Impulse control in Kalman-like filtering problems (Q1264405)

Summary: The authors develop an 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 jumps of the estimate variance from its current position down to zero and, as a result, enables one to obtain filtering equations for the Kalman estimate with zero variance for all post-jump time moments. 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.