A model selection rule for sinusoids in white Gaussian noise
A model selection rule for sinusoids in white Gaussian noise
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DOI：
10.1109/78.510621
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发表时间：
1996-07-01
影响因子：
5.4
通讯作者：
Djuric, PM
中科院分区：
文献类型：
--
作者：
Djuric, PM
正弦信号的模型选择问题通常是通过使用Akaike信息准则(AIC)和最小描述长度原则(MDL)来解决的，这些准则的流行部分源于它们可以被实现的本质上的简单手段，然而，如果它们不小心使用，它们可能产生误导的结果。AIC和MDL具有共同的形式，它们包括两个项，即数据项和惩罚项，数据项量化模型的残差，而惩罚项反映简约的愿望，而AIC和MDL的数据项相同，惩罚项不同，在大多数文献中，然而，AIC和MDL惩罚都是通过对每个附加的未知参数分配相同的权重来获得的，无论是相位、幅度还是频率。相反，本文证明了与幅度和相位参数相关的惩罚应该不同于与频率相关的惩罚。遵循贝叶斯方法，我们推导了正弦信号在高斯噪声中的模型选择准则，该准则还包括对数似然和惩罚项。仿真结果表明，我们的选择准则比常用的MDL和AIC有显著的改善。
The model selection problem for sinusoidal signals has often been addressed by employing the Akaike 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, in this paper, 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.