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Fast Time-Invariant Implementations for Linear Least-Squares Smoothing Filters
Massachusetts Institute of Technology, MA, USA.
Stanford University, CA, USA.
Stanford University, CA, USA.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1978 (English)In: Proceedings of the 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, 1978, 1156-1159 p.Conference paper, Published paper (Refereed)
Abstract [en]

We present a new solution for the fixed interval linear least-squares smoothing of a stationary random signal in additive white noise. By using the generalized Sobolev identity for the Fredholm resolvent of a covariance kernel, the smoothed estimate is expressed entirely in terms of time-invariant causal and anticausal filtering operations. These operations are interpreted from a stochastic point of view as giving some constrained (time-invariant) filtered estimates of the signal. From a computational point of view, the implementation presented here is particularly convenient, not only because time-invariant filters can be used to find the smoothed estimate, but also because a fast algorithm based on Levinson recursions can be used to compute the time-invariant filters themselves.

Place, publisher, year, edition, pages
1978. 1156-1159 p.
Keyword [en]
Least-squares, Smoothing, Linear, Fredholm resolvent, Levinson recursions
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-101006DOI: 10.1109/CDC.1978.268116OAI: oai:DiVA.org:liu-101006DiVA: diva2:664732
Conference
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, San Diego, CA, USA, January, 1979
Available from: 2013-11-16 Created: 2013-11-16 Last updated: 2013-11-16

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Ljung, Lennart

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