In this paper, we consider a deterministic parameter identification problem
for a nonlinear control system subject to disturbances and with output mea
sured by a sensor with fast dynamics. We study the effect of neglecting sen
sor dynamics on the set of parameter values that are consistent with the me
asurements. We show that when neglecting dynamics we must significantly mod
ify the corresponding static model of the sensor in order to obtain a set o
f parameter values that contains the true value and is consistent with the
measurements. We describe a correct model of the static sensor which is in
a sense minimal.