Kalman filter estimates the state of a dynamic system, even if the precise form of the system is unknown. The filter is very powerful in the sense that it supports estimations of past and even future states. The description of the standard Kalman filter and its algorithms with the two main steps, the prediction step and the correction step. Furthermore the extended Kalman filter is discussed, which represents the conversion of the Kalman filter to nonlinear systems. Finally these filter was tested on aircraft tracking, and sinus wave using MATLAB.