Marginalized sigma-point filtering

In this paper we present a method for estimatingmean and covariance of a transformed Gaussian random variable.The method is based on evaluations of the transformingfunction and resembles the unscented transform or Gauss–Hermite integration in that aspect. However, the informationprovided by the evaluations is used in a Bayesian frameworkto form a posterior description of the transforming function.Estimates are then derived by marginalizing the function fromthe analytical expression of the mean and covariance. An estimationalgorithm, based on the assumption that the transformingfunction is constructed by Hermite polynomials, is presented andcompared to the cubature rule and the unscented transform. Contraryto the unscented transform, the resulting approximation ofthe covariance matrix are guaranteed to be positive-semidefiniteand the algorithm performs much better than the cubature rulefor the evaluated scenario