ABSTRACT
Distilled to its most fundamental elements, the Kalman filter [1] is a predictor-corrector estimation algorithm that uses a dynamic system model to predict state values and a measurement model to correct this prediction. However, the Kalman filter is capable of a great deal more than just state observation in such a manner. By making certain stochastic assumptions, the Kalman filter carries along an internal metric of the statistical confidence of the estimate of individual state elements in the form of a covariance matrix. The essential properties of the Kalman filter are derived from the requirements that the state estimate be
• a linear combination of the previous state estimate and current measurement information
• unbiased with respect to the true state
• and optimal in terms of having minimum variance with respect to the true state.
