Optimal levels of perturbation signals for nonlinear system identification

A method is developed for determining the optimal levels of multilevel perturbation signals for nonlinear system identification, using condition numbers of submatrices of the Vandermonde matrix of the input levels vector. It is applicable when the perturbation signal is applied directly to a static nonlinearity. Optimal levels can be obtained for every order of nonlinearity less than the number of levels, and in most cases the optimal levels are not all distinct. The results show that there is no advantage in using signals with more than the minimum necessary number of distinct levels, although it may be advantageous if some of the distinct levels appear more than once in the input levels vector. The optimal levels are unchanged by multiple occurrences of every level of the input levels vector during a measurement period, and they are shown to be the global optima for pseudorandom perturbation signals derived from maximum-length sequences, in which the occurrence of the zero level is one less than the occurrences of the other levels during a period.