On posterior distributions for signals in Gaussian noise with unknown covariance matrix
2005 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 9, 3554-3571 p.Article in journal (Refereed) Published
A Bayesian approach to estimate parameters of signals embedded in complex Gaussian noise with unknown color is presented. The study specifically focuses on a Bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems. By integrating out uncertainties regarding the noise color, an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited. Several noninformative priors for the covariance matrix, such as the reference prior, the Jeffreys prior, and modifications to this, are considered. Some of the priors result in analytical solutions, whereas others demand numerical approximations. In the linear signal model, connections are made between the standard Adaptive Maximum Likelihood (AML) estimate and a Bayesian solution using the Jeffreys prior. With adjustments to the Jeffreys prior, correspondence to the regularized solution is also established. This in turn enables a formal treatment of the regularization parameter. Simulations indicate that significant improvements, compared to the AML estimator, can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior. The simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged.
Place, publisher, year, edition, pages
2005. Vol. 53, no 9, 3554-3571 p.
Research subject Signal Processing
IdentifiersURN: urn:nbn:se:ltu:diva-15102DOI: 10.1109/TSP.2005.853102Local ID: e9086be0-95a4-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-15102DiVA: diva2:988075
Validerad; 2005; 20061227 (ysko)2016-09-292016-09-29Bibliographically approved