On sigma-point set rotation in derivative-free filters

The paper deals with an analysis and illustration of the impact of the σ-point set rotation on the accuracy of the derivative-free approximation techniques and on the performance of filters utilizing these approximations. Namely, approximations based on the unscented transform and the Stirling interpolation are considered. It is shown that the covariance matrix factor used in the σ-point set computation can be multiplied by an arbitrary rotation matrix which rotates the σ-points along the surface of a hyper-ellipsoid defined by the covariance matrix. The rotation matrix can be thus considered as another user-defined parameter (in addition to the scaling parameter) greatly affecting the filter performance and therefore it needs to be carefully chosen. Choice of the appropriate σ-point set rotation is discussed and its impact on the filter performance is illustrated using a bearing-only tracking example.