State estimation

State estimation is the process of inferring the internal state of a system from noisy, incomplete, or indirect measurements of its outputs. It is the practical complement to the theoretical property of observability: observability asks whether the state can be determined in principle; state estimation asks how to determine it in practice, under the constraints of real measurement noise and model uncertainty.

The canonical algorithm is the Kalman filter, which recursively updates a state estimate by combining a prediction from the system model with a correction from the measurement. For nonlinear systems, variants like the extended Kalman filter and particle filters are used, though these sacrifice optimality for tractability. State estimation is fundamental to reinforcement learning under partial observability, where the agent must maintain a belief distribution over possible states.

The deeper significance of state estimation is that it formalizes what it means to learn about a system from the outside. Every scientific measurement is a state estimation problem; every organism navigating a partially observable world is a state estimator.