On observation control using impulse feedback design

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 observation control generates on-line computable jumps of the estimate variance from its current position towards zero and, as a result, enables us to instantaneously obtain the estimate, whose variance is closer or equal to zero. This kind of observation control is useful for fast high-accuracy estimation on a short time interval. The filtering equations over impulse-controlled observations are obtained in the conventional Kalman filtering problem, the filtering problem for Ito-Volterra processes, and the ellipsoidal filtering problem. The considered examples allow us to compare the properties of these filtering methodologies.