[From Bill Powers (2006.12.18.0020 MST)]
I found an old “track-analyze program” and set it so the model
uses no delay and a perfect output integrator instead of the optimum
delay and damping (“leakage”) settings. The person’s handle
behavior is aqua and the model’s handle behavior is orange. The white
wiggly line shows prediction error, and it is given numerically at the
top as 7.9% (RMS, as fraction of peak-to-peak amplitude). That’s a
14-sigma fit, or 7-sigma if you use the half-amplitude.
This is for tracking a moving target, so the disturbance variations are
about the same size as the handle excursions. Without actually
calculating the correlation coefficient, I think we can agree that it is
at least 0.9. This would also be the correlation between the disturbance
and the handled position. I thickened the lines so they’d be visible in a
smallish plot.
Best,
Bill P.
