Some relations between unscented and cubature kalman filters

Abstract

The unscented Kalman filter (UKF) and the cubature Kalman filter (CKF) are the popular nonlinear Gaussian sigma point filters. UKF propagates the sigma points by function evaluations using the unscented transformation (UT) and it is at first glance very different from CKF which is based on the spherical-radial cubature rule. In this paper, some relations between UKF and CKF are analyzed from the perspective of Mahalanobis distance ellipsoid. Two examples are given to demonstrate why UKF and CKF can achieve nearly the same accuracy.