DYNAMIC SYSTEM-IDENTIFICATION WITH ORDER-STATISTICS

Systems consisting of linear dynamic and memoryless nonlinear subsyste ms are identified. The paper deals with systems in which the nonlinear element is followed by a linear element, as well as systems in which the subsystems are connected in parallel. The goal of the identificati on is to recover the nonlinearity from noisy input-output observations of the whole system; signals interconnecting the elements are not mea sured. Observed values of the input signal are rearranged in increasin g order, and coefficients for the expansion of the nonlinearity in tri gonometric series are estimated from the new sequence of observations obtained in this way Two algorithms are presented, and their mean inte grated square error is examined. Conditions for pointwise convergence are also established. For the nonlinearity satisfying the Lipschitz co ndition, the error converges to zero. The rate of convergence derived for differentiable nonlinear characteristics is insensitive to the rou ghness of the probability density of the input signal. Results of nume rical simulation are also presented.