Abstract：In order to establish a high-precision BDS clock error prediction model, we propose a SAFA-FDGM(1,1) clock error prediction model based on the fractional-order discrete gray system optimized by the improved firefly algorithm. In order to avoid the firefly algorithm falling into the local optimal solution, and improve the firefly algorithm optimization ability. We introduce the inertia weight factor and improve the attractiveness factor and step factor, and use the improved firefly algorithm to automatically optimize the selection of the fractional-order factor of FDGM(1,1) model to improve the accuracy of FDGM(1,1) data fitting. We apply the clock error data of three different types of satellites, C02(GEO), C09(IGSO) and C12(MEO), for test analysis. The results show that the proposed clock error prediction model is superior to the traditional quadratic polynomial model and the GM(1,1) model, 3~6 h prediction error is less than 1 ns, and the 9~12 h prediction error is better than 2 ns, which has important reference value to establish BDS satellite universal clock error prediction model.
