  Many nonlinear extensions of the Kalman filter, e.g., the extended and the
unscented Kalman filter, reduce the state densities to Gaussian densities. This
approximation gives sufficient results in many cases. However, this filters
only estimate states that are correlated with the observation. Therefore,
sequential estimation of diffusion parameters, e.g., volatility, which are not
correlated with the observations is not possible. While other filters overcome
this problem with simulations, we extend the measurement update of the Gaussian
two-moment filters by a higher order correlation measurement update. We
explicitly state formulas for a higher order unscented Kalman filter within a
continuous-discrete state space. We demonstrate the filter in the context of
parameter estimation of an Ornstein-Uhlenbeck process.
