vibropendulous Errors
Pickoff Linearity
Closed-Loop Accelerometers
Open-Loop Versus Closed-Loop Sensors
Sensor Rebalance Servos
Binary Feedback
Ternary Feedback
Pulse Feedback and Sensors
The Voltage Reference Problem
Novel Accelerometer Principles
Surface Acoustic Wave Accelerometer
Fiber Optic AccelerometersThe Pendulous Accelerometer
A Generic Pendulous Accelerometer
Mass and Pendulum Length
Scale Factor
The Hinge
The Pickoff
The Forcer and Servo
The IEEE Model Equations
The Sundstrand "Q-Flex" Accelerometer
The Capacitive Pickoff
The Forcer
Other Electromagnetic Pendulous Accelerometers
Moving Magnet Forcers
Electrostatic Forcers
The Silicon AccelerometerVibrating Beam Accelerometers
The Vibration Equation
The Resolution of a Vibrating Element Accelerometer
The Quartz Resonator
Vibrating Beam Accelerometers in General
The Sundstrand Design
Accelerex Signal Processing
The Kearfott Design
Comparison of Free and Constrained Accelerometers
General Comparison of the Servoed Pendulum Accelerometer and Vibrating Beam Accelerometer
Comparison of Performance RangesThe Principles of Mechanical Gyroscopes
Angular Momentum
The Law of Gyroscopics
Parasitic Torque Level
The Advantage of Angular Momentum
The Spinning Top - Nutation
Equations of Spinning Body Motion
Coriolis Acceleration
Gyroscopes with One and Two Degrees of FreedomSingle Degree of Freedom Gyroscopes
The Rate Gyro
The Scale Factor
The Spin Motor
The Ball Bearings
Damping
The Pickoff
The Torsion Bar
Flexleads
Rate Gyro Dynamics
The Rate-Integrating Gyro
The Torquer
The Output Axis Bearing
The Principle of Flotation
Damping
Flotation Fluids
Structural Materials
A Magnetic Suspension
Self-acting Gas Bearings
Anisoelasticity in the Single Degree of Freedom gyroscope (SDFG)
Anisoinertia in the SDFG
Vibration Rectification
The SDFG Model Equation
A Digression into Accelerometers
The Pendulous-Integrating Gyro AccelerometerTwo Degree of Freedom Gyroscopes
The Two Degree of Freedom (Free) Gyro
The External Gimbal Type
Two-Axis Floated Gyros
Spherical Free Rotor Gyros
The Electrically Suspended Gyro
The Gas Bearing Free Rotor GyroThe Dynamically Tuned Gyroscope
The Dynamically Tuned Gyroscope (DTG) Tuning Effect
The Tuning Equations
DTG Nutation
Figure of Merit
Damping and Time Constant
Biases Due to Damping and Mistuning
Quadrature Mass Unbalance
Synchronous Vibration Rectification Errors
Axial Vibration at 1N
Angular Vibration at 2N
Wide Band Vibration Rectification Errors
Anisoelasticity
Anisoinertia
Pseudoconing
The Pickoff and Torquer for a DTG
The DTG Model EquationVibrating Gyroscopes
The Vibrating String Gyro
The Tuning Fork Gyro
Vibrating Shell Gyros
The Hemispherical Resonator Gyro
Scale Factor
Asymmetric Damping Error
The Vibrating Cylinder (START) Gyro
The Advantages of Vibrating Shell Gyros
The Multisensor Principle and Its Error SourcesThe Principles of Optical Rotation Sensing
The Inertial Property of Light
The Sagnac Effect
Sagnac Sensitivity - The Need for Bias
The Shot Noise Fundamental Limit
The Optical Resonator
The Fabry-Perot Resonator
Resonator Finesse
The Sagnac Effect in a Resonator
Active and Passive Resonators
Resonator Figure of Merit
Optical Fibers
Refraction and Critical Angle
Multimode and Single Mode Fibers
Polarization
Birefringent Fiber for a Sagnac Gyro
The Coherence of an Oscillator
Types of Optical GyroThe Interferometric Fiber-Optic Gyro
The History of the Fiber-Optic Gyro (FOG)
The Basic Open-Loop Interferometric Fiber-Optic Gyro (IFOG)
Biasing the IFOG
Non-reciprocal Phase Shifting
The Light Source
Reciprocity and the "Minimum Configuration"
Closing the Loop-Phase-Nulling
Acousto-Optic Frequency Shifters
Integrated Optics
Serrodyne Frequency Shifting
Fiber-to-Chip Attachment - The Jet Propulsion Laboratory IFOG
Drift Due to Coil Temperature Gradients
The Effect of Polarization on Gyro Drift
The Kerr Electro-Optic Effect
The Fundamental Limit of IFOG Performance
ConclusionsThe Ring Laser Gyro
The Laser
Stimulated Emission
The Semiconductor Laser
The Ring Laser
Lock-in
Mechanical Dither
The Magnetic Mirror
The Multi-oscillator
Shared-Mirror Ring Laser Gyro (RLG) Assemblies
The Quantum Fundamental Limit
Quantization NoisePassive Resonant Gyros
The Discrete Component Passive Ring Resonator (PARR)
The PARR Fundamental Limit
The Resonant Fiber-Optic Gyro (RFOG)
The Micro-Optic Gyro (MOG)
The MOG Fundamental Limit
IFOG, RFOG, and MOG Size Limits
Fundamental Limits for RFOG, IFOG, and RLG
ConclusionsTesting Inertial Sensors
Inertial Sensor Test Labs
Performance Test Gear
Environmental Test Gear
Qualification, Acceptance, and Reliability Tests
Accelerometer Testing
The Accelerometer Acceptance Test Procedure
Centrifuge Tests
Gyroscope Testing
Testing the Single Degree of Freedom (SDF) Rate Gyro
Testing SDF Rate-Integrating Gyros
Tombstone Tests
The Six-Position Test
The Polar-Axis (Equatorial Tumble) Test
The Servo Table Scale Factor Test
Vibration Tests
Testing the Dynamically Tuned Gyro
The Eight-Position Test
DTG Rate Testing
Testing Optical Gyros
The Sigma PlotDesign Choices for Inertial Instruments
A Platform or a Strapdown System?
Aiding the Inertial Measurement Units
Choice of Sensor Type
Differential Design
Using Resonance
Mechanical or Optical Gyros?
Reliability
Redundancy
Sensor Design Check Lists
Conclusions