In his 1960 famous publication (“A new approach to linear filtering and prediction problems”, Trans.ASME J. Basic Engineering., vol 82, March 1960, pp 34-45), Rudolf Kalman based the construction of the state estimation filter on probability theory, and more specifically, on the properties of conditional Gaussian

random variables. The criterion he proposed to minimize is the state vector covariance norm, yielding to the classical recursion : the new state estimate is deduced from the previous estimation by addition of a correction term proportional to the prediction error (or the innovation of the measured signal).