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. The formulation incorporates uncertainty in 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 a priori information is used in the constraints. Comparison of one version of the estimator with the minimum norm verifies the greater probability of resolution of the minimum norm but indicates in some instances the value of the incorporated uncertainties. Another version uses complex constraints and reduces to conventional maximum entropy or minimum norm under certain conditions