Currently there is still no specific analytical solution for the high order unscented transform (UT), thus high order UT can not be used to obtain high order unscented Kalman filter (UKF) with higher accuracy. In order to solve this problem, an analytical solution of high order UT is obtained by introducing a free parameterκon the basis of fifth-order cubature transform (CT), and the high order UKF is then obtained. It is illustrated that the existing fifth-order CT and fifth-order UT are two special cases of the high order UT whenκ=2 andκ=6?n, respectively. Furthermore, the optimal choice of parameterκin the high order UKF is analyzed and discussed for different dimensional systems, and the stability of the proposed method is discussed. Simulations based on the bearings-only tracking model and ballistic object reentry model show that the proposed method is correct and it has better performance as compared with the existing methods.