Fiber-based Raman spectroscopy in the context of in vivo biomedical application suffers from the presence of background fluorescence from the surrounding tissue that might mask the crucial but inherently weak Raman signatures. One method that has shown potential for suppressing the background to reveal the Raman spectra is shifted excitation Raman spectroscopy (SER). SER collects multiple emission spectra by shifting the excitation by small amounts and uses these spectra to computationally suppress the fluorescence background based on the principle that Raman spectrum shifts with excitation while fluorescence spectrum does not. We introduce a method that utilizes the spectral characteristics of the Raman and fluorescence spectra to estimate them more effectively, and compare this approach against existing methods on real world datasets.