Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 289-300
doi:10.1155/S1048953398000240
Filtering with a limiter
Tel Aviv University, Department of Electrical Engineering, Tel Aviv 69978, Israel
Received 1 September 1997; Revised 1 January 1998
Copyright © 1998 R. Liptser and P. Muzhikanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a filtering problem for a Gaussian diffusion process observed
via discrete-time samples corrupted by a non-Gaussian white noise. Combining the Goggin's result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we
construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.