Minimum cross entropy spectral estimation using nonlinear optimization

The minimum cross entropy method (MCEM) is a spectral estimation technique using nonlinear optimization. It has had success in estimating spectra when only a few autocorrelation lags are known. MCEM uses the cross entropy equation, an initial guess for the spectra, and the Lagrange multiplier technique. An implementation of MCEM using Levenberg-Marquardt optimization is compared to one using Newton-Raphson root-finding as well as to Burg´s maximum entropy. The Burg method resolved the spectra more than any of the other techniques; however, when a phase shift was introduced, the Burg method produced a biased estimate. Since the phase is not always a known quantity, this can be a serious problem. Because the prior estimate in the MCEM technique has such a strong effect in shaping the estimate, it should be used with care. Finally, the difference between the MCEM spectra obtained using Levenberg-Marquardt and those obtained using Newton-Raphson indicates that the algorithm used to find the spectra is as important as the equation used