This paper describes the application of data assimilation methods to CASMO-5 simulations of a Proteus research reactor experiment. Its focus is a comparison and evaluation of three prominent data assimilation methods: generalized linear least squares, MOCABA, and Bayesian Monte Carlo. These methods have not yet been extensively compared to date. The experiment is an interesting case study for this comparison because the measured reactivity worth response can be non-linear. This study investigates the effects that non-linearity has upon the agreement between the methods. The adjusted calculated values, calculation uncertainty, and nuclear data are all investigated to compare and evaluate the methods. The presented results provide evidence supporting the hypothesis that for linear responses, all of the data assimilation methods agree well. But when the responses become more non-linear, significant disagreements occur between generalized linear least squares results and those of MOCABA and Bayesian Monte Carlo.