[From Bill Powers (970302.1521 MST)]
I'm now satisfied that while my long recapitulation of Hans' derivation of
the "prediction" function was the same as his, the derivation itself is
faulty. If x(t) is the current angle of the theodolite and v(t) is the
current angular velocity, then
x(t+dt) := x(t) + v(t)*dt + 0.5*(u/J)*dt^2
v(t+dt) := v(t) + 0.5*u/J*dt
Hans' derivation omits the angular velocity at the start of the
time-interval, and effectively computes just an increment of position on
every iteration -- i.e., a velocity proportional to the applied torque. I
don't know exactly where the conceptual error was made, but however the
derivation in terms of incremental positions is done, if done correctly it
has to be equivalent to the above two program steps.
These program steps, with (u+d) in place of u, will have to be substituted
into the MCT model both in the "observation" function and in the "predictor"
function. The simple manner of deducing the disturbance will also be
incorrect (because now we have the correct quadratic function), and a more
complicated method will have to be used. I leave that work, thankfully, to Hans.
Best,
Bill P.