Two methods are presented for optimally calculating spatial distributions of neutron flux in a nuclear reactor core. Both techniques, Kalman filtering and maximum likelihood estimation, simultaneously account for all initial information contained in the nominal core specifications and in-core measurements, as well as all of the uncertainties within the system, to provide a minimum variance estimate of neutron flux. These methods resolve discrepancies in the initial information in a statistically optimal manner, thereby providing valuable insight into the nature of the optimal solution obtained. Despite radically different algorithms, both methods yield the same minimum variance estimate for the quantity of interest. The algorithms have been successfully tested for one-dimensional axial and two-dimensional x-y flux mapping problems with simulated in-core data sets.