Data reduction analysis for the Stanford Relativity Gyroscope Experiment

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 frame-dragging effect. The geodetic effect has a magnitude of 6.602 arcsec/year in the south-north direction. It is due to the orbital motion of a gyroscope in a curved space-time around the earth. The frame-dragging effect has a magnitude of 0.042 arcsec/year in the west-east 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 two-step Kalman filtering algorithm is developed based on the spectral separation principle. Slowly varying terms are treated as time-invariant 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 pseudo-measurements 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 one-year mission, the optimal initial gyro alignment is close to the apparent line-of-sight to the guide star. This analysis is the basis for a newly established fundamental experiment requirement.; Data reduction algorithms with a low resolution analog-to-digital converter (12-bit) are also studied. These include a data integration filter and a {dollar}Sigma{dollar}-{dollar}Delta{dollar} analog-to-digital converter. These algorithms are tested by simulations.