A model selection rule for sinusoids in white Gaussian noise
Djuric, P.M.
Signal Processing, IEEE Transactions on
Volume 44, Issue 7, Jul 1996 Page(s):1744 - 1751
Digital Object Identifier 10.1109/78.510621
Summary:The model selection problem for sinusoidal signals has often been
addressed by employing the Akaike (1974) information criterion (AIC) and
the minimum description length principle (MDL). The popularity of these
criteria partly stems from the intrinsically simple means by which they
can be implemented. They can, however, produce misleading results if
they are not carefully used. The AIC and MDL have a common form in that
they comprise two terms, a data term and a penalty term. The data term
quantifies the residuals of the model, and the penalty term reflects the
desideratum of parsimony. While the data terms of the AIC and MDL are
identical, the penalty terms are different. In most of the literature,
the AIC and MDL penalties are, however, both obtained by apportioning an
equal weight to each additional unknown parameter, be it phase,
amplitude, or frequency. By contrast, we demonstrate that the penalties
associated with the amplitude and phase parameters should be weighted
differently than the penalty attached to the frequencies. Following the
Bayesian methodology, we derive a model selection criterion for
sinusoidal signals in Gaussian noise which also contains the
log-likelihood and the penalty terms. The simulation results disclose
remarkable improvement in our selection rule over the commonly used MDL
and AIC
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