Minimum-free-energy method of spectral estimation: autocorrelation-sequence approach

Abstract

A new method of parametric spectral estimation, which is called minimum-free-energy (MFE) estimation, is introduced. The MFE method produces a generic theoretic estimation model that is particularly relevant to signal-analysis problems that suffer from incomplete and/or noisy data. In the general MFE formulation, the objective function is defined as a linear combination of a mean-square-error-energy expression and a signal entropy expression. This objective function form is analogous to a free-energy function in statistical thermodynamics. The negative coefficient of the entropy term is represented by an effective signal-processing temperature that drives noise-induced fluctuations in the statistical model. The model parameters that characterize the spectrum are determined commensurate with a minimum of the objective function. The mathematical details and solution methods are developed for a specific embodiment of the MFE method, called the MFE-ACS method, in which the error energy is defined as the window-weighted sum of the absolute square of the difference between the initial and final estimated values of the autocorrelation sequence. The order of the autocorrelation sequence used corresponds to the parametric model order for the spectral estimation procedure. Simulations for a variety of narrow-band and broadband test signals and combinations thereof are presented. These simulations are performed for a variety of signal-to-noise-ratio (SNR) scenarios. The MFE algorithms have a broad application domain because they are not restricted to narrow-band sources as are the signal–noise-subspace algorithms. The MFE-ACS algorithm is shown to compare quite favorably with the signal-subspace Tufts–Kumaresan noise-reduced modified-covariance algorithm for closely separated narrow-band sources in the low-SNR regime (∼10 dB).