State feedback control provides many advantages, such as stabilization and improved transient response. However, when state feedback control is considered for spatial control of a nuclear reactor, it requires complete knowledge of the distributions of the system state variables. Also, if the reactor is in a transient, flux mapping systems that are based on steady-state conditions are not appropriate for an accurate representation of the operating state of the reactor. A method is described for reconstructing the measurable and unmeasurable state variables in a nuclear reactor from output measurement data, which can be used to generate input for a feedback control system or serve as a core observer (estimator) in a reactor transient. The method is based on a Luenberger-type observer theory that is extended to infinite-dimensional distributed parameter systems. The method was applied to a simple reactor model in one spatial dimension and one energy group with xenon dynamics that exhibited spatial oscillations. The resulting observer was tested by using model-based data for measurement output. The results show that the spatial distributions of iodine, xenon, and neutron flux are estimated very well by the observer using information from a finite number of sensors.