# Measurement of Head-Related Transfer Functions: A Review
## 5 Single-Loudspeaker-Based Fast HRTF Measurement Methods  
Since only one loudspeaker is present, the step-wise mechanism can take a lot of time for measuring high-density HRTF datasets. This measurement mechanism is generally applied to measure HRTFs of dummy heads if the measurement time is not a critical problem. In order to accelerate the measurement process, the continuous mechanism is considered. As described in Section 4.2, the methods proposed in [80; 140; 160] are able to be used for continuously capturing 1D HRTFs (usually on the azimuth plane) either with a rotating subject (setup \(\rm S_{E}\) in Figure 9) or a rotating loudspeaker (setup \(\rm S_{G}\) in Figure 9) by using adaptive filtering algorithms [80] or conventional deconvolution approaches [140; 160]. To obtain HRTFs on both the azimuth and elevation planes (2D HRTFs), the 1D HRTF measurement process should be repeated with different loudspeaker positions (elevation angles) until all desired measurement points are covered [140]. This measurement mechanism can be regarded as a semi-continuous mechanism, since HRTFs are continuously measured only on the horizontal plane. Some researchers proposed a measurement system to continuously estimate 2D individual HRTFs by actively performing head movements [141; 165; 166; 167; 168; 169]. The setup \(\rm S_{I}\) in Figure 9 can be regarded as an example hardware configuration for the continuous measurement of 2D HRTFs. A loudspeaker is positioned in front of a subject, who sits on a chair and is equipped with a pair of in-ear microphones. In addition, a head tracker device (inertial sensor) is placed on the subject's head with a headband. During the measurement, the excitation signal (white noises or perfect sweeps) is played back via the loudspeaker and the subject is asked to rotate the head to cover different measurement directions. The acoustic signals (\(y(n)\)) and the orientation data (\(\varphi_{n},\theta_{n}\)) are recorded by in-ear microphones and the head tracker device, respectively. The adaptation of HRIRs can be performed either offline [142; 167; 168] or in real time [120; 169] with the NLMS algorithm:  
\[ \begin{split} e(n)&=y(n)-\mathbf{h}_{\rm est}^{T}( \varphi_{n},\theta_{n})\;\mathbf{x}(n),\\ \mathbf{h}_{\rm est}(\varphi_{n+1},\theta_{n+1})&= \mathbf{h}_{\rm est}(\varphi_{n},\theta_{n})+\mu\;\frac{\mathbf{x}(n)}{|| \mathbf{x}(n)||_{2}^{2}+\epsilon}\;e(n).\end{split}  \tag{26}\]  
It is possible that some measurement points are revisited many times when performing head movements. Hence, [PERSON] et al. [165] optimized the NLMS method to separately adapt the HRIRs at new and already measured points to speed up the convergence speed of the adaptation process. Besides the use of adaptive filtering algorithms, classic deconvolution methods combined with periodic excitation signals can also be used to measure HRIRs [140; 160; 170]. [PERSON] and [PERSON] [142] used a video monitor to display the head movement pattern, visited and unvisited measurement positions to prompt test persons to cover desired measurement directions (see \(\rm S_{I}\) in Figure 9). However, subjects can not constantly see the information when performing head movements (intermittent feedback [168]). To solve this issue, some researchers developed HRTF measurement systems based on VR/AR/MR HMDs (see \(\rm S_{I}\) and \(\rm S_{K}\) in Figure 9) that allow subjects to constantly see the information provided by HMDs during HRTF measurements (concurrent feedback [168]) [120; 166; 168; 169]. In addition, the inertial sensors integrated in the VR/AR/MR headsets can be used to record head orientation data. Objective and subjective evaluation results showed that the HRTFs measured with these dynamic measurement systems are comparable to those measured with conventional static systems [167].