# Measurement of Head-Related Transfer Functions: A Review
## 2 Principle of HRTF Measurements
### Microphone Position and In-Ear Microphones  
The HRTF measurement (\"direct measurement method\") requires a pair of miniature microphones to capture audio signals in the ear canals. However, the measurement results depend on the microphone positions, as the sound pressure changes along the ear canal [45; 90; 91; 92; 93]. The choice of the microphone position for recording sound pressures in the ear canal varies in different studies, e.g., at the entrance of the ear canal [94; 95; 96], \(2\,\mathrm{mm}\) inside the ear canal [45], \(5\)-\(10\,\mathrm{mm}\) deep to the entrance of the ear canal [97], close to the eardrum (\(1\)-\(3\,\mathrm{mm}\) from the eardrum) [90; 98; 99], etc. Those measurement results are difficult to compare due to the non-uniform distribution of sound pressures in the ear canal. It is clear that almost all localization properties including the ear canal resonance can be taken into account when measuring the sound pressure near the eardrum. However, inserting the miniature microphones into the ear canal is unpleasant and may harm subjects with an incorrect operation. Alternatively, [PERSON] et al. [100] proposed a method to estimate the HRTF spectra at the eardrum with the pressure-velocity (PU) measurement at the ear canal entrance. Several studies have investigated the need to record the excitation signal near the eardrum for the HRTF measurement [101; 102; 1]. [PERSON] [1] modeled the sound transmission within the ear canal with a one-dimensional transmission line, which was valid up to \(10\,\mathrm{kHz}\) by approximating the ear canal as a tube with a diameter of \(8\,\mathrm{mm}\), and considering it as a direction-independent part. Only the acoustic transfer path from a sound source in the free-field to the ear canal entrance was direction-dependent. [PERSON] and [PERSON] [101] verified this concept with psychoacoustic experiments, and refined the entire acoustic transfer path from an acoustic point source to the eardrum into three parts: one direction-dependent part, i.e., from the sound source to the blocked entrance of the ear canal, and two direction-independent parts, i.e., the transmission from the blocked to open entrance of the ear canal, and the transmission along the ear canal. Thus, the localization cues  
Figure 7: Block diagram for identifying an unknown discrete system with adaptive filtering approaches in the time domain [56]. contained in HRTFs can be well measured by placing the microphones at blocked entrances of the ear canals. [PERSON] et al. [102] further measured and evaluated HRTFs from various directions for blocked and open ear conditions, and the result was in agreement with the findings in [1,101], i.e., the direction-dependent characteristics of sound sources can be well captured by placing the microphones at entrances of blocked ears. The \"blocked ear technique\" is therefore generally applied in HRTF measurements for human subjects because of its convenience compared to the measurement in the ear canal. There are many commercially available in-ear microphones for HRTF measurements and binaural recordings at the ear canal entrance or in the ear canal, e.g., B & K 4101 (Bruel & Kjaer, Naerum, Denmark), DPA 4060 (DPA Microphones A/S, Alleroed, Denmark), MS-TFB-2 (The Sound Professionals, Hainesport, NJ, USA), MM-BSM-11 (Microphone Madness, Inc., Palm Coast, FL, USA), Soundman OKM II (Soundman e.K., Woltersdorf, Germany), MKE 2002 (Sennheiser, Wedemark, Germany), B & K 4182 (Bruel & Kjaer, Naerum, Denmark), ER-7C Probe Microphone (Etymotic Research, Inc., Elk Grove Village, IL, USA). In addition, some researchers prefer to design their own miniature microphones by embedding microphone capsules (e.g., Knowles FG series, Sennheiser KE3/KE4) in custom-made ear models or earplug [103, 104]. Some studies measured HRTFs with microphones placed in various hearing aids [64,105, 106], and the measurement results are useful for hearing instrument research, evaluating spectral distortions caused by hearing aids, and generating virtual sounds for hearing aid users, etc.