PS: You'll need to study the principle of INS a little closer.
Actually Megan, it's you that needs to do the study. You seem to be confusing your frames of reference.
An INS has a unique point of reference, that being a known, fixed starting point - effectively the point on the ground at which the system was initialised. Everything that subsequently happens to the aircraft, as far as the INS is concerned, is measured as an acceleration / deceleration in one of the 3 axes. Whether that's taxi, take-off, climb, cruise, turning or whatever.
Put simplistically, it's the aggregation of the effect of all the accelerations over time
relative to the starting point on the ground that provides the position information.
As an example, you fly at a constant airspeed on a constant heading in a zero wind condition so your airspeed and groundspeed happen to be the same. At this point the INS detects no acceleration or deceleration while in this zero wind situation, so a constant velocity relative to the reference point on the ground is recorded.
A headwind develops, so your groundspeed decreases, but your airspeed remains the same. The accelerometer in the INS
does measure a deceleration, relative to the reference point on the ground, however, and can therefore compute that the groundspeed has changed. The aircraft's velocity WRT the air is unchanged, but the aircraft's velocity WRT to the ground has indeed changed.
So an INS knows nothing about what the air is doing, other than accelerating or decelerating the aircraft in space, relative to the reference point on the ground.
FBW