Just to clarify in case of misunderstanding: my answer addressed the question what is perpendicular to the reference ellipsoid
Ok, I think I might have misunderstood it to mean that the definition of ground speed as given by Kayton was relative to the ellipsoid (which is also correct, even if that's not what you wished to emphasise!).
You point out that the accuracy of inertial navigation is dependent amongst other things upon the integrated effects of local gravity over the route of flight, not over some purely mathematical (engineering) construct such as the geodetic latitude. Indeed so,
That's correct. Inertial navigation systems incorporate a gravity model in order to account for the differences in the mass distribution of the Earth (as well as centrifugal acceleration due to rotation), and barometric (or GNSS) height aiding to control vertical channel instability. And I have the feeling you already know this perfectly well
Note that the "integrated effects of local gravity" are modelled to within the precision of the provided gravity model, and unmodelled residual errors are accounted for and controlled during Kalman filtering. So, as you say, the source of residual errors is neither purely mechanical nor mathematical, but a combination of the design limitations in both.
BOAC,
GROUND speed is ALWAYS speed relative to the ground. Nothing else, pure and simple.
Not so "pure and simple" I'm afraid. You will find that what we call ground speed is in effect the first integral of acceleration in a given reference frame which may or may not be physically referenced[*]. What I think you might be thinking of would be the first derivative of change of position over time, which
could be a perfectly valid definition (not without its own set of complications, mind you) but unfortunately is not what is used.
[*] Consider the following practical example: If you were measuring the ground speed of the Eiffel tower you will find that your answer will be either about zero, or ~3cm/yr, depending on whether you were using the ETRS89 or ITRF2008 reference systems (due to different velocity fields). In other words, even defining what "the ground" is presents a major problem, past a certain threshold of accuracy.