Abstract: The Gravity Probe B (GP-B) experiment, sponsored by NASA and launched on 20 April 2004, has estimated the geodetic and frame-dragging effects consistent with General Relativity with accuracies of 0.28% and 19% respectively. The GP-B spacecraft measured the non-Newtonian drift rates of four ultra-precise cryogenic gyroscopes placed in a circular polar low Earth orbit. Science data was collected from 28 August 2004 until cryogen depletion on 29 September 2005. The data analysis was complicated by two unexpected phenomena, a) a continually damping gyroscope polhode affecting the calibration of the gyro readout and b) two larger than expected Newtonian torques acting on the gyroscopes, comparable in magnitude to the relativistic effects. Experimental evidence strongly indicates that both effects are caused by non-uniform electric potentials (i.e. the patch effect) on the surfaces of the gyroscope rotor and its housing. The five-year long data analysis effort involved first determining the root cause for these classical effects, then developing mathematical models for them, and finally building an optimal estimator to determine them simultaneously with the relativistic drift rates. This talk will summarize the experiment design and on-orbit performance, but focus primarily on the details of the data analysis models, estimation methods and final results.