Constrained Newton Algorithm for Maximum Likelihood Modeling of Sums of Exponentials in Noise.

摘要

The problem is the estimation of stepped sine response parameters for a system excited near a resonance. A new Newton method is investigated in minimizing a variable projection functional which arises in the modeling of sums of exponentials in noise. We derive the Hessian matrix for the general variable projection functional, and implement a Newton algorithm which constrains the signal model to include poles at the excitation frequency and at DC. This algorithm achieves maximum likelihood performance, and offers computational advantage when the number of data points is moderate to large or when the model order is small.