System and method for determining exhaust temperature

A vehicle system, comprising:

• an engine including an intake passage and an exhaust passage;
• an exhaust catalyst coupled to the exhaust passage;
• an exhaust gas oxygen sensor coupled upstream of the exhaust catalyst, the sensor including a heater for maintaining the sensor at an operating temperature;
• a fuel injector coupled to an engine cylinder;
• an intake throttle coupled to the intake passage;
• and
• a controller with computer readable instructions stored on non-transitory memory for:
• during vehicle operation,
• capturing a duty cycle of the heater;
• converting an inverse of the duty cycle into a first exhaust temperature estimate;
• learning a transfer function based on transients during the vehicle operation;
• calculating a second exhaust temperature estimate based on the first exhaust temperature estimate and the learned transfer function;
• and
• adjusting engine operation based on the second exhaust temperature estimate.