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Backwards Markovian Models for Second Order Stochastic Processes
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Stanford University, CA, USA.
1976 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 22, no 4, 488-491 p.Article in journal (Refereed) Published
Abstract [en]

A state-space model of a second-order random process is a representation as a linear combination of a set of state-variables which obey first-order linear differential equations driven by an input process that is both white and uncorrelated with the initial values of the state-variables. Such a representation is often called a Markovian representation. There are applications in which it is useful to consider time running backwards and to obtain corresponding backwards Markovian representations. Except in one very special circumstance, these backwards representations cannot be obtained simply by just reversing the direction of time in a forwards Markovian representation. We show how this problem can be solved, give some examples, and also illustrate how the backwards model can be used to clarify certain least squares smoothing formulas.

Place, publisher, year, edition, pages
IEEE Information Theory Society , 1976. Vol. 22, no 4, 488-491 p.
Keyword [en]
Least-squares estimation, Markov processes, State estimation, Stochastic processes
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-100791DOI: 10.1109/TIT.1976.1055570OAI: oai:DiVA.org:liu-100791DiVA: diva2:663699
Available from: 2013-11-12 Created: 2013-11-12 Last updated: 2017-12-06

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Ljung, Lennart

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