In one embodiment a system including a resonator fiber-optic gyroscope configured to measure rotation rate is provided. The resonator fiber-optic gyroscope includes a sensing resonator have a first resonance frequency for a first laser beam propagation direction and a second resonance frequency for a second laser beam propagation direction, an optical mixer coupled to an output of the sensing resonator and configured to mix an output of the sensing resonator with a reference laser, wherein the optical mixer outputs a beat signal, and a resonance tracking electronics coupled to the optical mixer. The resonance tracking electronics are configured to demodulate the beat signal at a frequency offset to produce first in-phase and quadrature demodulated information, generate R-squared information from a sum of squares of the first in-phase and quadrature demodulated information, and demodulate the R-squared information at a resonance tracking modulation frequency.