# Combination of Robust Algorithm and Head-Tracking for a Feedforward Active Headrest
## 1 Introduction  
Active noise control (ANC) systems can effectively suppress noise at low frequencies by generating anti-noise with the same amplitude but opposite phase of the undesired noise. It has been widely used in many applications, such as headsets, trains, and cars [1; 2; 3; 4; 5]. However, it is difficult to control noise in large areas due to the complexity of the ANC system. Therefore, local ANC is proposed to control the noise in the proximity of an individual's ears. Active headrest is a popular application of local ANC and has been studied by many researchers [6; 7].  
The concept of an active headrest was proposed in 1953 by [PERSON] and [PERSON] [8]. Then, this method became famous when [PERSON] and his group built an active headrest prototype system based on feedback ANC algorithm and \(H_{2}/\mathrm{H}\mathfrak{o}\) feedback ANC algorithm, and analyzed its noise control performance in the 1990s [9; 10]. Using this system, the noise was controlled at an individual's ears, where error microphones were inconveniently positioned. Therefore, several remote microphone techniques (RMTs) [11] and virtual microphone arrangements (VMAs) [12] have been proposed to control the noise at a remote location [13; 14]. [PERSON] et al. applied the VMA algorithm to an active headrest system to control the noise at human ears in a prototype of a sleeping car [4], and achieved 16 dB attenuation for band-limited noise (100-300 Hz). However, the noise control performance of theactive headrest system with RMTs or VMAs degrades with head movements and head rotations [13]. To accommodate the condition of the head movement, [PERSON] et al. optimized the secondary path model for active headrest to improve noise control with min-max optimization when controlling the tonal noise [15]. [PERSON] et al. proposed an active headrest to control low-frequency noise with a head-tracking system in which Microsoft Kinect (Microsoft, Washington, DC, USA), was applied [16; 17]. However, user privacy issues need to be considered in practical applications for the public, because a camera on the Microsoft Kinect is always open to track the position of the passengers' heads. In addition, noise control performance degrades when the head rotates with these techniques. [PERSON] et al. designed a hat mounted with microphones to track the position of the ears and then control the tonal noise, even when the head was rotated [18; 19]. However, this system is not practical in some applications because a human cannot always wear a hat implemented with microphones.  
All these above-stated studies depend on adaptive filters, and error microphones are needed when controlling the noise. [PERSON] proposed a robust active headrest in which the control performance does not degrade with head rotations based on the optimal filter, and error microphones are not needed after the optimal filter is obtained if the frequency character of primary noise does not vary with time [20]. However, the performance degrades when the head moves.  
In this paper, to solve the aforementioned problems, a combination of a robust algorithm and head-tracking for a feedforward active headrest applied to a model of a sleeper on a high-speed train is introduced to reduce broadband noise. Control performance degradation issues with head rotations and movements when controlling broadband noise are solved. The remainder of the paper is structured as follows. Section 2 describes the design of the optimal filter coefficients with traditional algorithm of the active headrest. Section 3 presents the proposed combination of robust algorithm and head-tracking for an active headrest. Section 4 presents a series of experiments. Results show that the proposed active headrest system could effectively control broadband noise up to 700 Hz independent of head rotations or movements. Section 5 concludes the paper.