Identification and tracking of time-variant systems is relevant in many applications, such as acoustic echo cancellation, active noise control, or in acoustics, e.g., for fast acquisition of head-related transfer functions (HRTFs) via dynamic measurements. Unlike in many other applications, for acoustic measurements the excitation signals can be chosen and optimized for the specific measurement scenario. So far, for this optimization the impact of the group delay on the tracking behavior has not been explicitly considered as a design criterion. In this paper, the influence of time-variance in combination with the temporal properties (envelope, group delay) of the excitation signal is addressed. In simulations and in dynamic binaural room impulse response measurements it is shown how the group delay of the excitation sequence affects the progression in tracking.