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This paper describes a method for the online state estimation of systemsdescribed by a general class of linear noncausal time-varying differencedescriptor equations subject to uncertainties. The method is based on thenotions of a linear minimax estimation and an index of causality introducedhere for singular difference equations. The online minimax estimator is derivedby the application of the dynamical programming and Moore's pseudoinversetheory to the minimax estimation problem. It coincides with Kalman's filter forregular systems. A numerical example of the state estimation for 2D noncasualdescriptor system is presented.  Keywords: Kalman filtering, online state observer, guaranteed estimation,descriptor systems, singular systems, DAEs.

Recursive state estimation for noncausal discrete-time descriptor systems under uncertainties