The presence of polarization noise generated by the waveguide resonator limits the performance of a resonant integrated optical gyroscope (RIOG). Using silicon nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) to fabricate a waveguide with an ultralow-aspect-ratio can result in a resonator that only supports light transmission in a single-polarization state, suppressing polarization noise. We successfully fabricated a ${\mathrm{Si}}_3{\mathrm{N}}_4$ resonator with a bending radius of 17.5 mm, a finesse ($F$) of 150, a quality factor ($Q$) of $1.54\times {10}^7$, and a propagation loss of 1.2 dB/m. The ${\mathrm{Si}}_3{\mathrm{N}}_4$ resonator was used to construct a double closed-loop RIOG that showed long-term bias stability (3600 s) of 13.2°/h at room temperature, 14.8°/h at 40°C, 21.2°/h at 50°C, and 23.6°/h at 60°C. We believe this to be the best performance reported to date for a ${\mathrm{Si}}_3{\mathrm{N}}_4$ resonator-based RIOG. This advancement paves the way for the wider application of RIOGs.