The Kalman filter is an algorithm for estimating the mean vector and variance-covariance matrix of the unknown state in a state space model.

The Kalman filter is an "online" algorithm that takes a stream of input data in order to update estimates of the mean (usually a vector) and variance (generally a variance-covariance matrix) of the unobserved state in a state space model; as each piece of data is added in, the estimates are updated.

Each step he filter has a prediction step where the state mean and variance estimates at the time of the next observation based on previous information are generated, and an update step, where the new data is incorporated into those estimates. Under assumptions of (multivariate) normal state and observations, all past information is incorporated in the current estimate of the state mean and variance.

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