Abstract: The optimal recursive equation for the generalized discrete stochastic non-linear system is discussed. A singular values standard form for generalized discrete stochastic non-linear systems is given by singular value decomposition of a matrix. Under the two cases, the generalized discrete stochastic non-linear system is decomposed into two subsystems based on the standard form. The optimal recursive algorithm for this system is obtained by state estimation of subsystems. The result shows that this technique efficiently reduces the amount of computation for the generalized singular system.

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