This report serves two purposes. The first is to introduce the linear Kalman filter and the unscented Kalman filter to readers who are unfamiliar with either or both. To this end, it contains an extensive explanation of these methods, including all equations and interpretations which proved helpful to the author in realizing the second objective. Secondly, this report describes an original application of the unscented Kalman filter to the point reactor kinetics equations. The unscented Kalman filter's capacity to estimate the time-dependent behavior of a thermonuclear reactor is demonstrated, as well as its ability to refine prior estimates of the reactor-specific constants. Limits to the latter ability are expressed.