Aas 06-135 a Nonlinearity Measure for Estimation Systems

The concept of nonlinearity measures for dynamical systems is extended to estimation systems, which include both a dynamical model and a measurement model. For linear systems, propagation through linear dynamics and update by linear measurements both preserve the Gaussian property of a distribution of estimates. For nonlinear systems, how well a Gaussian distribution of estimates stays Gaussian is identified as a measure of the nonlinearity in the total estimation system. This measure can be used to compare the nonlinearity introduced by both the dynamics and the measurements for various representations of a system.