Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 1-8
Impulse control in Kalman-like filtering problems
University of Nevada at Reno, Department of Mathematics- 084, Reno 89557-0045 , NV, USA
Received 1 March 1997; Revised 1 August 1997
Copyright © 1998 Michael V. Basin and Mark A. Pinsky. 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.
This paper develops the impulse control approach to the observation process in Kalman-like filtering problems, which is based on impulsive modeling of the transition matrix in an observation equation. The impulse control generates the jumps of the estimate variance from its current position
down to zero and, as a result, enables us to obtain the filtering equations
for the Kalman estimate with zero variance for all post-jump time
moments. The filtering equations for the estimates with zero variances are
obtained in the conventional linear filtering problem and in the case of
scalar nonlinear state and nonlinear observation equations.