Lossless cascade networks and stochastic estimation
Abstract
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 give rise to cascade models that are lossless twoports, with a single parameter per layer. The cascade model is used to construct Levinsontype recursions for the prediction polynomials associated with structured nonstationary covariances.
 Publication:

IN: IEEE Conference on Decision and Control
 Pub Date:
 1989
 Bibcode:
 1989deco....1...17L
 Keywords:

 Cascade Control;
 Cholesky Factorization;
 Linear Filters;
 Stochastic Processes;
 Covariance;
 Delay Lines;
 Electronic Filters;
 Matrices (Mathematics);
 Polynomials;
 White Noise;
 Electronics and Electrical Engineering