Aspects and comparison of matrix decompositions in unscented Kalman filter

The paper deals with state estimation of nonlinear Gaussian systems with a special focus on the unscented Kalman filter. Its algorithm is based on specification of a set of so-called sigma points which are generated according to the covariance matrix of the state decomposed into a product of a matrix and its transpose. The paper analyzes utilization of different matrix decompositions within the unscented transform, which is a core of the unscented Kalman filter. It is shown that different decompositions may lead to significant differences in quality of approximations provided by the transform. The influence of the decompositions on the filter is demonstrated in an example.