View source for 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]]: 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|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.

[[Category:Systems]] [[Category:Technology]] [[Category:Mathematics]]