  This paper describes a method for the online state estimation of systems
described by a general class of linear noncausal time-varying difference
descriptor equations subject to uncertainties. The method is based on the
notions of a linear minimax estimation and an index of causality introduced
here for singular difference equations. The online minimax estimator is derived
by the application of the dynamical programming and Moore's pseudoinverse
theory to the minimax estimation problem. It coincides with Kalman's filter for
regular systems. A numerical example of the state estimation for 2D noncasual
descriptor system is presented.
  Keywords: Kalman filtering, online state observer, guaranteed estimation,
descriptor systems, singular systems, DAEs.
