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 modification 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 obtained 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.
- Autor/es: R. E. Kalman.
- Fecha: 1960-03
- Publicado en: ASME Journal of Basic Engineering, Series D, vol.82, pp.35-45, 1960.
- Idioma: Inglés
- Formato: PDF
- Contribución: Aníbal Figueiras.
- Palabras clave: Proceso de señal, Sistemas de control