  The use of Kalman filtering, as well as its nonlinear extensions, for the
estimation of system variables and parameters has played a pivotal role in many
fields of scientific inquiry where observations of the system are restricted to
a subset of variables. However in the case of censored observations, where
measurements of the system beyond a certain detection point are impossible, the
estimation problem is complicated. Without appropriate consideration, censored
observations can lead to inaccurate estimates. Motivated by the work of [1], we
develop a modified version of the extended Kalman filter to handle the case of
censored observations in nonlinear systems. We validate this methodology in a
simple oscillator system first, showing its ability to accurately reconstruct
state variables and track system parameters when observations are censored.
Finally, we utilize the nonlinear censored filter to analyze censored datasets
from patients with hepatitis C and human immunodeficiency virus.
