Kalman Filter Algorithm

The Kalman filter is an algorithm that estimates the unknown state of a changing system from a sequence of noisy measurements, producing an estimate that is typically more accurate than relying on any single measurement alone. It works in two alternating steps: a prediction step that projects the current estimate forward using a mathematical model of how the system evolves, and an update step that folds in each new measurement, weighting it by how much noise or uncertainty that measurement carries. The filter is named for the Hungarian-American mathematician Rudolf Kalman, though similar ideas had earlier roots in work by Thorvald Nicolai Thiele and Peter Swerling, and Richard Bucy's later theoretical contributions led to the algorithm's alternative name, the Kalman-Bucy filter. Stanley Schmidt built the first practical implementation around 1960, and the filter gained wide recognition after NASA incorporated it into the Apollo Guidance Computer for spacecraft navigation during the Apollo program; it remains a standard tool today in navigation, robotics, radar and signal processing.