  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.
