The Kalman filter is a powerful way of expressing the complicated, a potentially computational expense process of data fusion, down into a more simpler problem that can easily be solved. This is done making a few assumptions about system dynamics, the estimated state, error and noise properties.
Theoretically, the Kalman Filter is an estimator which solves the ‘linear quadratic estimation problem’, which just means that it estimates the instantaneous state of a linear dynamic system perturbed by random white noise, and it does it by taking a series of measurements that are linearly related to the state but which are also corrupted by random white noise.
So we want to calculate the estimated state, which is as close as possible to the true state, using a series of noisy measurements. The solution result is a statistically optimum estimate with regards to a quadratic function of the estimation error which means it is minimizing the squared mean error.
The Kalman filter is one of the greatest discoveries in the history of estimation and data fusion theory, and perhaps one of the greatest engineering discoveries in the twentieth century. It has enabled mankind to do and build many things which could not be possible otherwise. It has immediate application in control of complicated dynamic systems such as manufacturing processes, it is used in cars, aircraft, ships and spacecraft.
The Kalman filter is named after its inventor, Rodolf Emil Kalman who was born in Budapest in the year 1930. He immigrated to the US during WW2 and eventually ended up at MIT for a bachelor and masters in electrical engineering which eventually led to a role as a lecturer at Columbia University. The first practical use of the Kalman Filter was by the Ames