Model order selection for summation models

In this paper, we propose two model order selection procedures for a class of summation models. We exploit the special structure in the class of candidate models to provide a data dependent upper bound on the model order. The proposed upper bound is also a consistent estimator of model order. Further, MDL, AIC and MAP when accompanied with the data dependent prior exhibit an improved rate of convergence to their asymptotic behaviour and an improved detection rate for finite SNR and finite data lengths. Asymptotic properties of the maximum likelihood parameters are used to derive the proposed methods. All simulations use the complex undamped exponential model.