A transfer function approach to the linear discrete stationary optimal filtering for singular systems

By defining an optimal predictor for singular systems, a transfer function, in the Z-domain, is established for the stationary optimal state estimation filter of these systems. The associated return-difference matrix is given. By factorizing the spectral density matrix of the discrete observation vector, a method is proposed for computing the transfer function of the filter without using the generalized Riccati difference equation or the generalized Riccati algebraic equation associated with the state estimation filter.<>