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# Head tracking extends local active control of broadband sound to higher frequencies

## Abstract

Local active sound control systems provide useful reductions in noise within a zone of quiet which only extends to about one tenth of an acoustic wavelength. If active control is required above a few hundred hertz, this generally limits the movement of a listener to unrealistically small changes in head position. We describe a local active sound control system using a fixed array of monitoring microphones, in which the pressures at the ear positions are estimated from these microphone signals using head position information from an optical head tracker. These signals are then actively controlled to give robust attenuation at the ear positions, even as the listener moves their head. Feedforward control provides selective attenuation of noise and broadband attenuation of around 20 dB is measured up to excitation frequencies of 1 kHz under favourable conditions, with head tracking achieved in a few seconds. The active control performance is thus comparable with that achieved with active headphones, but without the listener having anything attached to their head.

## Introduction

Although active sound control headphones, which can reduce noise levels for frequencies up to about 1 kHz, are now widely available, their use is not convenient in many applications. Examples are when the listener is driving, or when sound control is required over long periods of time, in which case headphones can become uncomfortable. Local active control of sound is also possible using loudspeakers and microphones remote from the ears, particularly if virtual sensing algorithms are used1,2,3,4,5,6,7. The zone of quiet around such a virtual microphone position, within which an attenuation of 10 dB is achieved, is limited to a diameter which is typically about 1/10 of an acoustic wavelength, however8,9. At frequencies above a few hundred hertz, normal changes in head position, of 5 cm or so, will thus move the ears out of this zone of quiet and effective sound control will be lost.

## Results

Further experiments have been conducted with a human listener moving their head within the area defined by the grid above, when they were wearing in-ear microphones to monitor the pressure at their ear positions. The results are shown in Fig. 4, with a video of these experiments available in the supplementary material.

## Discussion

The main objective of this paper is to demonstrate the capacity for head tracking to extend the frequency range of control for broadband noise, and so these initial experiments are deliberately rather idealised. There are a number of practical applications for such a local active system for broadband noise control and several issues may need to be addressed in these cases, which are not considered in detail here, since the solutions are likely to be rather application-specific. In particular, we note that:

• First, direct access has been assumed to the primary source in order to provide a reference signal. In many practical applications, such as the control of road noise in cars10, this is not realistic and the reference signals have to be obtained from carefully located sensors placed on the vehicle. The type and position of the sensors is still a matter of active investigation in this and other applications.

• Secondly, it has been assumed in the experiments reported here that only a single broadband primary source is present, whereas in many practical applications there will be several, partially correlated, primary sources contributing to the disturbance signals. This kind of excitation would generate a more diffuse primary sound field than was experienced in the experiments described here, which will influence the accuracy with which the observation filter can estimate the signals from the error microphones. This has, to some extent, been taken into account here by selecting the position of the measurement monitoring microphones based on their performance when a number of different primary source locations are considered, but further work on this is clearly required when considering a specific application.

• Finally, the head tracking has been achieved here using a commercial system and we have only tracked the translational motion of the head. In practice the head will probably have rotational as well as translational motion, which will need to be tracked, and depending on the application, the speed of the head tracking system may be important in following rapid head movement.

One of the greatest barriers to the practical implementation of active noise control in vehicles, however, is cost. It is therefore significant that a number of automotive manufacturers are beginning to install head tracking devices in their vehicles to provide additional functionality, such as monitoring the alertness of drivers for example.

## Methods

The block diagram of the adaptive control algorithm used to control the broadband random pressures at the ears of the dummy head is shown in Fig. 5. The signals are generally vectors and the transfer responses are generally matrices in this diagram, in which x denotes the vector of reference signals related to the primary sources, which are assumed to be observed directly in these experiments. These reference signals are filtered by the FIR control filters in the matrix W, driven by the reference signals, x, to give the vector of control signals driving the two secondary loudspeakers, u. The observed signals at the monitoring microphone positions are produced by the summation of the random disturbance signals at these positions, d m , and the control signals filtered by the plant response G m . The unobserved signals at the virtual error sensors, e, are given by the sum of the random disturbances at these positions, d e , and the control signals filtered by the plant responses G e . The microphones in the two ears of the dummy head were used as error sensors during the initial training of the control system. The signals at the virtual error sensors are then estimated during control using the remote microphone technique7,12. The disturbance signals at the monitoring microphone are first estimated by subtracting an estimate of the contribution from the secondary source signals, obtained by filtering the control signals with Ĝm, which is an estimate of G m . These estimates of the disturbances at the monitoring microphones, $${\hat{{d}}}_{m}$$, are then filtered by an observation filter to estimate the disturbance signals at the virtual microphone locations. Finally, the error signals at the virtual microphone locations are calculated by adding an estimate of the contribution from the secondary sources at this point, using, Ĝe, which is an estimate of G e .

The observation filter that optimally estimates the disturbance signals at the virtual error microphones from those at the physical monitoring microphones can be calculated using a least-squares formulation11,14. It is given by a N m by JN m matrix of filter coefficients, where N m is the number of monitoring microphones, N e is the number of virtual error microphones, and J is the order of each individual FIR observation filter, which is equal to

$${{\bf{O}}}_{{\rm{opt}}}={({\{{{\boldsymbol{R}}}_{{mm}}{+}{\beta }{\bf{I}}\}}^{-1}\{{{\boldsymbol{R}}}_{{me}}\})}^{{\rm{T}}},$$
(1)

where R mm is the JN m by JN m matix of auto- and cross-correlations between the delayed disturbance signals at the monitoring microphones and R me is the JN m by N e matrix of cross-correlations between the delayed disturbance signals at the monitoring microphones and the disturbance signals at the error microphones. The regularisation parameter, β, is chosen to give a reasonable trade-off between the accuracy with which the disturbance signals are estimated at the virtual microphone positions and the robustness of this estimate to small changes in these positions and to the locations of the primary source. The 8 individual observation filters in the matrix Oopt that were used in the arrangement here each had 128 coefficients and were identified for each of the 20 head locations on the grid. It should again be emphasised that in contrast to the remote active control of tonal noise in11, where only the in phase and quadrature components of a single frequency reference signal have to be adapted to achieve control, the real-time control of broadband random noise requires digital filters for the controller, plant models and observation filter, in order to achieve control over a range of frequencies.

