Basin, Michael V.; Pinsky, Mark A. Impulse control in Kalman-like filtering problems. (English) Zbl 0905.34064 J. Appl. Math. Stochastic Anal. 11, No. 1, 1-8 (1998). 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. Cited in 2 Documents MSC: 34K20 Stability theory of functional-differential equations 93D99 Stability of control systems 93E11 Filtering in stochastic control theory 93B07 Observability Keywords:filtering equations; impulse control approach; Kalman-like filtering problems; transition matrix; observation equation; scalar nonlinear state and nonlinear observation equations PDFBibTeX XMLCite \textit{M. V. Basin} and \textit{M. A. Pinsky}, J. Appl. Math. Stochastic Anal. 11, No. 1, 1--8 (1998; Zbl 0905.34064) Full Text: DOI EuDML