process and measurement noise

When a robot tries to track something it cannot see directly — its true position, its real speed — it leans on two pictures of the world, and each comes with its own kind of fuzziness. One picture is a prediction: "based on how I was moving, I should now be roughly here." The other is an observation: "my sensor just told me I'm over there." Neither is perfect, and the two flavors of imperfection have names. Process noise is the slop in the prediction — all the little ways the real world refuses to follow the tidy rule the robot used. Measurement noise is the slop in the observation — all the little ways the sensor mis-reports what it sees.

Process noise comes from the prediction step relying on a simplified model of how things move, and reality always wandering a bit outside that model: a wheel slips, a gust shoves the drone, a motor pushes a touch harder than commanded. It is uncertainty in the motion itself — the gap between "how I assumed I'd move" and "how I actually moved." Measurement noise, by contrast, is uncertainty in the looking: a GPS jittering by a few meters, a camera blurring, a thermometer that wobbles around the true temperature. The robot's actual state may be perfectly steady, yet the sensor still hands back a slightly different number each time it checks.

Telling these two apart is the heart of how filters like the Kalman filter work, because the filter must decide how much to trust its own prediction versus a fresh sensor reading. If it believes the motion model is reliable but the sensor is jumpy, it leans on the prediction and shrugs off the noisy reading; if the sensor is crisp but the motion is unpredictable, it leans on the measurement instead. Get the balance of these two noises right and the estimate stays smooth and accurate; get it wrong and the robot either chases every sensor twitch or stubbornly ignores the real world.