A general procedure for nonlinear system identification using higher order statistics

A general formula is given for the conditional mean in terms of higher order statistics. Using this formula, a general scheme for nonlinear system identification is introduced including a broad range of nonlinearities which depends on the probability density function of the input. As a special case of that general scheme, the polynomial system identification problem is treated. It is shown that our general scheme yields straightforward theoretical results in the case of polynomial discrete-time system identification.