Lossless cascade networks and stochastic estimation

The notion of matrices with generalized displacement structure is introduced. An efficient procedure for Cholesky factorization of nonstationary covariances with such structure is presented. An inverse scattering interpretation of this procedure relates it to lossless cascade models with p+q-1 parameters per layer where { p, q} denotes the displacement inertia of the covariance matrix. Matrices with displacement inertia are of particular interest: they have given rise to cascade models that are lossless two-ports, with a single parameter per layer. The author uses the cascade model to construct Levinson-type recursions for the prediction polynomials associated with structured nonstationary covariances