抄録
The corrected least squares (CLS) approach using an overdetermined model is investigated to decide the number of sinusoids in additive white noise. The CLS estimation is different from the ordinary LS and the TLS approaches in that the noise variance is subtracted from the diagonal elements of the correlation matrix of the noisy observed signal data. Therefore the inversion of the matrix becomes ill-conditioned and then adequate truncation of the eigenvalue decomposition (EVD) should be done, since the rank of the matrix is equal to the number of sinusoids. Thus, in the overdetermined CLS approach, the estimation of the noise variance and the truncation of eigenvalues are mutually dependent, therefore it is required to decide them simultaneously. By introducing a multiple number of regularization parameters and determining them to minimize an MSE of the model parameters, we can give an optimal scheme for the truncation of eigenvalues to detect the number of sinusoids. Further, an iterative algorithm using only observed data is also given to determine the noise variance and the truncation number simultaneously.
