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Warning: repetitive question ahead. Please skip if you're tired of splitting hairs on these things.

Is there a detailed description of the major and minor GNC loops of the space shuttle? I've learned enough about the loops to get in trouble and not enough to get out of trouble yet.

I (think I) know the major loop ran at a slow rate (~0.5 Hz) and that it provided guidance and flight control with velocity and attitude readings determined from the latest IMU data. This was the most accurate data you could get.

I also (think I) know that the minor loop ran at a faster rate (~25 Hz) and that it provided approximate estimates of position and velocity until the next major cycle began. The estimates from the minor loop were good enough for control but not as accurate as major loop calculations.

So it seems you had two velocity sources. One was the integrating accelerometer itself in the space shuttle's stable platform IMU, which informed the major loop. The other was the approximate calculation done in the minor loop by integration using the trapezoid method. These were replaced by the major-loop numbers once those became available.

But to estimate velocity in the minor loop, you would need both the gravitational and inertial acceleration of the rocket. The gravitational acceleration was estimated using a gravity model (built on spherical harmonics, if I remember correctly). But what about the inertial acceleration?

For one, what the integrating accelerometer truly provided was (I think) the integrated acceleration, which is to say... velocity. You would differentiate this to get the instantaneous acceleration...

...but if you're not getting new data from the IMU until the next major cycle, then it seems the best you can work with is the last computed value for acceleration... which would mean you'd assume inertial acceleration to be constant from minor loop cycle to minor loop cycle until the next major cycle began?

Or did they have an equation to update the instantaneous inertial acceleration during minor loop cycles? All the equations I've seen of this stuff show how they updated velocity and position (with state propagation calculations) but none of those equations updated inertial acceleration itself... Just wondering what they assumed for it?

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