A method for reducing or eliminating bias instability in a stimulated Brillouin scattering, SBS, laser gyroscope, the method comprising: introducing a first pump signal propagating in a clockwise, CW, direction in an optical resonator of the SBS laser gyroscope (100, 200, 400); introducing a second pump signal propagating in a counterclockwise, CCW, direction in the optical resonator; generating a CCW first-order SBS signal in the optical resonator that propagates in the CCW direction; generating a CW first-order SBS signal in the optical resonator that propagates in the CW direction; increasing a power level of the first pump signal to above a threshold level such that the CW first-order SBS signal generates a CCW second-order SBS signal in the optical resonator; and increasing a power level of the second pump signal to above the threshold level such that the CCW first-order SBS signal generates a CW second-order SBS signal in the optical resonator; wherein above the threshold level, an intensity fluctuation of the first-order SBS signals disappear and their direct current, DC, power are clamped at substantially the same power level; wherein a Kerr effect bias instability of the SBS laser gyroscope (100, 200, 400) is reduced or eliminated by the clamped first-order SBS signals, characterized in that an intensity of the first pump signal is modulated at a first frequency by a first intensity controller (122, 422) optically coupled to an output of the first pump laser (120, 420) device; and an intensity of the second pump signal is modulated at a second frequency by a second intensity controller (126, 426) optically coupled to an output of the second pump laser (124, 424) device. introducing a first pump signal propagating in a clockwise, CW, direction in an optical resonator of the SBS laser gyroscope (100, 200, 400); introducing a second pump signal propagating in a counterclockwise, CCW, direction in the optical resonator; generating a CCW first-order SBS signal in the optical resonator that propagates in the CCW direction; generating a CW first-order SBS signal in the optical resonator that propagates in the CW direction; increasing a power level of the first pump signal to above a threshold level such that the CW first-order SBS signal generates a CCW second-order SBS signal in the optical resonator; and increasing a power level of the second pump signal to above the threshold level such that the CCW first-order SBS signal generates a CW second-order SBS signal in the optical resonator; wherein above the threshold level, an intensity fluctuation of the first-order SBS signals disappear and their direct current, DC, power are clamped at substantially the same power level; wherein a Kerr effect bias instability of the SBS laser gyroscope (100, 200, 400) is reduced or eliminated by the clamped first-order SBS signals, characterized in that an intensity of the first pump signal is modulated at a first frequency by a first intensity controller (122, 422) optically coupled to an output of the first pump laser (120, 420) device; and an intensity of the second pump signal is modulated at a second frequency by a second intensity controller (126, 426) optically coupled to an output of the second pump laser (124, 424) device.