In this paper, we consider a deterministic parameter identification problem for a nonlinear control system subject to disturbances and with output measured by a sensor with fast dynamics. We study the effect of neglecting sensor dynamics on the set of parameter values that are consistent with the measurements. We show that when neglecting dynamics we must significantly modify the corresponding static model of the sensor in order to obtain a set of 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.