Abstract: When the system model can not correctly describe the real system, the strong tracking unscented Kalman filter (UKF) can well make up the lack of robustness in the traditional UKF and ensure the accuracy of filtering. However, the computational load of strong tracking UKF is greatly increased due to the additional use of unscented transform. To solve this problem, the Taylor expansion is employed to analyze the mechanism of fading factor in UKF, an approximation fading factor introducing method is established, and the speedy strong tracking UKF is proposed based on the approximation introducing method. A qualitative analysis is carried out using statistical floatingpoint operations (flops)， which shows that the computational load of speedy strong tracking UKF is close to that of traditional UKF. The convergence is discussed based on the filtering convergence criterion. Simulation results demonstrate that speedy strong tracking UKF performs similarly compared with strong tracking UKF, while the computational load has been significantly degraded.