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In the last 20 years, single molecule FRET (smFRET), has emerged as one of the most  useful techniques in single-molecule spectroscopy~\cite{Weiss_1999,Hohlbein_2014}.  Except for  a few specific ensemble advanced  time-resolved measurements~\cite{Lerner_2014,Rahamim_2015}, techniques~\cite{Lerner_2014,Rahamim_2015},  smFRET uniquefeature is the  ability to resolve is resolving  conformational changes of biomolecules or measure measuring  binding-unbinding kinetics on heterogeneous samples. smFRET measurements on freely diffusing molecules (the focus of this paper) have the advantage  of probing molecules and processes withoutpossible  perturbation from surface immobilization~\cite{Dahan_1999,Eggeling_1998}.  The field of freely-diffusing smFRET data analysis, has seen a number of significant