There is no State Noise.
These are my favorite pictures I think, and will be much more thoroughly annotated later. For now, the main things to note are: In the first picture, I have started out the picture with a terrible initial guess, and a very small amount of uncertainty, ie, the guess is considered almost exact. If the guess is started with greater uncertainty, it is corrected to the real value almost immediately, and if it is started with no uncertainty, it is a fixed point and the filter has no effect.
In the second picture, observations are no longer direct. We have two observation variables: y1=x1+x2+noise, y2=x3+noise.
I need to realign the axes, etc to make the picture better, but you can see the filter is actually working! Very cool, I was delighted to see my algorithms work perfectly in this more complicated case involving psuedo-inverses and wierd dimensionality issues.