Reducing the measurement time of the Best Linear Approximation of a nonlinear system using improved averaging methods

The Best Linear Approximation to a nonlinear system is traditionally measured as a sample mean, considering that for linear systems it is the minimum variance Maximum Likelihood estimate for Gaussian excitations. This minimum variance is the basis of the usual measurement time vs. measurement quality trade-off and design. However due to a nonlinearity the sample mean is no more an optimal estimate and in consequently its variance is not an attainable theoretical minimum and can be improved. By using a limited a priori knowledge about the measured system the measurement time vs. measurement quality trade-off can be made sharper and we present a method where the reduction in the measurement variance can be realized solely as a part of the data processing, without affecting the measurement setup and protocol.