Determination of the number of sinusoidal signals in AR spectral estimation

In carrying out the AR spectral estimation of observed signals consisting of the sum of sinusoidal signal and white noise, since at low SNR many more false peaks occur than the number of sinusoids, a method which uses the eigenvalue decomposition of the correlation matrix to adopt only as many eigenvalues as the number of sinusoids, discarding the rest, is very effective. However, if the number of signals is unknown, how the discarding of eigenvalues should be determined becomes an important problem. In this paper, to select an appropriate number of eigenvalues of the correlation matrix of the observed data, a multiple number of adjustable parameters is introduced to square the prediction error and, by determining them optimally, determine the number of eigenvalues. Two new methods are proposed. The first method decides the truncation number of eigenvalues so that the Bayes information criterion with a priori distribution is minimized. The decision criterion is derived and its properties are investigated. The second method determines the number of sinusoids by computing adjustable parameters so that the AR spectrum of a given rank is the closest to the true AR model representing the sinusoidal signal model approximately, that is, the MSE criterion is minimum. Finally, the effectiveness of the authors' methods are investigated through numerical examples.