Estimating State from Noisy Observations
Botie is watching parts move along a conveyor. The camera reports slightly different positions from frame to frame, and sometimes misses a part completely. How can we combine what we know about the belt’s movement with those imperfect readings? We’ll build a position estimate, then test how well its reported uncertainty describes its errors.
Following an estimate through time
The belt moves between camera readings. Use that movement to predict a position, then decide how much a new reading should change the estimate.
- 01Ready to exploreKeep a Position Estimate Without Believing Every Detection
The conveyor’s motion and the camera suggest different positions. Carry the uncertainty of each into a position estimate that can be updated as the part moves.
- 02Ready to exploreWhen the Camera Misses a Frame, Keep Predicting Honestly
The camera misses a frame while the part keeps moving. Continue the motion estimate without pretending that a missing reading measured a position of zero.
When observation and model disagree
A nearby camera detection could belong to the wrong part. We’ll first check which detection we can reasonably use, then examine what happens when our motion assumptions are wrong.
- 03Ready to exploreA Plausible Position Might Belong to the Other Part
Two detections appear near the position Botie is following. Check which readings are plausible and whether that gives enough evidence to choose one.
- 04Ready to exploreA Small Covariance Can Be Confidently Wrong
Botie reports a small uncertainty while the position is wrong. Check the motion and camera assumptions against reference trajectories before changing the filter’s confidence.