Characteristic function based performance index for Bayesian filters

The paper deals with state estimation of nonlinear stochastic dynamic systems in the Bayesian framework. In particular, the stress is laid on an introduction of a performance index, which can inform about working conditions of the filter and about the quality of approximations used by the filter. The performance index is based on the characteristic function and two of its applications are treated: i) its usage as a non-Gaussianity measure to inform a Gaussian filter about the validity of its assumption and ii) its utilization as an optimization criterion providing parameters of a Gaussian mixture used to replace a Gaussian density to improve estimate quality.