# Research on the Robustness of Active Headrest with Virtual Microphones to Human Head Rotation
## 1 Introduction  
The active headrest is a local active control system that creates a quiet zone around the human ear through secondary sources and error microphones near the human head [1]. The \"electronic sound absorber\" proposed by [PERSON] and [PERSON] can be regarded as a prototype for an active headrest, which uses analogue circuits to adjust the output of a loudspeaker to reduce the noise at a microphone or absorb acoustic energy [1]. Since the 1980s, active headrest have been widely studied due to their potential applications in vehicles, factories, residential houses, etc. [2; 3; 4]. One of the main criteria for evaluating the performance of an active headrest is the size of the quiet zone it generates, which has proven to be very limited. For example, the 10 dB zone of quiet created in a free diffuse sound field when using a remote secondary source seems to be a sphere with a diameter of about one-tenth of a wavelength [5]. When the cancellation point is in the near field of a piston secondary source, the 10 dB zone of quiet forms a spherical shell with a diameter of no more than one-tenth of a wavelength around the secondary source at low frequencies, and becomes a sphere with a diameter of about one-tenth of a wavelength at high frequencies [6; 7]. To obtain higher noise reduction, error microphones should be placed as close as possible to human ears, which will interfere with the movement of the human head. Therefore, a virtual sensing technique has been applied to the active headrest to predict and control the sound pressure at human ears by placing physical microphones away from the human head, which is equivalent to placing a virtual microphone at the human ear and projecting the active quiet zone around it [8]. There are various techniques to predict acoustic signals at the human ear, such as the virtualmicrophone arrangement (VMA) [8], the remote microphone technique (RMT) [9; 10], the difference prediction approach [11] and the Kalman filter approach [12]. In practice, the primary sound field and plant responses change as the head moves, leading to the degradation of the performance for the active headrest using virtual sensing techniques [9]. At present, there are two main methods to solve this problem, a moving virtual microphone technique that creates moving quiet zones [9; 13] and a robustness optimization method [14]. For the former method, plant models and observation filters for different head positions are measured and stored in advance, where the observation filters are derived from the transfer functions of remote physical microphones and the virtual microphone in the primary sound field. A head tracking system then monitors the head position and updates the control filters using prestored models and filters corresponding to the head position, achieving a quiet zone that follows the movement of the head [9]. Head tracking technologies based on visual localization and infrared localization have been applied to active headsets [9; 15], and it has been shown that such methods can achieve good noise reduction performance as the human head moves to different positions. However, these methods suffer from high complexity and cost, due to an additional head tracking system and the considerable storage space. By optimizing the plant models, the latter method can improve the noise reduction performance of the system when the head deviates from the original position. [PERSON] et al. used this method to optimize the active headrest system, extending the 10 dB quiet zone at 250 Hz by 4-6 cm in the direction of lateral head movement [14]. However, other kinds of human head movement have not been considered. The performance improvement of this method is less than the former, but the system is less complex and easier to implement. Most previous research has considered head translation [9; 13; 14], while few have addressed head rotation [15]. To reduce the degradation of noise control performance when the head rotates, [PERSON] et al.