This source code, for example, contains the very first Kalman filter ever used - Kalman was invited over to Moffett field to give talks about his paper, which led to his theory was used in LM code. But I think everyone is very aware of the state of the art at the time, and things have advanced a lot since then. It is impressive to see them cramming that into such a limited processor. But, 'whatever' as to that aspect of it. This is a historical artifact of an amazing feat based on cutting edge research in mathematics/control theory.
So far as I can tell, the AGC maintained the state vectors for the KF. Ground control would run batch mode least squares solutions, and pass it on to the LM, where the updates to the state vector would be applied by hand. I freely admit to not having worked through the code, but I believe the state vector update computations occur here: http://www.ibiblio.org/apollo/listings/Comanche055/MEASUREME...
sources: http://www.ieeecss.org/CSM/library/2010/june10/11-Historical...
http://en.wikipedia.org/wiki/Apollo_Guidance_Computer
http://en.wikipedia.org/wiki/Apollo_PGNCS http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2009001...
However, these LoC have been written almost 50 years ago! That's truly fascinating.
- Today's processors and capabilities run circles around those of the Apollo. It might be interesting to know how they calculate a square root, not today.
- They have more sensors and inputs and have to think of new and advanced ways of making it all work together
http://www.ibiblio.org/apollo/listings/Comanche055/AUTOMATIC...