I don't know - and have never seen - martial notation systems out in the wild.
Here are a few small things that I've used that were helpful, to get started:
- RFF - Right Foot Forward
- LFF - Left Foot Forward
- FFK - Front leg Front Kick
- RFK - Rear leg Front Kick
- FRK - Front Roundhouse Kick
- RRK - Rear Roundhouse Kick
Now for more complex things like, say, the following movement:
You are in stance A facing direction X, left hand down block, right hand on hip. Look over right shoulder, right foot steps behind left foot to stance B facing direction Y, both hands come up in double head block.
I have no idea, but using the notation above as a guide, I would suggest:
- A -> X, LH DB, RH 0 (zero, meaning the initial position, base position, whatever)
- Look RS (right shoulder, as opposed to just to your right)
- RF behind LF - B -> Y
- LH+RH double high block
Now, this looks all neat out of context, but the key will be to be really consistent with this otherwise it's going to become unreadable REALLY QUICKLY. I never used this because my memory is excellent -- and I know one form that I'm still not sure, after five years or so of studying it, how I would write down.
This was the direct answer to your question. You can use this to describe two-person drills as well by prepending a number.
Truth be told, you probably ought to review your notes more often, and ask questions within one week at the most if you don't remember clearly. It's a lot of work, but it just has to be done in chunks - not all at once.