Nuclear data, especially fission yields, create uncertainties in the predicted concentrations of fission products in spent fuel. Herein, we present a new framework that extends data assimilation methods to burnup simulations by using data from post-irradiation examination experiments. The adjusted fission yields improve the bias and reduce the uncertainty of predicted fission product concentrations in spent fuel. Our approach modifies fission yields by adjusting the model parameters of the code GEF with post-irradiation examination experiments. We used the BFMC data assimilation method to account for the non-normality of GEF's fission yields. In the application that we present, the assimilation decreased the average bias of the predicted fission product concentrations from 26% to 15%. The average relative standard deviation decreased from 21% to 14%. The GEF fission yields after data assimilation agreed better with those in ENDF/B-VIII.O. For Pu-239 thermal fission, the average relative difference from ENDF/B-VIII.0 was 16% before data assimilation and 11% after. For the standard deviations of the fission yields, GEF's were, on average, 16% larger than those from ENDF/B-VIII.0 before data assimilation and 15% smaller after.