Data reduction analysis for the Stanford relativity gyroscope experiment
Abstract
This thesis discusses the data reduction simulation and error analysis for the Stanford Relativity Gyroscope Experiment. This experiment is designed to test the Einstein's general theory of relativity. Two untested relativistic effects are predicted for a gyroscope moving in a 650 km polar orbit around the earth: a geodetic effect and a framedragging effect. The geodetic effect has a magnitude of 6.602 arcsec/year in the southnorth direction. It is due to the orbital motion of a gyroscope in a curve spacetime around the earth. The framedragging effect has a magnitude of 0.042 arcsec/year in the westeast direction. It is due to the dragging of the 'inertial' frame by the massive rotating earth. The goal of this experiment is to detect these two effects to better than 0.5 milliarcsec/year. A Kalman filter is used to perform the data reduction simulation and error analysis. A twostep Kalman filtering algorithm is developed based on the spectral separation principle. Slowly varying terms are treated as timeinvariant in the first step filter. This filter is restarted for every orbital period. The second step filter uses the outputs from the first step filter as pseudomeasurements to estimate the slowly varying terms. This algorithm has the advantages of clearer physical insight, providing intermediate data for dynamical modeling, better numerical performance, and less computation time. A data reduction simulation is performed with realistic spacecraft roll dynamics. The sensitivity to spacecraft roll angle error is investigated. Studies show that data reduction can be successfully performed with only one roll angle measurement as well as one roll rate correction per roll period. Studies also show that spacecraft roll control error starts to have significant influence on the experiment accuracy when its RMS (Root Mean Square) value is bigger than 100 arcsec. <The initial gyro spin axis alignment has a significant effect on the experiment accuracy. &Studies show that, for a oneyear mission, the optimal initial gyro alignment is close to the apparent lineofsight to the guide star. This analysis is the basis for a newly established fundamental experiment requirement. Data reduction algorithms with a low resolution analogtodigital converter (12bit) are also studied. *These include a data integration filter and a sigmadelta analogtodigital converter. These algorithms are tested by simulations.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.........7Q
 Keywords:

 Critical Experiments;
 Data Reduction;
 Error Analysis;
 Gyroscopes;
 Kalman Filters;
 Relativistic Effects;
 Relativity;
 Accuracy;
 Analog To Digital Converters;
 Lateral Control;
 Mean Square Values;
 Roll;
 RootMeanSquare Errors;
 Sensitivity;
 Simulation;
 Spacecraft Motion;
 Instrumentation and Photography