A Polynomial Multiple Variance Method for Volterra Filter Identification

The article presents a methodology for accurately estimating the Volterra kernels of a discrete-time nonlinear system, even when the system order exceeds that of the Volterra series model. The approach involves conducting multiple measurements with the same excitation signal, scaled by different gain factors, and deriving the Volterra kernels via interpolation of the measured data. The methodology is thoroughly discussed, and the mean square deviation (MSD) of the estimated coefficients is calculated to determine the optimal gain factors that minimize the MSD. It is demonstrated that the optimal gains are constrained to a specific set of values, which are provided in the article. Experimental results, using both synthetic and real systems, showcase the effectiveness of the proposed methodology.