Two Amplitude Spectral Estimators with Rank-Deficient Covariance Matrix

In this paper, two nonparametric amplitude spectral estimators, which belong to the adaptive filtering-based approach, are proposed. In case of only several snapshots available, the filtering data, which is formed by weighting the snapshots with the traditional Fourier weight vector, contains more larger residual term besides the signal term at the frequency of interest. Those residual term dramatically reduce the accuracy of the spectral estimate at the frequency. By weighting the snapshots with Capon weight vector, the weighted data is slightly influenced by the other frequency components, and the corresponding filters perform better estimation accuracy and higher spectral resolution. Numerical examples are provided to demonstrate the performance of the new approaches