velocity = \frac{\Delta Displacement} {\Delta Time} , no? (or delta magnitude using your previous definition of vector magnitude)

oops

I think I'd write this as: magnitude(t) = \sqrt{E(t)^2 + N(t)^2}

It'd be interesting if we could project the noise "floor" into this space-- it could be a simple circular model. And then we could add synthetic noise to the time series; again I think we could use a pretty simple noise model to get the point across. But maybe this idea would be better for a different notebook?

typical "real world" horizontal noise: http://gaia.unavco.org/streamStatus/RT-GPS/plotGPSScatter6_SA.html

That's a good idea, working on this