Automatic navigation makes ocean-going and flying safer and less expensive: Safer because machines are tireless and always vigilant; inexpensive because it does not use human navigators who are, unavoidably, highly trained and thus expensive people. What is more, unmanned deep space travel would be impossible without automatic navigation. Navigation can be automated with the radio systems Loran, Omega, and the Global Positioning System (GPS) of earth satellites, but its most versatile form is completely self-contained and is called inertial navigation. It uses gyroscopes and accelerometers (inertial sensors) to measure the state of motion of the vehicle by noting changes in that state caused by accelerations. By knowing the vehicle's starting position and noting the changes in its direction and speed, one can keep track of the vehicle's present position. Mankind first used this technology in World War n, in guided weapons where cost was unimportant; only 20-30 years later did it become cheap enough to be used commercially. The electronics revolution, in which vacuum tubes were replaced by integrated circuits, has dramatically altered the field of inertial navigation. Early inertial systems used complex mechanical gimbal structures and mechanical gyroscopes with spinning wheels. The gimbals allowed the gyroscopes to stabilize a mass (called a "platform") so that it remained in a fixed attitude relative to a chosen coordinate frame, even as the vehicle turned around any or all of its three major axes.

1. 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.- Conclusions.- References.- 2. Gyro 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 Specifications.- References.- 3. The 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 Accelerometers.- References.- 4. The 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 Accelerometer.- References.- 5. Vibrating Beam Accelerometers.- The Vibration Equation.- The Resolution of a Vibrating Element Accelerometer.- The Quartz Resonator.- VBAs in General.- The Sundstrand Design.- Accelerex Signal Processing.- The Kearfott Design.- Comparison of Free and Constrained Accelerometers.- General Comparison of the SPA and VBA.- Comparison of Performance Ranges.- Conclusion.- References.- 6. The 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 Freedom.- Conclusion.- References.- 7. Single 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 SDFG.- Anisoinertia in the SDFG.- Vibration Rectification.- The SDFG Model Equation.- A Digression into Accelerometers.- The Pendulous-Integrating Gyro Accelerometer.- Conclusion.- References.- 8. Two 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 Gyro.- References.- 9. The Dynamically Tuned Gyroscope.- The 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 Equation.- Conclusion.- References.- 10. Vibrating 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 Sources.- Conclusion.- References.- 11. The 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 Gyro.- Conclusion.- References.- 12. The Interferometric Fiber-Optic Gyro.- The History of the Fiber-Optic Gyro.- The Basic Open-Loop 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 JPL 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.- Conclusions.- References.- 13. The 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 RLG Assemblies.- The Quantum Fundamental Limit.- Quantization Noise.- Conclusion.- References.- 14. Passive Resonant Gyros.- The Discrete Component Passive Ring Resonator.- The PARR Fundamental Limit.- The Resonant Fiber-Optic Gyro.- The Micro-Optic Gyro.- The MOG Fundamental Limit.- IFOG, RFOG, and MOG Size Limits.- Fundamental Limits for RFOG, IFOG, and RLG.- Conclusions.- References.- 15. Testing Inertial Sensors.- Inertial Sensor Test Labs.- Performance Test Gear.- Environm…