A Kalman filter is an optimal estimator for linear dynamical systems with Gaussian noise. Extensions to non-linear systems are included through the Extended KF and Unscented KF.
A Kalman filter is an optimal estimator for linear dynamical systems with Gaussian noise. This algorithm takes as a series of noisy measurements from the dynamical system and combines them to estimate possibly unknown variables. In fact, if the system meets the theoretical assumptions of having linear dynamics and Gaussian noise, there is no better estimate of the unknown system state. The filter itself is usually defined in terms of matrices, one for the system model, one for the control model, one for the process noise, one for the observation model and one for the measurement noise.