Title :
On the error of the optimal filtering of stationary processes with a small information rate
Author :
Pinsker, M.S. ; Prelov, V.V.
Author_Institution :
Inst. for Inf., Moscow, Russia
Abstract :
Upper and lower bounds for the mean-square error of the optimal (nonlinear) filtering of a discrete-time stationary process X={Xj } from the observations Y={Yj}, where Y=X+Z and Z={Z j} is a sequence of i.i.d. random variables, are obtained. These bounds are linear functions of the information rate I¯(X;Y). It is shown that the lower bound is asymptotically tight in the case, where I¯(X;Y) and the peak power of the signal X tends to zero
Keywords :
discrete time systems; mean square error methods; nonlinear filters; random processes; sequences; discrete-time stationary process; i.i.d. random variables; information rate; linear functions; lower bounds; mean-square error; nonlinear filters; optimal filtering; sequence; stationary processes; upper bounds; Diffusion processes; Error analysis; Information filtering; Information filters; Information rates; Mutual information; Random processes; Random variables; Upper bound;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.708937
