Estimate the hidden velocities
Can position and angle sensors reveal velocity when measurements are noisy?
Try it in the current lab
Pin a run, increase assumed sensor variance, and compare smoothness and delay of the estimate.
Open State estimate, compare true and estimated angle, and change the assumed sensor variance. Control still uses true state here.
The lab recalculates after a setting changes. Pin a run before changing one variable; the response and control-effort plots share the same replay time. PID experiments also show the P/I/D terms; estimator experiments show measured and estimated states.
What the system is doing
A discrete Kalman filter predicts from the model and corrects with position and angle measurements. Q and R express assumed process and sensor uncertainty.
Connect the design method
Only position and angle are measured. The filter predicts four states and corrects with those two measurements. Open Pole rate estimate to inspect a hidden velocity. Here the controller intentionally uses true state so you can isolate estimation from feedback.
innovation = measurement − predicted measurement