Adaptive estimation of the degree of system nonlinearity

Real systems more or less have nonlinear characteristics. In some applications it may be useful if one could measure the degree of the system nonlinearity, e.g. when one may want to know if the operating point of an electronic circuit is properly set. In stochastic dynamical system modeling based on observed input and output time series, it may be important to check first if the target system can be reasonably modeled as a linear system. Coherence function has been an index of system nonlinearity and conventionally used as a probe for the detection of system nonlinearity. However, in the case where the system output includes additive exogenous noise, low coherence value could not distinguish if the system is linear with additive output noise or the system is nonlinear. As an alternative, an index called the degree of system nonlinearity d.n. which is not affected by the presence of output noise has been previously proposed and effectively applied to the study of characterizing the heart rate variability. In some applications such as monitoring operating point of the electronic system, real time tracking of the degree of nonlinearity may be useful. This paper extends the previously proposed d.n. estimation method, adopting an adaptive signal processing method, to track changes in the degree of system nonlinearity based on observed system input and output time series