A New Approach to Linear Filtering and Prediction Problems

Abstract

The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ¿¿stat-tran-sition¿¿ method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.