A gyroscope for determining an angular rate output. The gyroscope includes a first demodulator configured to demodulate an angular rate measurement at a first bias modulation frequency to determine the angular rate signal and a second demodulator configured to demodulate the angular rate measurement at a second bias modulation frequency to provide a signal with ARW information. The gyroscope further includes an ARW estimator that provides an output that is proportional to ARW that is then stored in a memory. The second bias modulation frequency is an even order harmonic of the first bias modulation frequency.