Minimax adaptive filtering algorithm nonlinear systems with Volterra series of the second order

The study solves the problem of filtering nonlinear systems based on the minimax adaptive algorithm of nonlinear systems by Volterra series of the second order, provided that the autocorrelation functions of the useful signal and interference are known with some errors according to the criterion of the maximum standard error of filtering. The author analyses the stationary performance of a minimax adaptive Volterra filter of the second order with the least mean square (LMS) with a constant step size of µ with a time-varying setting. A quantitative assessment of the steadystate excess root-mean-square error (RMSE) has been established, in which the contribution of incorrect gradient adjustment and tracking error is well characterized. Then the optimal step size is set for a time-varying secondorder minimax Volterra filter. Thus, we can study the correlation between the excess MSE and the optimal step size, on the one hand, and the parameters of a time-varying nonlinear system, on the other hand. A simple solution with minimal root-mean-square error for the minimax Volterra filter is obtained, based on the assumption that the input signal of the filter is Gaussian. In addition, we propose an iterative factorization method for developing a subclass of minimax Volterra filters, which can greatly simplify filtering operations. In addition, an adaptive algorithm for the Volterra filter is investigated, as well as its average convergence and asymptotic excess root-mean-square error. Finally, the usefulness of the Volterra filter is demonstrated by its use in studies of nonlinear drift oscillations of moored vessels exposed to random sea waves.