Aerospace Sensor Systems and Applications

This book is about aerospace sensors, their principles of operation, and their typical advantages, shortcomings, and vulnerabilities. They are described in the framework of the subsystems where they function and in accordance with the flight mission they are designed to serve. The book is intended for students at the advanced undergraduate or graduate level and for research engineers who need to acquire this kind of knowledge. An effort has been made to explain, within a uniform framework of mathematical modeling, the physics upon which a certain sensor concept is based, its construction, its dynamics, and its error sources and their corresponding mathematical models. Equipped with such knowledge and understanding, the student or research engineer should be able to get involved in research and development activities of guidance, control, and navigation systems and to contribute to the initiation of novel ideas in the aerospace sensor field. As a designer and systems engineer, he should be able to correctly interpret the various items in a technical data list and thus to interact intelligently with manufacturers' representatives and other members of an R&D team. Much of the text has evolved from undergraduate and graduate courses given by the author during the past seventeen years at the Department of Aerospace Engineering at the Technion- Israel Institute of Technology and from his earlier research and development experience in flight control, guidance, navigation, and avionics at the Ministry of Defense Central Research Institute.

and historical background.- 1. Principles and Elements of Measurement Systems.- 1.0 Introduction.- 1.1 Elements in open-loop instruments.- Instruments, sensors, and systems.- Basic sensor elements.- Auxiliary functions and elements.- Equilibrium.- Definitions of sensor functions.- 1.2 Measures and units.- Basic measures.- Units and standards.- Reference values.- 1.3 Passive and active instruments.- Contact and remote sensing.- Tapping of energy sources.- Input impedance.- 1.4 Characteristics, resolution, and dynamic range.- Domain and range.- Linearity, resolution, and dynamic range.- Bias, dead zone, and saturation.- Hysteresis.- 1.5 Errors due to dynamics, nonlinearity, and noise.- System and measurement equations.- Classification of errors.- 1.6 Environmental interference.- Error model formulation.- Additive and scaling errors.- 1.7 Error compensation.- Isolation and protection.- Output compensation.- Input compensation.- 1.8 Estimation of characteristics by regression.- Error modeling.- Linear regression.- Precision of the estimate.- 1.9 Deflection instruments.- Excitation, response, and display.- Basic tradeoffs.- The role of the restoring force.- 1.10 Balancing instruments.- The force balance principle.- Linearization by forced balance.- The effect of additive noise.- Sensitivity to variations in parameters.- 1.11 Imperfections and limitations on precision.- Sensor dynamics and design parameter tradeoffs.- Performance parameters and further design tradeoffs.- Enhancement of bandwidth.- Considerations of bandwidth, dynamic range, and robustness.- 1.12 Effect of friction in instrument servomechanisms.- Linear model of DC motor.- The linear motor model including friction.- Effect of loop closure on minimum speed.- Problems.- References.- 2. Random Processes and Signals.- 2.0 Introduction.- 2.1 Statistical characterization of random variables.- Time averages of sample functions.- 2.2 Ensemble averages of sample functions.- Ensemble of sample functions.- The probability density function.- Expectation.- Generalized moments.- Stationarity.- Power and variance.- 2.3 Joint distribution, correlation.- Correlation.- Orthogonality.- The distribution law.- Autocorrelation.- 2.4 Correlation coefficient and functions.- The correlation coefficient.- The autocorrelation function.- The cross-correlation function.- 2.5 Time and ensemble averages, ergodicity.- Conditions for equivalence of time and ensemble averages.- Ergodicity.