1. A system for generating a resistance-to-temperature model and regenerating a particulate matter sensor, comprising: a particulate matter sensor having a heating element; and a controller coupled to an engine, the controller including: a sensing circuit configured to detect a soot loading on the particulate matter sensor and generate a regeneration request indicating a desired regeneration temperature, a heating circuit configured to receive the regeneration request, generate a heating command signal based on the regeneration request, and send the heating command signal to the heating element of the particulate matter sensor based on the regeneration request, an electrical resistance circuit configured to detect an electrical resistance of the heating element, a calibration circuit configured to generate a resistance-to-temperature model for the heating element based on electrical resistance data collected by the electrical resistance circuit at known temperatures and to determine an actual temperature of the heating element during heating of the particulate matter sensor based on the generated resistance-to-temperature model and the detected electrical resistance, and a temperature feedback circuit configured to modify the heating command signal according to a difference between the desired regeneration temperature and the actual temperature of the heating element during heating of the particulate matter sensor.