I believe there is reason to expect that the measure of the speed of light on the International Space Station would be greater than it is measured at the surface of the earth.
My expectation is based on a revision of the Minkowski diagram, which projects an observed world-line according to observed relative motion in space and observed motion in time. (Minkowski projects an observed world-line according to the observer’s motion in time, thereby treating the observer’s clock as an absolute -- a fundamental misrepresentation of special relativity.) The revision is able to graphically explain why the speed of light is invariable and a limit, and to represent the mirroring of the special relativistic relationship, effects which the Minkowski diagram is unable to produce. It can be seen and described at http://eujournal.org/index.php/esj/article/view/990 in section 3, titled “Minkowski and Relativistic Time.”
Here’s the prediction: Given the generally accepted principle that acceleration slows a body's clock compared to a non-accelerating body (as in the twin paradox), it seems to follow that the world-line of an accelerating observer would in some degree "catch up" with a ray of light. (In the revised spacetime diagram, an inertial acceleration would incline in the direction of the world-line of light, which lies along the space axis.) Given a constant acceleration at the earth’s surface of 9.80665 m/sec, our measure of c as 299,792,458 m/sec should be less than a measure by the ISS -- slower by roughly 9.8 m/sec, including an adjustment (infinitesimal at that acceleration) for our slower clock speed due to our constant acceleration by the earth’s surface. Experimental confirmation should be practicable by an experiment using laser interferometry on the ISS.
The prediction is counter-intuitive. If an observer’s clock is slowed by acceleration, the measure of the speed of light would be expected to increase, if it was expected to change at all. But at an acceleration of just 9.8 m/sec that component of the overall effect would be negligible.
If it is objected that the ISS is “accelerating” in its orbit of the earth, an orbiting body is actually moving uniformly in its own coordinate system, which is why objects float freely inside. Interferometry onboard would be un-accelerated and force-free.
If it is objected that measures of c at different level in a gravitational field should vary, and at least complicate the proposed experiment, I disagree. But in any case, un-accelerated observers at different levels in a gravitational field should measure the same speed of light if it is emitted and observed at the same level in the field.
Earth-bound experiments may not be practicable. The Atacama Observatory in Chile, for example, at an elevation of 5640 m, would have a reduced acceleration of only about .02 m/sec compared to sites at sea level -- probably too small an effect to be observed. Some sort of construction of a rapidly accelerating clock might be conceivable, and comparable with a clock undergoing only surface acceleration, but the ISS would be the ideal setting.