Kalman filter is a class of linear filters for predicting and/or smoothing time series. The value of the time series is usually a vector in a state space . Kalman filter is optimal for filtering many types of markov chains . The general structure of this class of filters was derived and studied by Rudolf E. Kalman.
Kalman filters are widely used for time series analysis (e.g. to predict stock prices or currency exchange rate) and in many technical measurement and control systems where it is necessary to track the state of the object of interest (e.g. position and velocity of a plane or a car, parameters of an engine, etc).
For mathematical detail of Kalman filters see Kalman filter (equations) .