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Kalman filtering and Riccati equations for descriptor systems

By Ramine Nikoukhah, Alan S. Willsky, Bernard C. Levy and Senior Member


Abstract-In this paper, we consider a general formulation of a discrete-time filtering problem for descriptor systems. It is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems. Using a “dual approach ” to estimation we derive a so-called “3-block ” form for the optimal filter and a corresponding 3-block Riccati equation for a general class of time-varying descriptor models which need not represent a well-posed system in that the dynamics may be either over or under constrained. Specializing to the time-invariant case we examine the asymptotic properties of the 3-block filter, and in particular analyze in detail the resulting 3-block algebraic Riccati equation, generalizing significantly the results in 1231, 1281, 1331. Finally, the noncausal nature of discrete-time descriptor dynamics implies that future dynamics may provide some information about the present state. We present a modifie

Year: 1992
DOI identifier: 10.1109/9.159570
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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