Brief Tutorial on the Kalman Filter

A derivation of the Kalman filter equations is presented which should provide a concise introduction to Kalman filter theory for scientists, engineers, and mathematicians alike. An elementary derivation of the basic Kalman filter, the 1-step Kalman predictor, is given first in 1-dimension and then in n-dimension. The well known prediction-correction formulation of the Kalman filter equations are derived for the filtered estimate, or current state estimate. Then, the state prediction is obtained from the filtered estimate. It is assumed that the reader has a background in probability theory and some exposure to stochastic processes.