control//state estimation

How to decide what a system is doing when no single source can be trusted to say it. Two voices speak about the same quantity: a **model** that predicts from what was known a moment ago (110 m for the car), and a **sensor** that asks the world directly (the GPS says 114 m). Both are imperfect and they disagree; state estimation turns that disagreement into the best available answer by weighting each voice according to how uncertain it is. The story of the two voices opens the Kalman filter.

How to decide what a system is doing when no single source can be trusted to say it. Two voices speak about the same quantity: a model that predicts from what was known a moment ago (110 m for the car), and a sensor that asks the world directly (the GPS says 114 m). Both are imperfect and they disagree; state estimation turns that disagreement into the best available answer by weighting each voice according to how uncertain it is. The story of the two voices opens the Kalman filter.

The vocabulary comes first, because half of the later confusions start here. The truth, the measurement and the estimate are three different objects with two different errors between them (estimate). Once time enters, the estimate splits into the prediction and the corrected estimate, the Physics and the Judge, with the Sensor between them (a priori and a posteriori).

The difference between what the sensor says and what I predicted is the innovation. Zero means the sensor told me nothing new; a large value means either the sensor knows something the model does not, or the sensor is broken.

What the state must contain is a sufficient state; how it is written, with its physics and its sensors, is the state-space model; whether the sensors can reveal it is controllability and observability.

The standard recipe for linear systems is the Kalman filter; how to learn how noisy a sensor is before trusting it is sensor calibration.