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Accurate estimation of catalyst bed temperatures is very crucial for effective control and diagnostics of aftertreatment systems. The architecture of most aftertreatment systems contains temperature sensors for measuring the exhaust gas temperatures at the inlet and outlet of the aftertreatment systems. However, the temperature that correctly reflects the temperature of the chemical reactions taking place on the catalyst surface is the catalyst bed temperature. From the Arrhenius relationship which governs the chemical reaction kinetics occurring in different aftertreatment systems, the rate of chemical reaction is very sensitive to the reaction temperature. Considerable changes in tailpipe emissions can result from small changes in the reaction temperature and robust emissions control systems should be able to compensate for these changes in reaction temperature to achieve the desired tailpipe emissions.