Adjustable Structure for Feedback Active Headrest System Using the Virtual Microphone Method

Abstract

Active headrest is an essential application for active noise control, capable of reducing low-frequency disturbance around an error microphone. However, in most cases, attaching microphones to ears is not feasible and noise attenuation performance is vulnerable to plant response variations. This paper presents a multichannel feedback active headrest system combined with the virtual microphone method and a manually adjustable headrest structure for users. Applying the virtual microphone method can transfer the attenuation target from the distant microphone to the ear. The proposed adjustable headrest structure allows for secondary loudspeakers and the corresponding microphone to be moved as a single unit while maintaining the relative distances between the secondary loudspeakers and microphones constant to ensure that the related plant responses are consistent. Experiments were conducted to validate the performance against multi-sinusoidal machine noise. The results demonstrate the benefits of the proposed structure over conventional structures. Additionally, the applicability of the three commonly used virtual sensing methods (the auxiliary filter method, remote microphone method, and virtual microphone method) in various practical conditions was verified when using the proposed adjustable headrest structure. Furthermore, 10 volunteers were involved in the evaluation, and the robustness of the proposed system for various users was confirmed.

1. Introduction

Owing to the increasing use of industrial machinery such as compressors and engines, noise pollution has become a critical problem affecting human health. Passive noise reduction methods are not only expensive and voluminous also but ineffective for low-frequency (below 500 Hz) noise [1]. Active noise control (ANC), based on the principle of destructive interference, can solve these problems by generating anti-noise with the same amplitude and opposite phase to the primary disturbance [2].

A popular ANC casing is an active headrest [3] in which secondary loudspeakers and error microphones are placed around the headrest to create a zone of quiet (ZoQ) near and around the ear. To extend the zone of high attenuation as well as to increase the reduction ratio, a multichannel system is utilized [4,5]. The strategies employed for multichannel active headrests can be divided into two types: feedforward and feedback systems [2]. Due to the disturbance typically originating from multiple sources, it is infeasible to obtain a time-advanced reference signal for feedforward control in some cases [6]. Thus, feedback controllers have been adopted for active headrests [4,6,7,8]. In the feedback ANC system, the reference signals are estimated from the measured error signals. Through this method, called the internal model control (IMC) [4], significant levels of noise reduction can be achieved, especially for narrowband or periodic disturbances [9].

The filtered-reference normalized least mean square (FxNLMS) algorithm is a common adaptive algorithm used in ANC systems [10,11] and aims to minimize the $l_2$-norm of the error signal vectors. Hence, the error microphone is required to be close enough to the target position because the ZoQ is generated around the microphone [12], even though it is inconvenient to place microphones on the ears. Therefore, virtual sensing (VS) methods have been proposed to solve this dilemma by transferring the ZoQ from the physical error microphones to the targets [13]. The ANC algorithms for the VS methods are divided into two stages. In the first stage, the microphones either are temporarily placed at the target positions to train additional filters that contain information concerning the optimal control filters, also known as the auxiliary filter method (AFM) [14,15], or the observation filters are placed between the physical monitoring microphones and target microphones, also known as the remote microphone method (RMM) [16,17,18]. In the second stage, the temporary microphones are removed. The AFM estimates the disturbances at the targets implicitly from the reference signals with pre-trained additional filters. The RMM estimates the disturbances at the target locations explicitly from the monitoring signals with the pre-modeled observation filters [19]. The virtual microphone method (VMM) is a special form of the RMM [20]. In the case of the VMM, the disturbances at the physical monitoring microphone and the target microphone are assumed to be identical. Therefore, the VMM is slightly affected by variations in the primary source and is suitable for low-frequency signals with long wavelengths only [20].

In practice, head movement is common and may deteriorate the noise attenuation performance [6]. Although a head-tracking device can mitigate this effect [5,17], additional estimation errors may become introduced, and head-mounted ANC systems are also impractical in most real-life applications [21,22]. Moreover, the characteristics of the disturbance signal, the location, and quantity of primary noise may vary. These variations influence the performance of VS methods to varying degrees [19,23]. In addition, all of the aforementioned studies have only been verified to be effective for selected participants. When the targets were switched to various users who have not been measured in advance, their performance was not quantitatively evaluated.

