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) The formulation and methods of solution of the problem apply without modifica- tion to stationary and nonstationary statistics and to growing-memory and infinite- memory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the co- efficients of the difference (or differential) equation of the optimal linear filter are ob- tained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.