In a process control system, the hidden properties of a catalyst are estimated by including those properties in hidden states within a state space model and solving the state space model based on measurable inputs and outputs of the process. The process may include defining a state space model for a process having a catalyst state comprising a hidden catalyst property; defining a set of empirically measurable input variables for the state space model, defining a set of output variables for the state space model, measuring a set of input values corresponding to the set of input variables; measuring a set of output values corresponding to the set of output variables; and estimating the hidden catalyst property based on the input values, the output values, and the state space model.