  Statistical modeling of animal movement is of critical importance. The
continuous trajectory of an animal's movements is only observed at discrete,
often irregularly spaced time points. Most existing models cannot handle the
unequal sampling interval naturally and/or do not allow inactivity periods such
as resting or sleeping. The recently proposed moving-resting (MR) model is a
Brownian motion governed by a telegraph process, which allows periods of
inactivity in one state of the telegraph process. The MR model shows promise in
modeling the movements of predators with long inactive periods such as many
felids, but the lack of accommodation of measurement errors seriously prohibits
its application in practice. Here we incorporate measurement errors in the MR
model and derive basic properties of the model. Inferences are based on a
composite likelihood using the Markov property of the chain composed by every
other observed increments. The performance of the method is validated in finite
sample simulation studies. Application to the movement data of a mountain lion
in Wyoming illustrates the utility of the method.
