Minimum variance estimates of gyroscopic drift parameters.
Minimum variance estimation for gyroscopic drift parameters, discussing optimal estimation procedure and noise model
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Minimum variance estimation for gyroscopic drift parameters, discussing optimal estimation procedure and noise model
Experimental cryogenic gyroscope drift data, discussing Fourier analysis and mathematical model
Calculating drift of electrostatic gyroscopes due to rotor asphericity
Statistical analysis of gyroscopic drift rate data for computer simulation of inertial navigator output error
It is the purpose of this paper to describe and indicate possible analytical approaches to some of the most significant mechanisms by which vibration induced drifts may occur, and to indicate, where possible, some means of alleviating them. In all cases we will not consider gimbal bearing friction, mass unbalance or other sources of steady extraneous torques on the gyro rotor. The mechanisms to be discussed are: Non-Newtonian viscosity in single degree of freedom (SDF) integrating-rate gyros, nonisoelasticity in SDF gyros, noncommutative effects for SDF stabilized platform, gimbal inertia effects, 2 DF gyros, and spin axis torque coupling in 2 DF gyros. High-frequency elastic resonances are not discussed explicitly in detail, because they are a more familiar problem and one which depends strongly on the details of each particular gyro design.
Gyroscopic drift and Markov process research in inertial guidance system components study
The following four tasks were studied: (1) modification of the calibration routines to calibrate the Inertial Measurement Unit gyroscope drifts with fixed platform heading; (2) modification of the calibration routines to calibrate the Inertial Measurement Unit accelerometers; (3) checking overall software again for errors; and (4) providing documentation on the above work describing changes to the present software, results of these changes and future operating procedures.
Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.
The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.
Analytical techniques for inflight compensation of gyro drift rates
An alternative approach to the design and fabrication of vibratory gyroscopes is founded on the use of fabrication techniques that yield best results in the mesoscopic size range, which is characterized by overall device dimensions of the order of a centimeter. This approach stands in contradistinction to prior approaches in (1) the macroscopic size range (the size range of conventional design and fabrication, characterized by overall device dimensions of many centimeters) and (2) the microscopic size range [the size range of microelectromechanical systems (MEMS), characterized by overall device dimensions of the order of a millimeter or less]. The mesoscale approach offers some of the advantage of the MEMS approach (sizes and power demands smaller than those of the macroscale approach) and some of the advantage of the macroscale approach (the possibility of achieving relative dimensional precision greater than that of the MEMS approach). Relative dimensional precision is a major issue in the operation of a vibratory gyroscope. The heart of a vibratory gyroscope is a mechanical resonator that is required to have a specified symmetry in a plane orthogonal to the axis about which rotation is to be measured. If the resonator could be perfectly symmetrical, then in the absence of rotation, a free vibration of the resonator could remain fixed along any orientation relative to its housing; that is, the gyroscope could exhibit zero drift. In practice, manufacturing imprecision gives rise to some asymmetry in mass, flexural stiffness or dissipation, resulting in a slight drift or beating motion of an initial vibration pattern that cannot be distinguished from rotation. In the mesoscale approach, one exploits the following concepts: For a given amount of dimensional error generated in manufacturing, the asymmetry and hence the rate-of-rotation drift of the gyroscope can be reduced by increasing the scale. The decrease in asymmetry also reduces coupling of vibrations to the external environment. Mechanical thermal noise and electronic measurement noise and drift can also be reduced by increasing the size of the resonator and its associated sensors.
Drift test data for cryogenic gyro noting rotor vibration damping, material and fabrication
Analysis of guidance system errors resulting from initial misalignments of both the accelerometer and stabilizing gyros, the drift of the stabilized element during flight and errors in measuring the vehicle motions
An oven-controlled crystal oscillator at 16.368 MHz provides clock signals to all GP-B components and synchronizes the data collection, transmission and processing. The sampled science data signals are stamped with the vehicle time, a counter of the 10Hz data strobe divided down from the clock. The GPS receiver supplies an external reference for time transfer between the vehicle time and coordinated universal time. Ground and space flight tests show the time transfer error is within 1 microsecond. The time latency between the effective sample time of science signals and the stamped vehicle time is verified to 1 ms in the ground tests. The GP-B satellite is controlled to roll with a period of 77.5 sec about an axis along the direction to the guide star to average out the disturbance torques fixed to the body of the satellite and reduce the gyroscope readout noise. The roll phase is determined on the ground to high accuracy with the telemetry data from two star trackers and used in the data analysis to separate the drifts of gyroscope spin axes in the orbital plane and perpendicular to the orbital plane. The flight data shows that the roll phase is controlled to within 40 arcsec with a measurement uncertainty of 7 arcsec.
Vibratory gyroscope zero rate error reduction through separation of driving and sensing frequencies by double modulation
Effect of nodal regression of orbit on gravity gradient precession of gyroscopic satellite in testing general theory of relativity
Work was conducted to develop an extremely low drift rate gyroscope and a very precise star tracker. A proposed relativity satellite will measure very accurately the theoretically predicted 'relativistic' precession of the gyroscope relative to an inertial reference frame provided by the star tracker. Aspects of precision spinning attitude control are discussed together with questions of gyro operation, and the hopping mode for lunar transportation. For the attitude control system of the lunar hopper, a number of control laws were investigated. The studies indicated that some suboptimal controls should be adequate for the system.
The Gravity Probe-B (GP-B) experiment is one of the most sophisticated and challenging developments to be undertaken by NASA. Its objective is to measure the relativistic drift of gyroscopes in orbit about the earth. In this paper, the experiment is described, and the strategy of phased procurements for accomplishing the engineering development of the hardware is discussed. The microcomputer is a very convenient and powerful tool in the management of GP-B. It is used in creating and monitoring such project data as schedules, budgets, hardware procurements and technical and interface requirements. Commercially available software in word processing, database management, communications, spreadsheet, graphics and program management are used. Examples are described of the efficacy of the application of the computer by the management team.