A convex optimization approach to ARMA modeling
2008 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 5, 1108-1119 p.Article in journal (Refereed) Published
We formulate a convex optimization problem for approximating any given spectral density with a rational one having a prescribed number of poles and zeros (n poles and m zeros inside the unit disc and their conjugates). The approximation utilizes the Kullback-Leibler divergence as a distance measure. The stationarity condition for optimality requires that the approximant matches n + 1 covariance moments of the given power spectrum and m cepstral moments of the corresponding logarithm, although the latter with possible slack. The solution coincides with one derived by Byrnes, Enqvist, and Lindquist who addressed directly the question of covariance and cepstral matching. Thus, the present paper provides an approximation theoretic justification of such a problem. Since the approximation requires only moments of spectral densities and of their logarithms, it can also be used for system identification.
Place, publisher, year, edition, pages
2008. Vol. 53, no 5, 1108-1119 p.
ARMA modeling, cepstral coefficients, convex optimization, covariance, matching, cepstral coefficients, covariance
IdentifiersURN: urn:nbn:se:kth:diva-17794DOI: 10.1109/tac.2008.923684ISI: 000258868400002ScopusID: 2-s2.0-51749100240OAI: oai:DiVA.org:kth-17794DiVA: diva2:335839
QC 201005252010-08-052010-08-05Bibliographically approved