The filtered-reference LMS algorithm15,16 used to update the control signal filters is

$${\boldsymbol{w}}(n+\mathrm{1)=}{\boldsymbol{w}}(n)-\alpha {\hat{{\boldsymbol{R}}}}^{T}({n})\hat{{\boldsymbol{e}}}({n}),$$
(2)

where w(n) is the vector of controller coefficients at the n-th sample, $${\hat{{\bf{R}}}}^{T}(n)$$ is the transpose of the matrix of reference signals filtered by the responses in Ĝ e , and ê(n) is the vector of estimated error signals at the virtual error microphones. The control system used 128 coefficients for each of the four control filters and was implemented on a dSPACE system at a sampling rate of 3 kHz, with anti-aliasing and reconstruction filters having a cut-off frequency of 1 kHz. A Microsoft Kinect (Kinect 1.0 for Windows), was used for head tracking, positioned about 1.5 m away from the dummy head. The information from the Kinect was decoded in real-time using plug-in software implemented in MaxMSP and this was passed to the dSPACE controller, which already stored the various plant responses and pre-calculated observation filters for the 20 head positions.

Using a frequency domain analysis, a sufficient condition for the stability of this adaptive algorithm can be derived17,18, as

$${\rm{Re}}({\rm{eig}}[{\hat{{\bf{G}}}}_{e}^{H}{\hat{{\bf{G}}}}_{e}+{\hat{{\bf{G}}}}_{e}^{H}\,{\hat{{\bf{O}}}}_{{\rm{opt}}}({{\bf{G}}}_{m}-{\hat{{\bf{G}}}}_{m})])\mathrm{ > 0}.$$
(3)

As the position of the listener’s head changes, then clearly the observation filter and the responses from the secondary sources to the virtual positions of the error microphones will also change. It is also found, however, that the responses from the secondary sources to the fixed monitoring microphones, G m , also changes somewhat, due to the physical presence of the head, and that these changes can compromise the accuracy of the estimated error signals, and the stability of the system. The potential effect of a difference between G m and Ĝ m on the stability of the system can be seen from equation (3) to be particularly significant if the observation filter has a large response at some frequencies. This emphasises the need for regularisation in the design of the observation filters. Both Ĝ m and Ĝ e were modelled here as 64 coefficient FIR filters, at each of the 20 dummy head positions and both were scheduled on the measured head position.

In a series of experiments conducted prior to control, all of these three responses, Ĝ m , Ĝ e and Ôopt, are identified as FIR filters from measurements made with the dummy head in each of the 20 separate positions on the grid shown in Fig. 1 and these are then stored in the control system. During real-time control, the head tracker is used to measure the head position and the closest pre-calculated head position is identified, as shown in Fig. 5(b). The responses associated with this head position are then used in the control algorithm shown in Fig. 5(a).

In operation, both an observation filter and the plant responses are selected based on the tracked head position, although it would also be possible to interpolate a larger number of these from the more limited number of measured responses. The feedforward control approach provides selective attenuation, only for sounds that are coherent with the reference signals. Although the usual causality issues associated with the time-advance of the reference signals are still present, causality problems associated with the estimation of the remote microphone signals are avoided by using the observation filter to calculate a delayed version of these signals13,19.

The convergence time of the adaptive algorithm in equation (2) depends on the overall delay in the plant response, Ĝ e 17, which includes both the modelling delay and also the acoustic and electrical delays of the system. The modelling delay used for the observation filter in these experiments was 0.7 ms, which was not large, compared with the delay due to the acoustic propagation between the loudspeaker and microphone and that due to the anti-aliasing and reconstruction filters in this case, which was about 1.3 ms in total. So although, in principle, the modelling delay will increase the convergence time of the adaptive control algorithm, this increase is small in the experiments reported here, since the overall delay is not dominated by the modelling delay and the disturbances is also stationary. The control filter thus only had to adapt when there was a change of head position, in which case the time taken for the head tracker to acquire a new position was significantly greater than the adaptation time of the filter. There may be some applications, with small acoustic delays and nonstationary disturbances, in which this modelling delay does become important in determining the convergence time and so limits the control performance.

All methods were carried out in accordance with the relevant guidelines and regulations of the University of Southampton and all experimental protocols were approved by the University of Southampton. Informed consent was obtained from the subject participated in the experiment for Fig. 4.

### Data Availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

This research is jointly funded by an EPSRC industrial CASE studentship (Award no. 14220108) with Jaguar Land Rover (JLR). The authors are especially thankful to Dr Delphine Nourzad and Mr Xavier Vinamata of JLR for their support as industrial supervisors.

## Author information

Stephen J. Elliott wrote the main manuscript text and Woomin Jung conducted the experiments and analysed the results. All authors reviewed the manuscript.

### Competing Interests

The authors declare no competing interests.

Correspondence to Woomin Jung.