# Space Shuttle: What are the filters in the attitude error calculation?

Here's a schematic from the space shuttle training manuals showing how the "attitude" error signal used to drive the thrust vector controllers was determined.

"Attitude" in quote marks because it was in fact a mix of attitude error, attitude rate error, and normal acceleration error signals.

The errors would be separately gained, then filtered, then summed, then filtered again then be gained again if the crew flipped a manual switch, then be filtered again---before finally at last being sent to the thrust vector controllers.

That's a lot of filtering! And now I'm wondering: what the purpose? To remove high-frequency noise? Or to smooth the error signal again and again and again in case the preceding operation (gaining through nonlinear/discontinuous lookup tables, summing) had made the signal... insufficiently smooth?

And more importantly! What would the filters look like? Would they be low-pass filters (I want to say yes)? Would they have different cutoff frequencies? Is there an algorithm for them that I could look at (since so many space shuttle algorithms are public on the web)?

• See here for info on the orbiter FCS filters: ntrs.nasa.gov/api/citations/19850008594/downloads/… – Organic Marble May 17 at 20:58
• Oh man every answer I get from you is gold. Ha ha. Thank you :) – user39728 May 18 at 1:15
• @OrganicMarble: any chance you have a reference for the bending filter algorithm itself, or at least a good practical/mathematical description of them? – user39728 May 18 at 23:56
• No, this is kinda out of my wheelhouse. I just know enough about it to know the answer already posted is wrong. – Organic Marble May 19 at 2:18

## 1 Answer

These are Kalman filters, which model the physics and the noise to calculate the optimal match between sequential measurement updates and the differential equations which determine how the (not directly knowable, but increasingly well estimated) true state of the system changes with time.

• Do you have a source that states the indicated filters in the control loop (not in the navigation system) are Kalman filters? – Organic Marble May 17 at 20:59
• Thanks Ryan! Any references to confirm they're Kalmans? – user39728 May 17 at 21:59
• One way around the requests for supporting sources would be to change to "Many of these filters are most likely Kalman..." and then to go on and explain why that is likely to be so. The Kalman filter is a kind of low-pass filter that works particularly well when presented with discrete time series that include some kinds of noise. Consider quoting comments or answer(s) to Digital low pass filter vs Kalman filter in DSP SE, – uhoh May 18 at 0:49
• and/or answer(s) to What is the Kalman filter? How does it differ with the low pass filter?, invoke the heritage and compelling story of how NASA and Rudolf E. Kálmán met each other. "Kálmán had more success in presenting his ideas, however, while visiting Stanley F. Schmidt at the NASA Ames Research Center in 1960. This led to the use of Kálmán filters during the Apollo program, and furthermore in the NASA Space Shuttle..."(still inconclusive) – uhoh May 18 at 0:52
• Okay, so having read @OrganicMarble’s paper, it seems clear those are not Kalman filters but in fact bending filters there to attenuate resonance frequencies that might excite the vehicle’s structural bending modes :) – user39728 May 18 at 23:55