Marginalized sigma-point filtering

In this paper we present a method for estimating mean and covariance of a transformed Gaussian random variable. The method is based on evaluations of the transforming function and resembles the unscented transform or Gauss-Hermite integration in that aspect. However, the information provided by the evaluations is used in a Bayesian framework to form a posterior description of the transforming function. Estimates are then derived by marginalizing the function from the analytical expression of the mean and covariance. An estimation algorithm, based on the assumption that the transforming function is constructed by Hermite polynomials, is presented and compared to the cubature rule and the unscented transform. Contrary to the unscented transform, the resulting approximation of the covariance matrix are guaranteed to be positive-semidefinite and the algorithm performs much better than the cubature rule for the evaluated scenario.