## 1 Introduction  
Local active noise control systems aim to create a localised zone of quiet at the physical error sensor (typically a microphone) by minimising the acoustic pressure at the physical error sensor location with secondary sound sources (typically loudspeakers). While significant attenuation may be achieved at the physical sensor location, the zone of quiet tends to be very small. Also, the sound pressure levels outside the zone of quiet are likely to be higher than the original disturbance alone with the active noise control system present. This is illustrated in Fig. 1 (a), where the zone of quiet located at the physical error sensor is too small to extend to the observer's ear and the observer in fact experiences an increase in the sound pressure level with the active noise control system operating. [PERSON] et al. [1] investigated the spatial extent of the zone of quiet when controlling pressure with a remote secondary source in a pure-tone diffuse sound field. The zone of quiet generated at the microphone was found to be defined by a _sinc_ function, with the primary sound pressure level reduced by 10 dB over a sphere of diameter one tenth of the excitation wavelength, \(\lambda/10\). The zone of quiet generated at the sensor location may be enlarged by minimising the acoustic energy density instead of the acoustic pressure. As the control of acoustic pressure and pressure gradient at a point is equivalent to minimising the acoustic energy density at that point [2], [PERSON] and [PERSON] [3] investigated the control of both pressure and pressure gradient in a diffuse sound field with two secondary sources. Minimising both the pressure and pressure gradient along a single axis produced a 10 dB zone of quiet over a distance of \(\lambda/2\), in the direction of pressure gradient measurement. This is considerably larger than the zone of quiet obtained by minimising pressure alone. As the zone of quiet generated at the physical error sensor is limited in size for active noise control, virtual acoustic sensors were developed to shift the zone of quiet to a desired location that is remote from the physical sensor. This is shown in Fig. 1 (b) where the zone of quiet is shifted from the physical sensor to a virtual sensor located at the observer's ear. Using the physical error signal, a virtual sensing algorithm is used to estimate the pressure at a fixed virtual location. Instead of minimising the physical error signal, the estimated pressure is minimised with the active noise control system to generate a zone of quiet at the virtual location. A number of virtual sensing algorithms have been developed to estimate the pressure at a fixed virtual location including _the virtual microphone arrangement_[4], _the remote microphone technique_[5], _the forward difference prediction technique_[6], _the adaptive LMS virtual microphone technique_[7], _the Kalman filtering virtual sensing method_[8] and _the stochastically optimal total diffuse field virtual sensing technique_[9]. It is, however, likely that the desired location of attenuation is not spatially fixed. This occurs, for example, when the desired location of attenuation is the ear of a seated observer and the observer moves  
Figure 1: Comparison of local active noise control (a) at a physical sensor; and (b) at a virtual sensor. their head, thereby moving the virtual location. As a result, a number of moving virtual sensing algorithms have been developed to generate a virtual microphone capable of tracking a moving virtual location including _the remote moving microphone technique_[10], _the adaptive LMS moving virtual microphone technique_[11] and _the Kalman filtering moving virtual sensing method_[12]. This paper will review the spatially fixed and moving virtual sensing algorithms developed for active noise control. Additionally, the performance of these virtual sensing algorithms in numerical simulations and in experiments is discussed and compared.