  The advancement of in-vehicle sensors provides abundant datasets to estimate
parameters of car-following models that describe driver behaviors. The question
of parameter identifiability of such models (i.e., whether it is possible to
infer its unknown parameters from the experimental data) is a central system
analysis question, and yet still remains open. This article presents both
structural and practical parameter identifiability analysis on four common
car-following models: (i) the constant-time headway relative-velocity (CTH-RV)
model, (ii) the optimal velocity model (OV), (iii) the follow-the-leader model
(FTL) and (iv) the intelligent driver model (IDM). The structural
identifiability analysis is carried out using a differential geometry approach,
which confirms that, in theory, all of the tested car-following systems are
structurally locally identifiable, i.e., the parameters can be uniquely
inferred under almost all initial condition and admissible inputs by observing
the space gap alone. In a practical setting, we propose an optimization-based
numerical direct test to determine parameter identifiability given a specific
experimental setup (the specific initial conditions and input are known). The
direct test conclusively finds distinct parameters under which the CTH-RV and
FTL are not identifiable under the given initial condition and input
trajectory.
