A method of estimating the oxygen storage capacity of a catalyst includes providing an engine system having an internal combustion engine and an exhaust system having a catalyst and an oxygen sensor, providing a three-way catalyst observer model having a Kalman filter and a three-way catalyst kinetic model, estimating a three-way catalyst next time step state and a modeling error, linearizing the three-way catalyst observer model, filtering the estimated three-way catalyst next time step state, and calculating a covariance.