Parameter Estimation Method Using Volterra Kernels for Nonlinear IIR Filters

In this paper, we propose a parameter estimation method using Volterra kernels for the nonlinear IIR filters, which are used for the linearization of closed-box loudspeaker systems. The nonlinear IIR filter, which originates from a mirror filter, employs nonlinear parameters of the loudspeaker system. Hence, it is very important to realize an appropriate estimation method for the nonlinear parameters to increase the compensation ability of nonlinear distortions. However, it is difficult to obtain exact nonlinear parameters using the conventional parameter estimation method for nonlinear IIR filter, which uses the displacement characteristic of the diaphragm. The conventional method has two problems. First, it requires the displacement characteristic of the diaphragm but it is difficult to measure such tiny displacements. Moreover, a laser displacement gauge is required as an extra measurement instrument. Second, it has a limitation in the excitation signal used to measure the displacement of the diaphragm. On the other hand, in the proposed estimation method for nonlinear IIR filter, the parameters are updated using simulated annealing (SA) according to the cost function that represents the amount of compensation and these procedures are repeated until a given iteration count. The amount of compensation is calculated through computer simulation in which Volterra kernels of a target loudspeaker system is utilized as the loudspeaker model and then the loudspeaker model is compensated by the nonlinear IIR filter with the present parameters. Hence, the proposed method requires only an ordinary microphone and can utilize any excitation signal to estimate the nonlinear parameters. Some experimental results demonstrate that the proposed method can estimate the parameters more accurately than the conventional estimation method.