A New Approach to Linear Filtering and Prediction Problems

The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the state-transition method of analysis of dynamic systems. New results are: (1) formulation applies without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (2) A nonlinear difference equation is derived for the covariance matrix of the optimal estimation error. (3) The filtering problem is shown to be the dual of the noise-free regulator problem.