# A Review on Head-Related Transfer Function Generation for Spatial Audio
## 3 Measurement and Estimation  
Binaural mannequins with standard dimensions can be employed for the measurement of HRTFs [40]. In the literature, several HRTF databases created by head and torso (HAT) simulators can be found [41]. These standard measurements help for the investigation of important aspects, such as the spatial resolution [42; 43] and the listener distance from the loudspeaker [44; 45]. However, standardisation does not catch individual differences between the HRTFs. The use of in-ear microphones placed in the ear canal of real subjects can solve this problem and allows to obtain individual (or personalised) HRTFs [18; 19; 20; 21; 46; 47; 48]. Two methods exist for HRTF measurement: deconvolution approaches and systems based on adaptive filters [49]. The most used methods are the ones based on deconvolution, and they can be categorised depending on the type of signal given as input, i.e., pseudo random sequences [47; 50; 51; 52; 53; 54; 55; 56; 57; 58] or sweep signals [59; 60; 61; 62; 63]. Pseudo random sequences embrace maximum length sequences (MLSs) [51; 52; 53; 54; 55], inverse repeated sequences (IRSs) [56; 57], and Golay codes [58]. The sweep signals can consider multiple exponential/logarithmic sweep [64; 65] and multi-sine approaches [66]. In [67], a comparison of the most used deconvolution methods can be found, and in [68], the MLS method is compared with the sweep. Regarding the adaptive filtering approach, it is employed in HRTFs measurements in [69] for the first time, and then it is also applied in [45; 70]. Usually, the normalised least mean square (NLMS) algorithm is applied for adapting the filter coefficients [71]. An accurate review of HRTFs measurement methods is reported in [49]. Various problems can occur and influence the measurement of HRTFs. Examples are the nonlinear distortions introduced by the acquisition system, noise produced by the environment, reflections, the type of sound source, and the temperature alteration [49; 72]. The environment-based problems can be solved by using an anechoic chamber, and the nonlinear distortions can be prevented by applying the correct stimuli and technique [73; 74; 75]. Perfect periodic sequences (PPSs) and orthogonal periodic sequences (OPSs) are employed for measuring the HRTFs in [76] considering a real car environment, demonstrating robustness against non-linearities. PPSs can be applied for identifying Legendre non-linear (LN) filters [74; 77] or Wiener non-linear (WN) filters [78; 79], while the OPSs can determine functional link polynomial (FLiP) filters that include LN and WN filters [80; 81; 82]. The data acquisition process traditionally requires specialised equipment and controlled environments, which can limit its practical applicability. To address these challenges, in [83], the authors investigate the possibility of measuring the HRTF in a simplified experimental setup with a single sound source and a tracking system to acquire information about the head position and orientation in real-time. In this setup, the subject moves their head freely by sampling different directions while the source emits, in a non-anechoic environment, sequences of exponential frequency-modulated sweeps alternated with silences. Similarly, in [66], the authors propose a novel method for efficiently generating individualised HRTFs, in which a multisine signal is used to collect acoustic data as the listener moves freely, with a motion capture system tracking the head movements to ensure accurate positional data. This setup allows the acquisition of noisy, but plentiful, HRTF samples. Further details regarding this approach are provided in Section 6. As an alternative approach to address the challenges associated with specialised equipment and controlled environments, the authors of [84] introduce a method for deriving personalised HRTFs using binaural recordings and head tracking data from consumer devices like earbuds with microphones and inertial measurement units (IMUs).