To solve the above problems, this paper presents a multichannel feedback active headrest system in combination with the VMM and a headrest structure that can be manually adjusted by the users. The secondary loudspeakers and the corresponding microphone are integrated into a single unit in the proposed headrest structure. The user can freely adapt each unit to maintain the relative distances between the ears and each unit constant. A series of real-time experiments were conducted to demonstrate the attenuation performance of the proposed active headrest system with respect to multi-sinusoidal machine noise. The necessity and superiority of the proposed headrest structure over two conventional structures [4,22] was confirmed using the three VS methods. This validation considered the variations in the distances from the secondary loudspeakers to the ears and the case of head movement as well. Subsequently, comparisons were carried out between the VS methods to deal with primary source variations. In addition, the applicability of the three VS methods when utilizing the proposed adjustable headrest structure was verified through the aforementioned experiments. Furthermore, the robustness of the proposed system in response to user variations was validated by involving 10 volunteers of various statures using comparisons with different structures.

The remainder of this paper proceeds as follows. Section 2 describes the proposed adjustable structure. The adaptive feedback algorithm and the VS methods are briefly analyzed in Section 3. The experimental setup is explained in Section 4. In Section 5, the noise cancellation performance and robustness of the proposed active headrest system are validated through numerous experiments. Finally, Section 6 concludes the paper.

2. Proposed Adjustable Headrest Structure

The 3D design model of the proposed manually adjustable headrest structure for users is shown in Figure 1. In the proposed structure, there are four loudspeakers (Aura, D132803), each with a diameter of 6.35 cm, placed symmetrically in pairs on either side of the head facing the ears to generate a secondary sound field that cancels the disturbances. Two monitoring microphones (B&K, 4189) are mounted approximately 2 cm in front of the loudspeakers on each side and on the same horizontal plane as the ears. Each pair of secondary loudspeakers with the corresponding microphone are installed to form a single unit. Both the left and right sides of the headrest have a removable frame to support two loudspeakers and a microphone, which ensures that each unit can be adjusted by users to the required position. Thus, the relative positions of the secondary loudspeakers to the physical microphones and ears remain constant. Consequently, the proposed headrest structure can maintain the secondary paths (from the secondary loudspeakers to the microphones) and other related plant responses that are approximately invariant. The key differences between the proposed arrangement and those in the previous studies are that this structure guarantees the stability of plant responses while improving comfort and convenience [4,7,21,22].

3. ANC Algorithms for Active Headrest

In this section, a multichannel adaptive feedback algorithm based on the IMC applied to an active headrest is reviewed. The VS methods used for moving the target ZoQ are investigated subsequently. The multichannel ANC systems are formulated with J secondary sources, M physical monitoring error microphones, and V target (virtual) error microphones.

3.1. Adaptive Feedback Algorithm

A block diagram of the typical multichannel feedback FxNLMS algorithm is shown in Figure 2. ${\mathbf{s}}_m\left(n\right)$ and ${\mathbf{s}}_v\left(n\right)$ represent the secondary paths from the secondary loudspeakers to the physical and target microphones, respectively.

In this system, the output signal vector is defined as

$$\mathbf{y}\left(n\right)={\mathbf{w}}^{\mathrm{T}}\left(n\right)\mathbf{x}\left(n\right),$$

(1)

where $\mathbf{y}\left(n\right)={\left[y_1\left(n\right),y_2\left(n\right),\dots ,y_j\left(n\right),\dots ,y_J\left(n\right)\right]}^{\mathrm{T}}.$$y_j\left(n\right)$ indicates the output signal of the jth secondary loudspeaker at the time sample n and ${(·)}^{\mathrm{T}}$ denotes the matrix transpose operator. The control filter matrix is expressed as

$$\mathbf{w}\left(n\right)=\left[\begin{array}{c}{\mathbf{w}}_{11}\left(n\right),{\mathbf{w}}_{12}\left(n\right),...,{\mathbf{w}}_{1J}\left(n\right),{\mathbf{w}}_{21}\left(n\right),...,{\mathbf{w}}_{VJ}\left(n\right)\end{array}\right],$$

