A Scattering Theory Framework for Fast Least-Squares Algorithms,
Abstract
In scattering theory the Riccati equation arises in a natural family of equations evolving forwards as well as backwards in time. The authors show how this framework allows an interesting derivation of the fast Chandrasekhar-type equations for linear least-squares filtering of processes generated by a time-invariant, finite-dimensional linear system driven by white noise. The processes are not required to be stationary. The same ideas can be used to obtain Levinson- and Cholesky-type differential equations for the impulse responses of the whitening filter and the innovations representation of such processes. The scattering framework brings out clearly both the significance of the time-invariance of the parameters of the underlying finite-dimensional system and of the associated family of nonstationary processes. For stationary processes, it also becomes clear that the assumption of finite-dimensionality is unnecessary, but the proper extension of the nonstationary class of processes raises some interesting questions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1975
- Accession Number
- ADA029790
Entities
People
- L. Ljung
- Thomas Kailath
Organizations
- Stanford University