NEW MAXIMUM-ENTROPY SPECTRUM USING UNCERTAIN EIGENSTRUCTURE CONSTRAINTS

A number of modern spectral estimators are shown to have a common generic formulation. These include minimum variance, MUSIC, and maximum entropy. A new maximum entropy spectral estimator is derived using constraints on the modal powers or the expected-square projections of the data onto the eigenvectors of the data covariance matrix. Formulation is derived to allow incorporation of uncertainty into the modal power constraints and the signal versus noise subspace separation. The resulting estimators have forms which incorporate all other modern estimators including maximum entropy and minimum norm. The new estimators allow further development when various a priori information is used in the constraints. Comparison of one version of the new maximum entropy estimator with minimum norm verifies the greater probability or resolution of minimum norm but indicates in some instances the value of the incorporated uncertainties; the value shows up in one case in mean-squared error in the estimation of the frequencies of two sinusoids and in another case involving rank uncertainty wherein the proposed estimator is seen to be significantly more robust. Another version uses complex constraints and reduces to conventional maximum entropy or minimum norm under certain conditions.