(2)

where ${\mathbf{w}}_{vj}\left(n\right)$ is the $\left(L_w\times 1\right)$ coefficient vector of the control filter from the $v\mathrm{th}$ input signal to the $j\mathrm{th}$ output signal.

$$\mathbf{x}\left(n\right)={\left[\begin{array}{c}{\mathbf{x}}_1^{\mathrm{T}}\left(n\right),{\mathbf{x}}_2^{\mathrm{T}}\left(n\right),...,{\mathbf{x}}_v^{\mathrm{T}}\left(n\right),...,{\mathbf{x}}_V^{\mathrm{T}}\left(n\right)\end{array}\right]}^{\mathrm{T}},$$

(3)

is the matrix with the last $L_w\times V$ reference signals and

$${\mathbf{x}}_v\left(n\right)={\left[x_v\left(n\right),x_v(n-1),\dots ,x_v\left(n-L_w+1\right)\right]}^{\mathrm{T}}.$$

(4)

$x_v\left(n\right)$ is synthesized based on the IMC and expressed as

$$x_v\left(n\right)=e_v\left(n\right)-{\widehat{y}}_s\left(n\right),$$

(5)

where $e_v\left(n\right)$ denotes the signal measured by the vth error microphone installed at the desired position and is given by $e_v\left(n\right)=d_v\left(n\right)+y_s\left(n\right)$. $d_v\left(n\right)$ represents the disturbance signal received by the vth error microphone. $y_s\left(n\right)$ and ${\widehat{y}}_s\left(n\right)$ denote the output signal vector $\mathbf{y}\left(n\right)$ filtered by the actual and estimated secondary paths, respectively.

Utilizing the FxNLMS algorithm, the updated equation for the control filter coefficient vector ${\mathbf{w}}_{vj}\left(n\right)$ can be expressed as

$${\mathbf{w}}_{vj}(n+1)={\mathbf{w}}_{vj}\left(n\right)-\mu \sum _{v=1}^V\frac{{\mathbf{r}}_v\left(n\right)e_v\left(n\right)}{\Vert {\mathbf{r}}_v\left(n\right){\Vert }^2+\beta },$$

(6)

where ${\mathbf{r}}_v\left(n\right)={[r{}_v\left(n\right),r{}_v(n-1),\cdots ,r{}_v(n-L_w+1)]}^{\mathrm{T}}$ is the filtered reference signal vector that is derived from the convolution of the reference signal with the estimated secondary path. $∥·∥$ denotes the $l_2$-norm of the vector. $\mu$ and $\beta$ are the step size and regularization factor, respectively.

3.2. Auxiliary Filter Method

The AFM consists of the tuning stage and control stage, as shown in Figure 3. During the tuning stage, additional filters are trained by modeling the transfer matrix between the reference signals and the monitoring error signals after the control filters converge to the optimum, as shown in Figure 3a. The reference signals are synthesized from the monitoring error signals based on the IMC. The modeled additional filters $\mathbf{g}\left(n\right)$ can be observed as a matrix with $M\times L_{\mathrm{AF}}$ rows and M columns. The additional filter from the $m_x$th reference signal to the mth physical monitoring signal is given by ${\mathbf{g}}_{m_{x}m}\left(n\right)={\left[g_{0,m_{x}m}\left(n\right),g_{1,m_{x}m}\left(n\right),\dots ,g_{L_{\mathrm{AF}}-1,m_{x}m}\left(n\right)\right]}^{\mathrm{T}},$ and the mth residual error signal $e_{\mathrm{T},m}\left(n\right)$ can be described as

$$e_{\mathrm{T},m}\left(n\right)=e_m\left(n\right)+{\mathbf{g}}_{m_{x}m}^{\mathrm{T}}\left(n\right){\mathbf{x}}_{m_x}\left(n\right),$$

