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Fast Time-Invariant Implementations for Linear Least Squares Smoothing Filters
Stanford University, CA, USA.
Stanford University, CA, USA.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Stanford University, CA, USA.
1979 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 24, no 5, 770-775 p.Article in journal (Refereed) Published
Abstract [en]

We present a new solution for the fixed interval linear least-squares smoothing of a random signal, finite dimensional or not, inadditive white noise. By using the so-called Sobolev identity of radiative transfer theory, the smoothed estimate for stationary processes is expressed entirely in terms of time-invariant causal and anticausal filtering operations; these are interpreted from a stochastic point of view as giving certain constrained (time-invariant) filtered estimates of the signal. Then by using a recently introduced notion of processes close to stationary, these results are extended in a natural way to general nonstationary processes. From a computational point of view, the representations presented here are particularly convenient, not only because time-invariant filters can be used to find the smoothed estimate, but also because a fast algorithm based on the so-called generalized Krein-Levinson recursions can be used to compute the time-invariant filters themselves.

Place, publisher, year, edition, pages
IEEE Control Systems Society , 1979. Vol. 24, no 5, 770-775 p.
Keyword [en]
Least-squares estimation, Smoothing methods, Time-invariant implementation, Krein-Levinson recursions
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-102124DOI: 10.1109/TAC.1979.1102152OAI: oai:DiVA.org:liu-102124DiVA: diva2:668556
Available from: 2013-12-01 Created: 2013-12-01 Last updated: 2017-12-06

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Ljung, Lennart

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