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Exhaust pressures (P3) are hard parameters to measure and can be readily estimated, the cost of the sensors and the temperature in the exhaust system makes the implementation of an exhaust pressure sensor in a vehicle control system a costly endeavor. The contention with measured P3 is the accuracy required for proper engine and vehicle control can sometimes exceed the accuracy specification of market available sensors and existing models. A turbine inlet exhaust pressure observer model based on isentropic expansion and heat transfer across a turbocharger turbine was developed and investigated in this paper. The model uses 4 main components; an open loop P3 orifice flow model, a model of isentropic expansion across the turbine, a turbine and pipe heat transfer models and an integrator with the deviation in the downstream turbine outlet parameter.