## 2 Materials and Methods
### System Latency Measurement  
Latency is regarded as one of the critical concerns in virtual audio systems [29]. To ensure that accurate results are obtained from the designed experiments, it was necessary for the system latency of the binaural audio system to be sufficiently low. One of the key factors was the use of a high-quality wired head tracker, as the performance of the head tracker itself has a considerable influence on accuracy, precision, and low latency in binaural audio systems [30]. Any experiment that utilizes binaural audio systems requires the latency of the system to be as low as possible, optimally below 50 ms. Although a theoretical latency value could be calculated, a more precise experimental approach was employed so that the actual value could be determined.  
The binaural audio system was mounted on a dummy head, along with a simple electrical circuit for light detection consisting of a 9V battery, a light-emitting diode, and a high-quality photoresistor. A specialized SOFA file was implemented in the binaural audio system, where a Dirac impulse with amplitude 0.5 was set up for the frontal HRTF directions (within 6\({}^{\circ}\) of great angle error), while amplitude 0 was set up for all other directions. A looping 10-kHz sinusoidal tone was played into the binaural system, with the dummy head positioned in the frontal direction (i.e., where the 10-kHz tone was audible).  
A laser pointer was directed toward the photoresistor, which decreased the element's resistance, causing the voltage on the photoresistor to rise. With the sudden rotation of the dummy head, the laser beam moved away from the photoresistor, leading to a drop in voltage. At the same time, the head-tracker of the binaural system detected movement of the dummy head, causing the system to change azimuth and change HRTF to amplitude 0 (i.e., the sound was no longer audible). The latency was subsequently calculated as the time difference between the exact moment the voltage began to rise on the photoresistor and the moment the audio output of the binaural system switched from audible to inaudible.  
A two-input sound card was utilized to record both the audio output of the binaural system and the voltage change on the photoresistor. Modern external sound cards typically have a capacitor in series with the input to block DC voltages from entering the sound card. Therefore, the required voltage drop could be observed as a starting point for the change in the AC recorded signal. To maximize the voltage drop effect, the measurement was conducted in a controlled environment devoid of external light sources.  
The latency of the individual HRTF selection setup was measured to be 35 ms, which was deemed sufficiently low for the progression of the experiment described in Section 2.3.  
Ten latency measurements were conducted on the binaural system setup designed to test localization accuracy. The obtained latency values spanned from 69 to 78 ms, with an average result of 73 ms. Given that the time interval between 2 successive knocks of the sound stimulus was 283 ms and that the latency was nearly 4 times shorter than the mentioned interval, the obtained latency was deemed sufficiently low for the progression of the localization accuracy experiment.