Ladder Forms in Estimation and System Identification.
Abstract
Ladder forms are probably the most promising canonical forms in estimation and system identification. Many record applications, such as in geophysical signal processing, high resolution ('maximum entropy') spectral estimation and speech encoding, justify the interest in these forms. They appear in many contexts, such as scattering and network theory and the theory of orthogonal polynomials. The state-space model ladder realizations are very closely related in (block) Schwarz matrix canonical forms, which generally appear in the context of stability analysis. In fact they are the natural 'stability canonical form' for (discrete-time) Lyapunov equations since the associated positive definite (covariance) matrices are diagonal resp. an identity. This fact leads also to close connections to square-root algorithms including the ones of Cholesky and Chandrasekhar type, since again Ladder forms are the natural canonical forms. In realization theory these forms are obtained via orthonormal state-space bases using Gram-Schmidt type procedures. Ladder forms have many other advantages, such as lowest computational complexity, good numerical behavior, stability 'by inspection' properties and relations to physical properties such as reflection or partial correlation coefficients, and perhaps absorption coefficients.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1977
- Accession Number
- ADA053171
Entities
People
- M. Morf
Organizations
- Stanford University