- 2.6 Mathematical operations on random processes.- Autocorrelation of the sum of random functions.- Cross-correlation between a random function and its time derivatives ?.- Filtering of white noise, Markov processes.- Further properties of correlation functions.- Elementary prediction ?.- 2.7 Input-output relationships.- Convolution.- Nonstationary processes.- Output power in the steady state.- Response of linear systems to white noise.- Response of linear systems to slowly varying input.- Single, double, and triple integration.- 2.8 Spectral analysis.- The self-spectrum.- Parseval’s theorem.- Spectral decomposition.- Cross-spectrum.- Problems.- Appendix A2: Integration of power density spectra.- References.- 3. Inertial Force Sensors―Accelerometers.- 3.0 Introduction.- 3.1 Specific force readings on moving platforms.- Elementary strapdown mechanization for vehicle guidance.- 3.2 Leveling the supporting platform.- Mathematical Schuler pendulum.- Physical Schuler pendulum.- 3.3 Schuler frequency on other planets.- 3.4 Force balance accelerometers.- Pickoff considerations.- Spring-mass accelerometer model.- The capacitive detector.- Implementation of loop closure.- The Q-flex accelerometer.- 3.5 Measurement of angular acceleration.- Possible approaches.- Angular accelerometers.- Accelerometer pairs.- Differentiating angular rates.- 3.6 Integrating accelerometers.- 3.7 Vibrating beam accelerometers.- Background.- Principle of operation.- Acceleration-to-frequency conversion.- Double ended tuning fork.- Crystal controlled oscillation.- Signal processing system.- Frequency-to-acceleration conversion algorithm.- Resolution and dynamic range.- Sensitivity to clock frequency variations.- Frequency response and sensitivity to extraneous vibration.- 3.8 Piezo and capacitive transducers.- Piezo sensors/transducers.- Piezoelectric accelerometers.- Piezoresistive sensors.- Variable capacitance accelerometers.- Problems.- References.- 4. Inertial Rotation Sensors.- 4.0 Introduction.- 4.1 The free gyroscope.- Basic mechanization and dynamics.- Torque and precession relationships.- Effects of mechanical imperfections.- 4.2 The vertical gyroscope.- Description and imposing the vertical.- Dynamical model and erection process.- 4.3 Error sources in the vertical.- Error due to gyro drift rate.- Elimination of drift rate errors by integral control.- Errors induced by off-great-circle motion.- Coriolis acceleration.- The cut-out mechanism.- Errors due to atmospheric turbulence.- 4.4 The directional gyroscope.- Description.- Imposing the horizontal.- Effects of motion and drift rate.- Effects of aircraft angular rates.- Slaving to a compass.- 4.5 Gyrocompassing.- Geometry and motion.- Directional error in the steady state.- 4.6 The single axis deflection rate gyro.- Description.- Dynamical model.- Imperfections and limitations.- Bandwidth.- Drift rate.- Scale factor errors.- Nonlinearity and hysteresis.- Saturation.- 4.7 The floated rate integrating gyro (RIG).- Description.- Mathematical model.- Summary of properties.- Pendulous integrating gyro accelerometer (PIGA) ?.- 4.8 The dynamically tuned gyro (DTG).- Description of the dry tuned rotor gyro.- Principle of operation.- The analytical model: error sources ?.- Rotor tuning.- Performance as a free gyro.- Operation in closed loop.- Performance characteristics.- Summary of main properties.- 4.9 Very high-precision free gyroscopes.- The gas-bearing gyroscope ?.- The electrostatically supported gyroscope (ESG).- Problems.- Appendix A4: Euler angle transformation.- Appendix B4: Electrostatic flotation ?.- References.- 5. Applications of Rate Gyros.- 5.0 Introduction.- 5.1 Two-axis platform.- Description.- Angular stabilization by rate gyros.- Control loops and disturbances.- Summary of principal properties.- Application to target tracking.- 5.2 Gyroscopic seeker head.- Description and definition of variables.- Dynamics and control.- Detection of angular deviation―amplitude modulation.- Detection of angular deviation―phase modulation.- 5.3 Application to missile homing.- Homing equations.