Robust One-Step Estimation of Impulsive Time Series

Abstract: The paper deals with the estimation of a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, i.e. an impulsive time series. This modeling concept arises in, e.g., endocrinology when episodic hormone secretion events and elimination rates are simultaneously estimated from sampled hormone concentration measurements. The pulsatile secretion is modeled with a train of Dirac impulses constituting the input to a linear plant, which represents stimulated hormone secretion and elimination. A previously developed one-step estimation algorithm effectively resolves the trade-off between data fit and impulsive input sparsity. The present work improves the algorithm so that it requires less manual tuning and produces more accurate results through the use of an information criterion. It is also extended to handle outliers and unknown basal levels that are commonly recognized issues in biomedical data. The algorithm performance is evaluated both theoretically and experimentally on synthetic and clinical data.