Order Estimation of Superimposed Nonlinear Complex Cisoid Model Using Adaptively Penalizing Likelihood Rule: Consistency Results

Abstract

Recently a novel approach of model order selection based on penalizing adaptively the likelihood (PAL) function was introduced in [1]. In this paper, we use the PAL method for order estimation of complex valued nonlinear exponential (cisoid) model and study its asymptotic statistical properties. We investigate the asymptotic statistical properties for the 1-dimensional cisoid model under the assumption of circularly symmetric gaussian error distribution and establish that the PAL estimator is consistent. We also present simulation examples to compare the performance of PAL rule with the commonly used information criteria based rules.