Marginalized sigma-point filtering
Paper in proceedings, 2011
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.
Sigma point filtering