Control of Kalman-like filters using impulse and continuous feedback design
Michael Basin, Mark A. Pinsky · Discrete and Continuous Dynamical Systems - B · 2002
This paper develops the observation control method for refining theKalman-Bucy estimates, which is based on impulsive modeling of the transitionmatrix in an observation equation, thus engaging discrete-continuous observations.The impulse observation control generates on-line computable jumps of the estimatevariance from its current position towards zero and, as a result, enables us to instantaneouslyobtain the estimate, whose variance is closer to zero. The filteringequations over impulse-controlled observations are obtained in the Kalman-Bucy filteringproblem. The method for feedback design of control of the estimate variance isdeveloped. First, the pure impulse control is used, and, next, the combination of theimpulse and continuous control components is employed. The considered examplesallow us to compare the properties of these control and filtering methodologies.