Sigma point and particle approximations of stochastic differential equations in optimal filtering

The unscented transform (UT) is a relatively recent method for approximating non-linear transformations of random variables. Instead of the classical Taylor series approximations, it is based on forming a set of sigma points, which are propagated through the non-linearity. The unscented Kalman filter (UKF) is an alternative to the extended Kalman filter (EKF), which utilizes the unscented transform in the filter computations. However, in its original form, the UKF is a discrete-time algorithm and it cannot be directly applied to estimation problems, where the state dynamics are modeled in continuous-time as stochastic differential equations. In the talk I will review the Taylor series, sigma-point (unscented) and particle approximations of stochastic differential equations in optimal (Bayesian) filtering context and present some applications of the methods in navigation systems and in monitoring of chemical processes.