The prompt fission neutron spectra (PFNS) of the low-incident-energy neutron-induced fission reactions n + 229-238U and n + 235-242Pu have been systematically evaluated using differential experimental data and the Los Alamos model (LA model). Using the first-order, linear Kalman filter, the LA model parameters are constrained using the experimental data and an evaluation of the PFNS and its uncertainties across a suite of isotopes' results. Correlations between isotopes of each actinide are presented through the model parameter correlations, and the resulting evaluations can be used to fill in inconsistencies within the ENDF/B-VII.1 library where PFNS data are scarce or in need of an update.