(7)

where $e_m\left(n\right)$ denotes the mth physical monitoring error signal. The updated equation for this additional filter vector obtained using the NLMS algorithm [24] is as follows:

$${\mathbf{g}}_{m_{x}m}(n+1)={\mathbf{g}}_{m_{x}m}\left(n\right)-\frac{{\mu }_{\mathrm{AF},\mathrm{T}}{\mathbf{x}}_{m_x}\left(n\right)e_{\mathrm{T},m}\left(n\right)}{{∥{\mathbf{x}}_{m_x}\left(n\right)∥}^2+{\beta }_{\mathrm{AF},\mathrm{T}}},$$

(8)

where ${\mu }_{\mathrm{AF},\mathrm{T}}$ and ${\beta }_{\mathrm{AF},\mathrm{T}}$ denote the step size and the regularization factor of the NLMS algorithm, respectively. During the control stage, pre-trained additional filters are used to approximate the physical monitoring error signals to the estimated values of these signals in the tuning stage. This implies that the disturbances at the virtual microphones are minimized when the mean square of the effective residual error signal $e_{\mathrm{C},\mathrm{m}}\left(n\right)$ is the least [23]. Thus, the cost function can be stated as

$$\mathrm{J}=\min e_{{}_{\mathrm{C},\mathrm{m}}}^2\left(n\right),$$

(9)

where $e_{\mathrm{C},\mathrm{m}}\left(n\right)=e_m\left(n\right)+{\mathbf{g}}_{m_{x}m}^{\mathrm{T}}\left(n\right){\mathbf{x}}_{m_x}\left(n\right).$ The updated equation for the control filter is given by

$${\mathbf{w}}_{\mathrm{AF}}(n+1)={\mathbf{w}}_{\mathrm{AF}}\left(n\right)-{\mu }_{\mathrm{AF},\mathrm{C}}\sum _{m=1}^M\frac{{\mathbf{r}}_m\left(n\right)e_{\mathrm{C},m}\left(n\right)}{\Vert {\mathbf{r}}_m\left(n\right){\Vert }^2+{\beta }_{\mathrm{AF},\mathrm{C}}},$$

(10)

where ${\mu }_{\mathrm{AF},\mathrm{C}}$ and ${\beta }_{\mathrm{AF},\mathrm{C}}$ represent the step size and the regularization factor, respectively.

3.3. Remote Microphone Method

The RMM ensures that the disturbance signals at the virtual error microphones can be evaluated by the primary noise signals at the physical monitoring microphones via the pre-modeled observation filters. A block diagram of the RMM in the tuning and control stages is shown in Figure 4.

In the tuning stage shown in Figure 4a, temporary microphones were placed at the target positions. The disturbance signals measured by the physical monitoring microphones and the target microphones were used to estimate the observation filters and can be expressed as

$${\widehat{\mathbf{O}}}_{mv}={\mathbf{R}}_{d_m{d}_v}{\left({\mathbf{R}}_{d_m{d}_m}+{\beta }_O\mathbf{I}\right)}^{-1}.(m=1,2,...,M;v=1,2,...,V)$$

(11)

where ${\mathbf{R}}_{d_m{d}_v}$ is the cross-power spectral density matrix of ${\mathbf{d}}_m\left(n\right)$ and ${\mathbf{d}}_v\left(n\right)$ and where ${\mathbf{R}}_{d_m{d}_m}$ is the auto-power spectral density matrix of ${\mathbf{d}}_m\left(n\right)$. $\mathbf{I}$ is the identity matrix, and ${\beta }_O$ serves as the regularization factor. ${\mathbf{d}}_v\left(n\right)=[d_v\left(n\right),d_v(n-1),...,d_v(n-L_O+1)]$ and ${\mathbf{d}}_m\left(n\right)=\left[d_m\left(n\right),d_m(n-1),...,d_m(n-L_O+1)\right]$ represent the vectors of the disturbance signals at the $m\mathrm{th}$ physical and $v\mathrm{th}$ virtual error microphones, respectively. $L_O$ is the tap length of the observation filters. In the control stage shown in Figure 4b, the disturbance at the $m\mathrm{th}$ physical monitoring microphone can be calculated as

$${\widehat{d}}_m\left(n\right)=e_m\left(n\right)-{\widehat{\mathbf{s}}}_m\left(n\right)\mathbf{y}\left(n\right),$$

