Forward-Only and Forward-Backward Sample Covariances – A Comparative Study
1999 (English)In: Signal Processing, ISSN 01651684, Vol. 77, no 3, 235-245 p.Article in journal (Refereed) Published
In some applications the covariance matrix of the observations enjoys a particular symmetry: it is not only symmetric with respect to its main diagonal but also with respect to the anti-diagonal. The standard forward-only sample covariance estimate does not impose this extra symmetry. In such cases one often uses the so-called forward-backward sample covariance estimate. In this paper, a direct comparative study of the relative accuracy of the two sample covariance estimates is performed. An explicit expression for the difference between the estimation error covariance matrices of the two sample covariance estimates is given. This expression shows quantitatively the gain of using the forward-backward estimate compared to the forward-only estimate. The presented results are also useful in the analysis of estimators based on either of the two sample covariances. As an example, spatial power estimation by means of the Capon method is considered. Using a second-order approximation, it is shown that Capon based on the forward-only sample covariance (F-Capon) underestimates the power spectrum, and also that the bias for Capon based on the forward-backward sample covariance is half that of F-Capon.
Place, publisher, year, edition, pages
1999. Vol. 77, no 3, 235-245 p.
Forward-only sample covariance; Forward-backward sample covariance; Performance analysis; Centro-Hermitian matrix; Direction estimation; Capon method; Maximum likelihood method
IdentifiersURN: urn:nbn:se:kth:diva-82192DOI: 10.1016/S0165-1684(99)00037-7OAI: oai:DiVA.org:kth-82192DiVA: diva2:498025
NR 201408052012-02-112012-02-112012-02-11Bibliographically approved