A new method for estimating gain factors in amplitude panning system is proposed. The method is based on particle velocity and balanced sound energy formulation. A scale factor is employed in amplitude panning system and thus, an overdetermined system of equation is derived in particle velocity equation. To obtain the analytic solution of the overdetermined equation, the sound energy identical formula is considered and then the unique gain factors are estimated. The proposed method is able to reproduce sound source direction and control the distance perception in a flexible two- or three-dimension loudspeaker setup. Subjective evaluations show that the proposed technique in an aspheric loudspeaker setup maintains the sound direction and controls the distance perception at the listening point.
