## 4 Conclusion  
This paper has reviewed virtual sensing algorithms for active noise control. A summary of the spatially fixed and moving virtual sensing algorithms, including their characteristics, advantages and disadvantages, is given in Table 1.  
Spatially fixed virtual sensing algorithms estimate the error signal at a spatially fixed location that is remote from the physical error sensor. The virtual microphone arrangement [4] projects the zone of quiet away from the physical microphone using the assumption of equal primary sound pressure at the physical and virtual locations. A preliminary identification stage is required in this virtual sensing method in which models of the transfer functions between the secondary source and microphones located at the physical and virtual locations are estimated. These secondary transfer functions, along with the often invalid assumption of equal sound pressure at the physical and virtual locations, are used to obtain an estimate of the error signal at the virtual location. The remote microphone technique [5] is an extension to the virtual microphone arrangement that uses an additional filter to compute an estimate of the primary pressure at the virtual location using the primary pressure at the physical microphone location. In theory, a perfect estimate of the tonal sound pressure may be achieved at the virtual location with the remote microphone technique provided accurate models of the tonal transfer functions are obtained in the preliminary identification stage. The forward difference prediction technique [6] is a fixed gain virtual sensing algorithm that fits a polynomial to the signals from a number of physical microphones in an array. The pressure at the virtual location is estimated by extrapolating this polynomial to the virtual location. This virtual sensing method does not require a preliminary identification stage, nor are FIR filters or similar to model the complex transfer functions between the sensors and the sources. The forward difference prediction virtual sensors are, however, sensitive to phase and sensitivity mismatches and relative position errors between the physical microphones in the array. The adaptive LMS virtual microphone technique [7] employs the LMS algorithm to adapt the weights of physical microphones in an array so that the weighted sum of these signals minimises the mean square difference between the predicted pressure and that measured by a microphone placed at the virtual location. The adaptive LMS virtual microphone technique can compensate for relative position errors and sensitivity mismatches adversely affecting the forward difference prediction technique. The Kalman filtering virtual sensing method [8] uses Kalman filtering theory to obtain an optimal estimate of the error signal at the virtual location. In this virtual sensing method, the active noise control system is modelled as a state space system whose outputs are the physical and virtual error signals. The Kalman filtering virtual sensing method does not require a number of FIR or IIR filter matrices to compute an estimate of the virtual error signals, instead a compact state space model is used. Also, this virtual sensing algorithm is derived with measurement noise included on the sensors. The stochastically optimal tonal diffuse field virtual sensing method generates stochastically optimal virtual microphones and virtual energy density sensors specifically for use in pure tone diffuse sound fields [9, 55]. Although a perfect estimate of the pressure at the virtual location may be obtained with the remote microphone technique [5], the stochastically optimal tonal diffuse field virtual sensing technique is much simpler to implement being a fixed scalar weighting method requiring only sensor position information. This virtual sensing method is independent of the source or sensor locations within the sound field and can compensate for changes in the sound field that may alter the transfer functions between the sensors and the sources.