A constrained Newton algorithm for maximum likelihood modeling of sums of exponentials, in noise

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