(12)

where $e_m\left(n\right)$ denotes the error signal obtained from the $m\mathrm{th}$ physical microphone. The disturbance signal at the $v\mathrm{th}$ virtual microphone is then evaluated with the pre-trained observation filters and is expressed as

$${\widehat{d}}_v\left(n\right)=\sum _{m=1}^M{\widehat{\mathbf{O}}}_{mv}{\widehat{\mathbf{d}}}_m\left(n\right).$$

(13)

Therefore, the estimated virtual error signal used to update the control filter in Equation (6) can be denoted as

$${\widehat{e}}_v\left(n\right)={\widehat{d}}_v\left(n\right)+{\widehat{\mathbf{s}}}_v\left(n\right)\mathbf{y}\left(n\right).$$

(14)

3.4. Virtual Microphone Method

The only difference between the VMM and the RMM is that the former assumes that the interference at the physical monitoring microphone and the target microphone is the same, viz. $d_m\left(n\right)=d_v\left(n\right)$. Under this assumption, the observation filter matrix can be regarded as an identity matrix in the VMM. Only the secondary paths, from the secondary loudspeakers to the monitoring microphones and to the target microphones, need to be modeled in advance. However, the VMM is appropriate for low-frequency (below 500 Hz) signals [20]. Thus, this assumption is only applicable when the distance between the target microphone and the physical monitoring microphone is significantly smaller than the wavelength of the disturbances.

4. Experimental Setup

Figure 5 shows the active headrest system and the overall schematic setup in a room. The reverberation time of this room is $T_{60}=0.42$ s. Two microphones at the ears of a dummy head (G.R.A.S., KEMAR Head & Torso) were employed as target error microphones. The left-side and right-side support frames in the proposed headrest structure were initially positioned 3 cm away from the left and right ears of the dummy head. The primary disturbance signals originate from machine noise at different speeds. At the first speed, there were three dominant narrowband noise components at 168 Hz, 210 Hz and 252 Hz, and at the second speed, the noise components were at 171 Hz, 228 Hz and 285 Hz. There were two primary loudspeakers placed in front and to the left of the dummy head at a distance of 2.5 m.

The controller was implemented on a digital signal processor (TI, TMS320C6678) platform with a sampling frequency of 8 kHz, the analog to digital converter was MAXIM MAX11049 with 16-bit resolution, and the digital to analog converter was TI DAC7644 with 16-bit resolution. Their conversion times were short enough to meet the low-latency requirements of the ANC.

All algorithms in this study require modeling the secondary paths in advance. Using bandlimited white noise $\le 2$ kHz, the secondary paths were modeled as FIR filters by an adaptive system identification method based on the NLMS algorithm [24].

Table 1. Common measurement conditions in all experiments.

Parameters	Values
Tap length of the estimated secondary paths	512
Tap length of control filters $L_w$	512
Tap length of additional filters $L_{\mathrm{AF}}$	512
Tap length of observation filters $L_O$	512
Step size $\mu$, ${\mu }_{\mathrm{AF},\mathrm{T}}$, ${\mu }_{\mathrm{AF},\mathrm{C}}$	0.001, 0.01, 0.001
Regularization factor $\beta$, ${\beta }_{\mathrm{AF},\mathrm{T}}$, ${\beta }_{\mathrm{AF},\mathrm{C}}$, ${\beta }_O$	${10}^{-6},{10}^{-6},{10}^{-6},{10}^{-8}$

lists the common measurement conditions.

