An internal combustion engine has a cylinder configured to combust an air-fuel mixture and expel an exhaust gas and a turbocharger for generating a pressurized airflow to the cylinder. The turbocharger includes a turbine scroll defining an inlet and an outlet, an exhaust gas driven rotating assembly having a turbine wheel disposed inside the turbine scroll, and a waste-gate defining an opening. A first sensor detects turbine outlet pressure. A second sensor detects turbine inlet temperature. A controller determines an effective area of the waste-gate opening and an exhaust gas mass flow-rate. The controller also determines a turbine inlet pressure in response to the detected turbine outlet pressure and the turbine inlet temperature, and the determined waste-gate opening effective area and the exhaust gas mass flow-rate. The controller additionally regulates a supply of fuel to the cylinder corresponding to the pressurized airflow affected by the determined turbine inlet pressure.