A two-dimensional nonlinear distributed-parameter optimal state estimation algorithm has been developed and applied to an exothermic packed bed catalytic reactor. Temperature and concentration profiles were estimated from limited temperature and/or concentration measurements. Orthogonal collocation was used to solve the differential sensitivity and filtering equations. Both simulations and on-line experiments with a pilot scale packed bed reactor for the partial oxidation of methanol have been used to study the effects of measurement choice, model parameter errors, and unmeasured process disturbances. Excellent tracking of the reactor profiles was achieved with only one or two properly placed temperature sensors.