How nonlinear system identification can benefit from recent time-varying tools: The time-varying best linear approximation

In the past, the Best Linear Approximation (BLA) has proven to be a good tool for the identification (generation of initial estimates) of several nonlinear model structures. However, in case of high nonlinear distortion levels, the measurement time can become very high (high number of realizations M) to reduce the uncertainty of the BLA to a reasonable level. Moreover, a number of existing methods are based on C (≥ 2) different BLAs (corresponding to C different classes of input signals). The total number of experiments is given by the product MC. In this paper, a novel approach is proposed to reduce the number of experiments to one by combining recently developed tools for linear time-varying systems and (slowly) nonstationary inputs. In particular, it will be shown how an input signal with a time-varying standard deviation (or set point) allows one to extract all corresponding BLAs in a single experiment. These BLAs can be used to generate high-quality initial estimates of nonlinear block-structures. The results are supported by numerical simulation experiments.