To verify the necessity and superiority of the proposed headrest structure, two more forms of the headrest structure were compared. The first comparative structure typically incorporates secondary loudspeakers and error microphone fixed together at a certain distance from the left and right sides of the head. In the second type of comparative structure, the user can adapt the positions of the monitoring error microphones to be close to the ears while maintaining the positions of the secondary sources fixed. The two comparative structures mentioned above are denoted as a fixed structure [4] and a movable microphone structure [22], respectively.

5. Real-Time Experimental Results and Discussion

This section comprehensively compares the noise reduction performance of various headrest structures when employing the VS methods. The performance of different structures was verified by varying the distances from the secondary loudspeakers to the ears, and then, the effect of head movement on the various headrest structures was compared. Next, the performance of the active headrest system combined with the three VS methods against varying primary sources was compared. Additionally, through the above experiments, the applicability of the different VS methods when using the proposed adjustable headrest structure was verified. Finally, 10 volunteers participated in the test, and the robustness of the proposed system was validated. It is worth mentioning that the noise attenuation performance at the ears controlling the signals at the physical monitoring microphones without using the VS methods was inferior to that of the VMM in all experiments and, therefore, was not included in the comparisons.

5.1. Experiment 1: Varying the Distances between the Secondary Loudspeakers and the Ears

To justify the necessity of the proposed adjustable structure, a reasonable number of comparison experiments were performed using three VS methods by moving the support frame on each side of the headrest away from the ears horizontally to the left or right. All plant responses including secondary paths were remodeled after each movement. In this experiment, the fixed structure, as described in Section 4, was considered identical to the proposed adjustable structure because in these two structures, the secondary loudspeakers and error microphone were fixed together and moved with the secondary loudspeakers. For the movable microphone structure, as illustrated in Section 4, the only difference with the fixed structure was that the physical monitoring microphone was always placed close to the ear. The first machine noise was employed as the disturbance signal to drive the No.1 primary loudspeaker.

Figure 6 shows the noise reduction at the left ear when the secondary loudspeakers were moved to various distances with different VS methods and headrest structures. The X-axis represents the distance that the left-hand side secondary loudspeakers were moved to the left, the Y-axis represents the distance that the right-hand side secondary loudspeakers were moved to the right, and the Z-axis indicates the attenuation of the total sound pressure level (SPL) at the left ear. As the noise reduction effectiveness was almost identical in both ears, only the attenuation results of the left ear are illustrated. It was clear that, as the secondary loudspeakers moved away from the ears, there was only a slight degradation in the performance for the AFM and RMM, regardless of the headrest structures. With the fixed structure/proposed adjustable structure, the performance of the VMM was inferior to that of the RMM by 5 dB attenuation when both sides of the secondary loudspeakers and the associated physical monitoring microphone were moved by no more than 2 cm, whereas a substantial performance degradation was observed when moved farther away. This was because of the enhanced difference in the primary disturbance at the physical microphone and the target microphone as the distance increased. Thus, the assumption $d_m\left(n\right)=d_v\left(n\right)$ became increasingly incompatible. In contrast, the performance of the VMM in the movable microphone structure was slightly better than that of the fixed structure/proposed adjustable structure and was affected less by the secondary loudspeaker movement. This was due to the assumption $d_m\left(n\right)=d_v\left(n\right)$ being essentially satisfied and almost unaffected in the movable microphone structure. However, in some cases, placing microphones near the ears was impractical and uncomfortable [6]. Hence, the user had to adjust the position of the support frame as a trade-off between the movable area and the attenuation performance when applying the proposed adjustable headrest structure. For the same distance between the secondary loudspeaker and the ear, the performance of the AFM and RMM was similar and superior to that of the VMM.

