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.