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Abstract
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- 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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Keyword
- Least-squares
- Smoothing
- Linear
- Fredholm resolvent
- Levinson recursions
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- kon (subject category)
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- Levy, Bernard C.
- Kailath, Thomas
- Morf, Martin
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- ENGINEERING AND TECHNOLOGY
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- Linköping University
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