5.2. Experiment 2: Varying Head Positions

In the practical application of active headrest, it is necessary to satisfy the need for a sufficient movable space for the head. Moreover, it is inconvenient to re-estimate any transfer function in some circumstances. To validate the superiority of the proposed headrest structure while taking the above issues into consideration, appropriate comparison experiments were carried out with fixed structure and movable microphone structure. In these two comparative structures, as illustrated in Section 4, the secondary sources were fixed at a horizontal distance of 10 cm from the left and right ears. The dummy head was moved in steps of 3 cm within the $-6\mathrm{cm}\le x\le 6\mathrm{cm}$ sideways range, as illustrated in Figure 5b. The configuration of the primary source was identical to that described in Section 5.1. All of the required transfer functions were derived from those measured at the initial position and no longer re-estimated. After each head movement, the secondary loudspeakers and monitoring microphones in the proposed structure were adjusted together, keeping their relative distances to the ears constant. For the movable microphone structure, the positions of the monitoring error microphones were adapted to be close to the ears of the dummy head and the fixed headrest structure was not adjusted in any way.

Figure 7 shows the results of the total SPL attenuation at the ears when the dummy head was moved to different positions with various headrest structures. It could be observed that, when using the same VS method, the SPL reduction performance with the proposed headrest structure was optimal and stable at all positions compared to the other two structures. Moreover, when the proposed structure was utilized, the noise attenuation performances of the AFM and RMM were at the same level. When using the VMM, the performance was generally approximately 4 dB lower than that of the RMM. At the initial position, the performance with the movable microphone structure was slightly inferior to that with the proposed structure. This was because the secondary loudspeaker was farther away from the error microphone, which resulted in an increased delay in the acoustic path; thus, the performance of the feedback controller was degraded [2]. The fixed structure performed the worst at the nominal position. The reason for this phenomenon was the long distance between the physical microphone and the target microphone resulting in decreased accuracy of the estimated transfer functions [17]. In particular, utilizing the VMM with the fixed structure corresponded to a significant drop in performance, due to the long distance between the monitoring microphone and target error microphone causing the assumption $d_m\left(n\right)=d_v\left(n\right)$ to be unsatisfied. Considering the effect of head movement, both the fixed structure and movable microphone structure were affected by the transfer function perturbations and the performance of all of the VS methods was degraded. The movable microphone structure mitigated the effects of the perturbations to some extent and performed better than the fixed structure. Therefore, it could be verified that the proposed headrest structure is guaranteed to provide effective and stable performance for practical applications. With the proposed adjustable structure applied, the AFM and RMM performed at the same level and outperformed the VMM when the head moved slightly.

5.3. Experiment 3: Varying Primary Sources

In some cases, the primary sources are usually uncertain [6]. With the dummy head and proposed structure in the nominal position, four different primary disturbance configurations were investigated, as shown in

Table 2. Comparison between the reduction (dB) attained by various methods with four disturbance configurations at the left and right ears of the dummy head.

Disturbance Configuration	Direct Control	AFM	RMM	VMM
Noise 1, Position 1	26.90/26.23	24.45/23.33	24.20/23.06	19.29/19.46
Noise 2, Position 1	25.33/25.18	3.64/4.67	12.92/13.49	19.50/19.32
Noise 1, Position 2	26.59/25.31	7.86/8.68	2.88/3.11	19.03/19.79
Noise 1, Position 1 & 2	27.72/26.69	11.07/11.40	8.46/9.20	18.75/18.59

. As a benchmark for the optimal possible performance with this setup, the signals obtained from the target microphones at the ears of the dummy head were applied as error signals for direct control. The secondary paths, additional filters, and observation filters that need to be pre-modeled were measured for the first disturbance configuration only and applied generically to all other configurations.

Figure 8 illustrates the amplitude spectrum with and without cancellation at the left ear in the case of various algorithms and different disturbance configurations. According to the results shown in Table 2 and Figure 8, the maximum attenuation performance for all the configurations was achieved when the target microphones were directly controlled. It was hardly affected by any changes to the primary source. The performance of the RMM was mainly influenced by varying the positions of the primary source. In contrast, the efficiency of AFM was more susceptible to varying disturbance signal characteristics and less sensitive to changes in the primary source positions. As the quantity of the primary source increased, the performance of the AFM and RMM fell between the attenuation for configurations 1 and 3 while the AFM produced a better performance. Compared to the AFM and RMM, the VMM was less affected by changes in primary sources. This was attributed to the fact that, when the configuration of the primary noise was switched, the pre-trained additional observation filters was inappropriate and the effectiveness of the AFM/RMM deteriorated drastically, as a result [19]. The VMM eliminates the requirement for these additional transfer functions but, therefore, had the worst performance in the nominal condition (configuration 1).

