1. A process variable transmitter, comprising: a sensor sensing a process variable and providing a sensor value indicative of the sensed process variable; a memory storing a filtered sensor value that is calculated based on an average of a number of previously received sensor values, and a filtered rate of change value that is an average of a number of previously calculated rate of change values, the filtered rate of change values indicating rate of change of previously received sensor values; and a controller receiving the sensor value from the sensor that senses the process variable, and comparing the sensor value to the filtered sensor value to obtain an estimate of the rate of change value, the controller further comparing the estimate of the rate of change value to the filtered rate of change value to obtain a deviation value, and identifying a sensor characteristic indicative of whether the sensor is operating correctly based on the deviation value.