Scattering theory and linear least squares estimation—II. Discrete-time problems

✍ Scribed by B. Friedlander; T. Kailath; L. Ljung

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 796 KB
• Volume: 301
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(76)90133-2

✦ Synopsis

A certain ('star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g. the distinctions between time and measurement updates, predicted and jiltered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The diflerences between the discrete-time and continuoustime cases are noted.