An Unscented Transformation for Conditionally Linear Models

A new method of applying the unscented transformation to conditionally linear transformations of Gaussian random variables is proposed. This method exploits the structure of the model to reduce the required number of sigma points. A common application of the unscented transformation is to nonlinear filtering where it used to approximate the moments required in the Kalman filter recursion. The proposed procedure is applied to a nonlinear filtering problem which involves tracking a falling object.