# Fingerprinting Acoustic Localization Indoor Based on Cluster Analysis and Iterative Interpolation
## 1 Introduction  
With the development of signal processing technology and artificial intelligence technology, voice interaction has been gaining extensive attention in the smart device field [1; 2; 3]. Nowadays, the autonomous robot, as the representative of intelligent equipments, is expected to interact with people in a human-like way [4], and voice interaction can effectively improve its intelligence level. During human-robot interaction (HRI) process, acoustic localization technology can provide necessary reference for robot's pose adjustment to enhance the HRI reliability [5; 6]. In recent years, great advancement of theory and application has been made in acoustic localization field. Most existing acoustic localization methods are parametric positioning methods, which are based on the space geometrical propagation models of acoustical signal [6; 7; 8; 9; 10; 11]. Usually, these models are simplified with the assumptions of the sound source and the transmission channel listed as follow:  
1. The sound source is a particle without size and shape. 2. The signal propagates in homogeneous space. 3. The sound signal is omnidirectional. The geometry model acoustic localization methods can achieve acceptable results outdoors, where the actual signal propagation model is similar to the ideal assumptions mentioned above. However, for indoor circumstances, the signal propagation model may be altered by the multipath effect, shadowing effect, fading effect, and delay distortion from walls, floors, furniture, or ceilings [12; 13]. Meanwhile, it is difficult to provide compensation for model distortion analytically [14; 15]. Different from the acoustic localization methods based on geometry model, the fingerprinting acoustic localization method simply adopted in our previous work [16], as a nonparametric location approach, can effectively accomplish sound positioning task according to the idea of environment perception. Compared with the precondition of the parametric localization method mentioned above, avoiding dramatic environment changes in target area, as the necessary requirement of the fingerprinting localization method, is easier in the practical application [17; 18]. Many studies indicate that the positioning accuracy of non-parametric positioning method largely depends on the sampling density [19; 20]. Therefore, for high resolution positioning indoor, considerable amount of sampling work for the database construction is needed in the offline phase. Additionally, during the online phase, the involved algorithms need considerable number of data, and large amounts of memory and computation resources to carry out the target position estimation in real time. Interpolation is a mathematical tool to estimate the value of a function at a certain point using available values at other arguments. Interpolation methods for scattered data are widely implemented in mathematical, industrial and manufacturing applications. Radial basis function (RBF) [21], Linear [22], Inverse Distance Weighting (IDW) [23], and kriging [24] are well-known interpolation methods for positioning database expansion. Even though the numerous methods are effective to reduce sampling task quantity under the premise of ensuring the positioning accuracy [25], there are still many problems in the existing interpolation methods to be solved. In our previous work [26], the interpolation methods were executed in global interpolation way, which resulted in the rapid expansion of virtual RPs quantity and increase the calculation amount for RP matching [27]. Meanwhile, the conventional interpolation methods usually rely on the experience of the implementer and cannot accurately reckon the quantity of virtual RPs needed. In this paper, we propose an iterative interpolation method to refine the interpolation scope and, at the same time, the interpolation process can be monitored to avoid unnecessary virtual RPs.