A combined order selection and parameter estimation algorithm for undamped exponentials

We propose an approximate maximum likelihood parameter estimation algorithm, combined with a model order estimator for superimposed undamped exponentials in noise. The algorithm combines the robustness of Fourier-based estimators and the high-resolution capabilities of parametric methods. We use a combination of a Wald (1945) statistic and a MAP test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders. Experiments using simulated data and synthetic radar data demonstrate improved performance over MDL, MAP, and AIC in places of practical interest.