Sigma-Point Set Rotation in Unscented Kalman Filter: Analysis and Adaptation

Abstract

The paper deals with analysis and illustration of the impact of the σ-point set rotation on the approximation quality of the unscented transformation and the estimation performance of the unscented Kalman filter. It is shown that the covariance matrix factor, used in σ-point computation, can be multiplied by an arbitrary rotation matrix which moves the σ-points along the surface of a hyper-ellipsoid related to the covariance matrix. The rotation matrix can be thus considered as another user-defined parameter (in addition to the scaling parameter) and the unscented Kalman filter with adaptive selection of both user-defined parameters is proposed. The impact of fixed or adaptively selected parameters on the performance of the unscented Kalman filter is illustrated by a numerical study.