Abstract: A fuel control compensation system for sensor degradation in an exhaust system of a vehicle includes a first module that determines a response time of a signal generated by a sensor of the exhaust system. A second module determines an offset gain based on the response time and a nominal response time. Fuel control of an engine of the vehicle is regulated based on the offset gain.

Abstract: Methods and apparatus are provided for controlling the heating of an oxygen sensor in a motor vehicle. The apparatus comprises an oxygen sensor for measuring oxygen levels in exhaust gases of a motor vehicle. The oxygen sensor comprising a heater rod, an outer electrode surrounding the heater rod, and a shell surrounding the outer electrode and configured for mounting the oxygen sensor in the motor vehicle. A first electrical connection coupled to the outer electrode and a second electrical connection coupled to the shell are configured to facilitate measurement of capacitance between the outer electrode and the shell during operation of the motor vehicle.