Kalman filter

The Kalman filter (named after its inventor, Rudolf Kalman) is an efficient recursive computational solution for tracking a time-dependent state vector with noisy equations of motion in real time by the least-squares method. It is used to separate signal from noise so as to optimally predict changes in a modeled system with time.

Peter Swerling actually developed a similar algorithm earlier. Stanley Schmidt is generally credited with developing the first implementation of a Kalman filter. It was during a visit of Kalman to the NASA Ames Research Center that he saw the applicability of his ideas to the problem of trajectory estimation for the Apollo program, leading to its incorporation in the Apollo navigation computer.

A wide variety of Kalman filters have now been developed, from Kalman's original formulation, now called the simple Kalman filter, to Schmidt's extended filter, the information filter, and a variety of square-root filters, developed by Bierman, Thornton and many others.

Kalman filtering is used extensively in control systems engineering.

For longer implementations, look at the implementations page

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