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MA Estimation in Polynomial Time
Systems and Control Group, Uppsala University, Uppsala,Sweden.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Optimization and Systems Theor, Royal Institute of Technology, Stockholm, Sweden.
1999 (English)Report (Other academic)
Abstract [en]

The parameter estimation of moving-average (MA) signals from second-order statistics was deemed for a long time to be a difficult nonlinear problem for which no computationally convenient and reliable solution was possible. In this paper we show how the problem of MA parameter estimation from sample covariances can be formulated as a semidefinite program which can be solved in polynomial time as efficiently as a linear program. Two methods are proposed which rely on two specific (over)parametrizations of the MA covariance sequence, whose use makes the minimization of the covariance fitting criterion a convex problem. The MA estimation algorithms proposed here are computationally fast, statistically accurate, and reliable (i.e. they never fail). None of the previously available algorithms for MA estimation (methods based on higher-order statistics included) shares all these desirable properties. Our methods can also be used to obtain the optimal least squares approximant of an invalid (estimated) MA spectrum (that takes on negative values at some frequencies), which was another long-standing problem in the signal processing literature awaiting a satisfactory solution.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1999. , 24 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2126
Keyword [en]
Moving-average, Estimation, Time-series analysis, Semidefinite programming, Linear matrix inequalities, Linear stochastic system
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-55699ISRN: LiTH-ISY-R-2126OAI: diva2:316451
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08

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