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Scattering theory and linear least squares estimation: Part I: Continuous-time problems

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3 Author(s)
Ljung, L. ; Lund Institute of Technology, Lund, Sweden ; Kailath, T. ; Friedlander, B.

The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. We show that this framework is very appropriate also for estimation problems, and that it enables us to give simple derivatitions of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behavior of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.

Published in:

Decision and Control including the 14th Symposium on Adaptive Processes, 1975 IEEE Conference on

Date of Conference:

10-12 Dec. 1975