Survey of nonlinearity and non-Gaussianity measures for state estimation

The paper addresses state estimation of nonlinear stochastic dynamic systems. In particular, the stress is laid on the selection and performance monitoring of estimators based on measures assessing the validity of the assumptions under which the estimators have been proposed. The main focus is placed on summary and unification of the measures of nonlinearity and non-Gaussianity which might be used in state estimation. Discussions include analysis of the measures for stability, consistency, and validity. Using both local and global measures of nonlinearity (MoNL) include differential geometry, least squares, and convex optimisation while measures of non-Gaussianity (MoNG) include moment matching and volume differencing.