A comparative study of adaptation algorithms for nonlinear system identification based on second order Volterra and bilinear polynomial filters

Nonlinear filtering techniques have recently become very popular in the field of signal processing. In this study we have considered the modeling of nonlinear systems using adaptive nonlinear Volterra filters and bilinear polynomial filters. The performance evaluation of these nonlinear filter models for the problem of nonlinear system identification has been carried out for several random input excitations and for measurement noise corrupted output signals. The coefficients of the two candidate filter models for are designed using several well known adaptive algorithms, such as least mean squares (LMS), recursive least squares (RLS), least mean p-norm (LMP), normalized LMP (NLMP), least mean absolute deviation (LMAD) and normalized LMAD (NLMAD) algorithms. Detailed simulation studies have been carried out for comparative analysis of Volterra model and bilinear polynomial filter, using these candidate adaptation algorithms, for system identification tasks and the superior solutions are determined.