Abstract: The optimal recursive equation for the generalized discrete linear system is discussed. A singular values standard form for generalized discrete stochastic linear systems is given by singular value decomposition of a matrix. In two cases, the generalized discrete stochastic linear system is decomposed into two subsystems based on the standard form. The optimal recursive equations for this system are obtained by state estimation of subsystems.

Key words: generalized system, singular value decomposition, state estimation, recursive equation