Nonlinearity and non-Gaussianity measures for stochastic dynamic systems

The paper deals with an assessment of nonlinear stochastic dynamic systems according to their nonlinearity. Knowledge of a degree of nonlinearity is important for many reasons, such as for a decision whether the system state should be estimated by a global method or a local method suffices, or for an adaptation procedure of some local estimation methods. The paper provides a brief overview of measures on nonlinearity (MoNL) and their discussion. Then, several measures of non-Gaussianity (MoNG) are proposed to capture properties of the state random variable that are manifestation of the nonlinearity. Finally, the paper demonstrates advantages of the MoNGs over the MoNLs in a numerical example.