On the Convergence Rate of the Unscented Transformation

Nonlinear state-space models driven by differential 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 first order Taylor expansion is a fast alternative. However, the approximation error becomes non-negligible with strongly nonlinear functions. Unscented transformation was