The parametric array loudspeaker (PAL) is an application of the parametric acoustic array in air, which can be applied to transmit a narrow audio beam from an ultrasonic emitter. However, nonlinear distortion is very perceptible in the audio beam. Modulation methods to reduce the nonlinear distortion are available for on-axis far-field applications. For other applications, preprocessing techniques are wanting. In order to develop a preprocessing technique with general applicability to a wide range of operating conditions, the Volterra filter is investigated as a nonlinear model of the PAL in this paper. Limitations of the standard audio-to-audio Volterra filter are elaborated. An improved ultrasound-to-ultrasound Volterra filter is proposed and empirically demonstrated to be a more generic Volterra model of the PAL.