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State estimation infers an unobserved state of a dynamical system from its observations and a model of its evolution. An observed position can help estimate an unobserved velocity; repeated noisy observations can help distinguish changes in the state from measurement noise. The result should describe both an estimate and its uncertainty. A Kalman filter does this exactly for a linear Gaussian state-space model, maintaining a conditional expectation and conditional covariance.

The time at which information is available matters. Causal state filtering estimates the present state from observations available now. State prediction estimates a future state from those same observations. Later observations can improve an estimate of a past state, but that is a different information set from the one a live controller had. Kalman explicitly distinguishes these estimation tasks in A New Approach to Linear Filtering and Prediction Problems (1960), section Optimal Estimates.

State prediction estimates a future state of a dynamical system using observations already available. A state-space model supplies the transition law. Unlike causal state filtering at the next time, the prediction has not yet incorporated that next observation; a Kalman prediction step therefore includes uncertainty from new process noise.