- The effect of gyro drift rate―stationary target.- The effect of gyro drift rate―moving target.- Accelerating target.- 5.4 Beam riding guidance.- Geometry and motion.- Guidance equations and effect of target maneuver.- The effect of seeker head noise.- 5.5 Three-axis platform for inertial navigation.- Reference axes.- Gimbaled mechanization.- Mathematical model-velocity Schuler tuned platform.- Summary of principal properties.- Positional Schuler tuning.- Velocity and positional error propagation.- Strapdown mechanization and the analytical platform.- 5.6 Stability augmentation―effect of gyro bandwidth.- Background.- Effect on roll rate control.- Problems.- Appendix A5: Direction cosines and quaternions.- Direction cosines.- Incremental Euler transformations.- Quaternions.- References.- 6. Coriolis Angular Rate Sensors.- 6.0 Introduction.- 6.1 Rotating Coriolis angular rate sensors.- Description.- General equations for specific force.- Accelerometer triad readings.- 6.2 Combined angular rate and acceleration sensing.- Signal separation by demodulation.- Imperfections.- 6.3 Rockwell-Collins rotating Coriolis sensor.- Schematic description.- Principle of operation and signal processing.- Technical data.- 6.4 Dithered accelerometers.- Geometry.- Signal separation by demodulation.- 6.5 Dithered accelerometer pairs.- Geometry.- Signal preprocessing.- Readings of accelerometer pairs.- Force and angular rate components.- 6.6 Silicon mechanization of dither.- The shuttle mechanism.- Silicon micromechanization ?.- 6.7 Sensor output signal processing.- Conversion of frequency variations to pulse counts.- Signal description.- 6.8 Projected performance characteristics.- Concluding comments.- Problems.- References.- 7. The Interferometric Fiber-Optic Gyro.- 7.0 Introduction.- 7.1 The Sagnac interferometer.- Mechanization by discrete optical components.- Fiber-optic mechanization.- 7.2 Effect of angular rate on Sagnac phase shift.- Effect in vacuum.- Effect in optical medium.- 7.3 Relationship between power output and phase shift.- Phase characteristics―biasing and modulation.- The need for a90 deg phase shift.- Extraction of angular rate by phase dither.- Implementing nonreciprocity by phase modulation.- Implementation of a 90 deg phase shift.- 7.4 Implementing the IFOG in a closed loop.- Phase nulling laser gyro (PNLG).- Implementation by Serrodyne shifter.- Technical realization of the PNLG ?.- Sensitivity and resolution.- Discrete phase nulling.- Limitations and imperfections.- 7.5 Effect of photon shot noise.- Effect on Sagnac phase uncertainty.- Sources of bias errors.- Recent IFOG test results.- Problems.- References.- 8. The Ring Laser Gyro.- 8.0 Introduction.- 8.1 Operating principle.- Description.- The interference fringe pattern.- 8.2 Technical description.- Spontaneous oscillation.- Path length control.- 8.3 The lock-in phenomenon.- The effect of lock-in on the RLG characteristic.- Prevention of lock-in by mechanical dither.- Removing the dither signal from the output.- Alternative methods for lock-in compensation.- The differential laser gyro―performance data.- Typical performance data.- Scale and drift error maps of angular rate sensors.- Concluding remarks.- Problems.- References.- 9. Filtering, Estimation, and Aiding.- 9.0 Introduction.- 9.1 Complementary filtering.- Basic formulation.- Compass-aided heading gyro.- Doppler-inertial ground speed estimation.- The baro-inertial altimeter.- Complementary filtering for discrete measurements ?.- 9.2 Equivalence of the CF and the stationary KF.- Formulation for inertial navigation.- The CF as the Luenberger observer ?.- Inclusion of noise.- The optimum observer.- The steady-state Kalman filter.- The augmented system model ?.- 9.3 Aircraft attitude angle estimation.- Background.- Gravity aiding.- Magnetic aiding.- Aiding by aircraft kinematics.- Aiding by the aircraft dynamical model ?.- Problems.- Appendix A9: Equations of aircraft dynamics.- Appendix B9: Extended Kalman filter formulation.- Appendix C9: Aircraft aerodynamic coefficients.- References.