In a presentation on Gravity Probe B,
(see http://www.wyp-ptm.org/presentations/ptm2_everitt.pdf slides 3 and 6. You might have to wait a good while for it to download)
there is a reference to 9 degrees of freedom. I am familiar with 6 degrees of freedom, namely translational motion along 3 spatial axes and rotational motion about those 3 axes (i.e., roll, pith and yaw).
What would be the additional 3 degrees of freedom they are referring to here?
Interdimensional time travel?
vibratory motion?
WAG.
A rigid body has the six degrees of freedom you mentioned. A mechanism or flexible body can have as many DOF as you feel like keeping track of. Maybe the Gravity Probe has three hinge joints or a ball joint (I lost my patience waiting for the slides to download). Either would account for three extra DOF.
In robotics, a degree of freedom is how you can move. Suppose I lost a hand. What’s left of my arm would have 4 degrees of freedom. 3 for my shoulder and 1 for my elbow.
I think they’re counting velocity and position as separate degrees of freedom. With 3 degrees each for velocity, position and attitude (orientation) you get 9 degrees.
But they’re not separate. One completely determines the other, up to a constant factor. I wonder why they would do that.
They are coupled in the sense that the time history of one will allow you to compute the other. But they are separate in the sense that if want to specify the new status of your spacecraft, it takes 9 numbers.
Though I think it’s actually 10… It takes 7 numbers to specify an orbit (google for “orbital elements” - or you can think of them as initial position, initial velocity and start time). And 3 to specify attitude.
That’s an 84 MB file for those of you still waiting for it to complete. 
Anyway, Hyperelastic’s comment may be the relevent one. On page 44 of 45, it gives a table with a bunch of things and the degrees of freedom of control needed:
Telescopes - 3 DOF
GP-B 9 DOF
STEP - 18 DOF
ST-7 - 18 DOF
LISA - 57 DOF
So there’s no reason to expect the GP-B’s 9 degrees of freedom to be the 9 degrees of freedom in some overarching sense.
From a physical perspective there are 6 DOF that define a point in space, x,y,z,roll, pitch,yaw.
DOF is also used in robotics to define the number of axes of movements in the system. For example a scara robot has a minimum of 2 DOF, a shoulder and elbow. It can also have a Z axis and a rotational axis for a total 4.
In this case the 9 DOF are from three sensors that each provide three feedback states; a three DOF accelerometer, a three DOF magnetometer and a three DOF gyroscope. 3+3+3=9. In the end the combined data cannot give you more than the position and orientation data of x/y/z/roll/pith/yaw. Velocity and acceleration are not considered additional DOF. They define rates of change of the position data.
A bit late to the party, but
Only 6 independent ones, actually. It might sometimes be convenient to define a seventh (or eighth or ninth or…), but it’ll be derivable from the other six.
Life, liberty and the pursuit of happiness?
Zombie or not, this is interesting.
My suspicion is this - the 9 DOF refer to the control of the satellite. So this is about making sure the satellite is located correctly to keep the experiment working. Gravity-B needed to be pointed at a precise star, so that is 3 DOF. Then is needs to maintain attitude, also 3 DOF. Then it needed to maintain the position of the spherical gyroscopes exactly inside their little cells, and used thrusters to nudge the satellite if the spheres moved too close to the edge of a cell. That is translation in a further 3 DOF. So a total of 9 DOF for satellite control. Arguably some are coupled, but the actual control mechanisms tend to work in the 3 orthogonal dimensions.
The STEP satellite - (Satellite Test of the Equivalence Principle) needs to control the accelerations of the satellite as well - otherwise it can’t control the forces it is trying to test equivalence of. So you add accelerations to the degrees of freedom, orientation, attitude, position, and get 18.