## 1 Introduction  
Three-dimensional spatial sound localization includes directional (i.e., azimuth and elevation) and distance localization. Lateral localization mainly depends on interaural differences, such as the interaural time difference (ITD) and the interaural sound level difference (ILD), caused by different transmission paths from sound sources to the left/right ear. Vertical localization, on the other hand, mainly relies on the change in the magnitude spectrum when sound waves propagate to the ears, that is, the spectral cue. Head-related transfer functions (HRTFs), defined as the system transfer function of the sound filter from a sound source to human eardrums in the frequency domain, include the aforementioned ITD, ILD, and spectral characteristics. One major application of binaural HRTFs is the creation of a virtual auditory display (VAD). A VAD can not only be used as an experimental platform in research of binaural hearing, but also has various applications in such fields as virtual reality, mobile communication, and multimedia [1; 2; 3]. From a physical point of view, HRTFs are closely related to human physiological structures. For example, different head sizes result in different levels of ITD,and different shapes and sizes of pinnae lead to different spectral characteristics. Therefore, HRTFs are individual-dependent, and each specific individual owns a specific set of HRTFs (individualized HRTFs). Previous literatures have reported that the use of non-individualized HRTFs in VADs, especially in the case of a static situation, often leads to a series of problems, such as increased front-back confusion and inside-of-head localization [4]. Therefore, to guarantee the authenticity of VADs, it is necessary to use individualized HRTFs for signal processing. Acoustic measurement and numerical simulation are two primary approaches to obtain individualized HRTFs accurately [5; 6; 7; 8; 9; 10; 11]. However, acoustic measurement is time-consuming and requires a special apparatus; the calculation suffers from high requirements for computer performance and the scanning of physiological structures. Therefore, these two methods cannot support practical applications. In order to solve conflicts between the need for and acquisition of individualized HRTFs, researchers have proposed a method called the customization of individualized HRTFs. Customization (i.e., approximate acquisition) refers to simplifying the process of acquisition of individualized HRTFs as much as possible, while preserving individual auditory characteristics. As VADs have wide application, the customization of individualized HRTFs has attracted widespread attention. Because HRTFs are closely related to individual physiological structures, HRTF customization based on anthropometric parameters is natural. [PERSON] et al. [12] suggested that the similarity of anthropometric parameters between individuals corresponded to the similarity of their HRTFs. So, it is possible to select best-matching HRTFs from an HRTF baseline database according to the deviation in pinnae parameters. Then, subsequent studies on the optimization of matching parameters were carried out [13; 14; 15; 16; 17; 18; 19; 20; 21]. [PERSON] et al. [13] explored the statistical relationships between HRTF characteristic vectors and anthropometric parameters. [PERSON] and [PERSON] [14] studied the similarity between anthropometric parameters, and proposed an improved database-matching method using four pinna-related anthropometric parameters. [PERSON] et al. [15] first estimated the frequencies of the two lowest spectral notches (N1 and N2) by a listener's pinnae anthropometry, and then selected the best-matching HRTFs, of which N1 and N2 were the closest to the estimates. [PERSON] pointed out that the differences in anthropometric dimensions between individuals would cause the overall translation of HRTFs along with the frequency axis, and thus proposed a frequency-scaling method for customizing individualized HRTFs [16; 17].