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Traditionally, a three-way catalyst (TWC) is controlled to a set heated exhaust gas oxygen (HEGO) sensor voltage (typically placed after the monitored catalyst) that corresponds to optimal catalyst efficiency. This limits the control action, as we rely on emissions breakthrough at the HEGO sensor to infer the state of catalyst. In order to robustly meet the super ultra-low emission regulations, a more precise TWC control around the oxidation level of catalyst is desirable. In this work, we developed a comprehensive set of models to predict the oxygen storage capacity using measured in-vehicle signals only. This is accomplished by developing three models; the first model is a linear in parameter regression model to predict the feed gas emissions from measured signals like engine speed and air-to-fuel ratio (A/F). The second model is a low-dimensional physics based model of the three-way catalyst to predict the exhaust emissions and oxidation state of the catalyst.