On the convergence rate of the unscented transformation Annals of the Institute of Statistical Mathematics 2013; 65, 889-912
Date
02/19/2013Abstract
Nonlinear state-space models driven by dierential equations have
been widely used in science. Their statistical inference generally requires computing
the mean and covariance matrix of some nonlinear function of the state
variables, which can be done in several ways. For example, such computations
may be approximately done by Monte Carlo, which is rather computationally
expensive. Linear approximation by the rst order Taylor expansion is
a fast alternative. However, the approximation error becomes non-negligible
with strongly nonlinear functions. Unscented transformation was proposed to
overcome these diculties, but it lacks of theoretical justication. In this paper,
we derive some theoretical properties of the unscented transformation and
contrast it with the method of linear approximation. Particularly, we derive
the convergence rate of the unscented transformation.