Abstract
This paper provides detailed descriptions of the numerical estimation algorithms used to fit physics-based models to the data from the Gravity Probe B spacecraft, as well as the scientific results of the experiment, and the statistical and systematic uncertainties. The first paper in this series of three data analysis papers derives the mathematical expressions for the signals to be analyzed, and the second paper deals with science data acquisition and their preparation for the relativistic drift rate estimation. The data from each of the four gyroscopes are partitioned into six segments, each spanning several weeks to several months. These segments are first analyzed individually to check the validity of the mathematical models and the accuracy of the estimation routine by examining the consistency of the relativistic drift rate estimates from each of these 24 gyro-segments. Then, the drift rate estimates and uncertainties are calculated for each individual gyroscope and for the four gyroscopes combined. These results are presented and compared with each other and with the prediction of general relativity.