A resonator fiber optic gyroscope (RFOG) comprising: at least one laser (102, 104 and 106); and a resonator in operational communication with the at least one laser (102, 104 and 106) to receive clockwise (CW) laser light and counterclockwise (CCW) laser light produced by the at least one laser (102, 104 and 106); characterized by : a resonance hopping control system in communication with an output of the resonator and the at least one laser (102, 104 and 106), the resonance hopping control system is configured to control an output of the at least one laser (102, 104 and 106) to periodically unlock, hop and lock frequencies of the laser light traveling in the CW and CCW directions in the resonator to multiple resonance frequencies of the resonator to average out bias errors due to resonance asymmetries; wherein the RFOG is configured is configured to measure center frequencies of resonances in the CW and CCW directions of the resonator when the signals indicate the light is locked on the resonance frequencies, determine differences between the measured center frequencies of the resonances in the CW and CCW directions, and determine a rotation rate of the gyroscope based at least in part on the determined differences. at least one laser (102, 104 and 106); and a resonator in operational communication with the at least one laser (102, 104 and 106) to receive clockwise (CW) laser light and counterclockwise (CCW) laser light produced by the at least one laser (102, 104 and 106); characterized by : a resonance hopping control system in communication with an output of the resonator and the at least one laser (102, 104 and 106), the resonance hopping control system is configured to control an output of the at least one laser (102, 104 and 106) to periodically unlock, hop and lock frequencies of the laser light traveling in the CW and CCW directions in the resonator to multiple resonance frequencies of the resonator to average out bias errors due to resonance asymmetries; wherein the RFOG is configured is configured to measure center frequencies of resonances in the CW and CCW directions of the resonator when the signals indicate the light is locked on the resonance frequencies, determine differences between the measured center frequencies of the resonances in the CW and CCW directions, and determine a rotation rate of the gyroscope based at least in part on the determined differences. a resonance hopping control system in communication with an output of the resonator and the at least one laser (102, 104 and 106), the resonance hopping control system is configured to control an output of the at least one laser (102, 104 and 106) to periodically unlock, hop and lock frequencies of the laser light traveling in the CW and CCW directions in the resonator to multiple resonance frequencies of the resonator to average out bias errors due to resonance asymmetries; wherein the RFOG is configured is configured to measure center frequencies of resonances in the CW and CCW directions of the resonator when the signals indicate the light is locked on the resonance frequencies, determine differences between the measured center frequencies of the resonances in the CW and CCW directions, and determine a rotation rate of the gyroscope based at least in part on the determined differences. <EOS>