Based on all the above experiments with the proposed adjustable headrest structure applied, when the primary source was stable, it was confirmed that the AFM and RMM had similar performance, and they outperformed the VMM. When the primary source changed and it was not feasible to re-measure any transfer function in some cases, the effectiveness of the AFM and RMM decreased while the VMM provided the most stable performance as a trade-off. Therefore, it was important to choose the appropriate VS methods based on the details of the application instead of just the nominal performance.

5.4. Experiment 4: Varying Test Listeners

In previous experiments, the effectiveness of the proposed active headrest system was validated using a dummy head. To further investigate the robustness of the proposed system against varying users, 10 volunteers of various statures were invited to assess the attenuation performance.

The second disturbance configuration in Section 5.3 was used to set up the primary source. To evaluate the performance of the noise reduction, microphones were attached to the ears. After the participant was seated, the proposed headrest structure was realigned so that the distances from the secondary loudspeakers to the physical monitoring microphones and ears were approximately consistent with when the dummy head was employed. The fixed headrest structure and movable microphone structure with the same setup as illustrated in Section 5.2 were also added for comparison. The required transfer functions that were derived from those measured with the dummy head were not re-estimated. Figure 9 demonstrates the attenuation of the total SPL at the left and right ears of all participants before and after the control with the VMM.

As shown in Figure 9, the noise reduction results using fixed and movable microphone structures were all below 15 dB and the latter was generally better than the former. In several cases of fixed structure, the attenuation was less than 6 dB. When applying the proposed structure, the noise reduction performance achieved for all participants was at the same level and the disturbance was nearly attenuated to the background noise level. In addition, the secondary paths and other plant responses changed slightly when the support frames were repeatedly adjusted. However, the results indicate that the maximum difference in performance was less than 4 dB attenuation. Consequently, it could be concluded that the proposed active headrest system is robust and applicable for users with varying statures.

6. Conclusions

In this paper, a multichannel feedback active headrest system combined with the VMM and a manually adjustable headrest structure for users was presented. The VMM transfers the noise reduction target from the physical monitoring microphone to the ear and avoids placing the microphone at the target during the control stage. The proposed headrest structure was developed to allow the secondary loudspeakers and the corresponding error microphone to be flexibly moved as a single unit by the users. This arrangement ensured that the relative position between each unit and the ear was constant, and thus maintained the stability of the secondary paths and other related plant responses. A series of experiments were conducted to validate the noise attenuation performance of the proposed system. The results confirm the necessity and superiority of the proposed headrest structure compared to the conventional fixed structure and the movable microphone structure. With the proposed adjustable structure utilized, the AFM and RMM achieved the same noise reduction performance level, and they outperformed the VMM when the primary source was stable. When encountering the varying primary source (including the characteristics, position, and quantity) and the practical issue where it was not feasible to re-measure any transfer function, the effectiveness of the AFM and RMM decreased while the performance of the VMM remained stable as a trade-off. This was because, when applying the AFM and RMM, the additional filters and observation filters that need to be trained in advance were dependent on the primary source. Hence, it is necessary to select an appropriate VS method according to the details of the application. Moreover, the comparative results of the trials involving 10 volunteers of different statures validated that the proposed active headrest system is robust and applicable to users of varying statures. This research will contribute to the design of active headrest for people working around engines, where primary sources are dominantly multi-sinusoidal and continuously changing.

In this study, all disturbance signals were considered for narrowband noise only. In the future, the attenuation performance of the proposed system against broadband interference will be explored.